Shortage of Physicians In Canada Essay -- Canadian Health Care System

Birth Control Policy Essay Example | Topics and Well Written Essays - 1250 words

Conception prevention Policy - Essay Example For example, a few speculations, for example, the open decision hypothesis put more accentuation and center at the degree of people instead of concentrating on the institutional level. The open strategy making process is typically at the core of successful administrations arrangement. It has been expressed that the procedure of approach making regularly happens six significant stages (Howlett, et al 2009). These are plan setting, dynamic, arrangement definition, execution, assessment lastly end or restoration. Wellbeing involves open intrigue. Hence the administration association in issues concerning wellbeing is as a rule to a more noteworthy degree. The administration typically details approaches for various reasons. A few arrangements are typically detailed with the end goal of populace control. Populace control is really the quintessence of conception prevention. The wellbeing approach is activated by the craving and need to address a few issues. These are extensively clarified as; the human services arrangement looks to be exhaustive enough to incorporate the most noteworthy number of the residents conceivable. This is one reason why a few people were stating that usage of the arrangement will be over the top expensive and might cause the citizen a great deal of cash. Inclusion doesn't really mean access. These two can be totally unrelated. For example, an individual may be under the inclusion of a specific human services conspire yet for some other explanation neglects to obtain entrance. Inclusion likewise implies a more extensive extent of the arrangements of the protection and other wellbeing plans. For example, there is another government order that requires protection plan to likewise accommodate anti-conception medication. The arrangement additionally looks to guarantee that the social insurance being concurred is very reasonable to everybody. This stems from the idea that human services is a fundamental assistance that every single individual ought to approach. Thus it is significant that the social insurance cost is reasonable. Social insurance is a significant help. This can

The Worst Advice Weve Heard About Plagiarizing

The Worst Advice Weve Heard About Plagiarizing Plagiarism isnt a fun topic. Lets face itâ€"anyone who has spent time in academic pursuits has heard the stern lectures from professors warning of the dangers of plagiarism. The consequences of it can be equally unsettling: a failing grade, a feeling of disgrace, loss of credibility, and even expulsion are all very real possibilities.But dont worry, weve got your back, and will discuss the absolute worst advice weve heard about plagiarizing. Pay attention and youll avoid the embarrassment and destruction of credibility that plagiarism can bring.Bad Idea #1: You can use whole sentences or paragraphs from WikipediaSince Wikipedia content is created by a conglomeration of several writers and editors, there is a false assumption that entire sentences or passages can be lifted from it and used in otherwise original papers.The operative word here is false. Regardless of how many writers contributed to a passage or content, and regardless of the fact that the content is online and highly ed ited, its still plagiarism to claim the text as your own. In addition, Wikipedia content will be easily picked up by any online plagiarism detector since it is a highly visited website and therefore highly ranked in search engine algorithms.Its also important to keep in mind that Wikipedia is not considered to be a legitimate source in academic research and writing. Treating it as a source could result in a lowered grade and plagiarizing it could most certainly result in thatâ€"or worse.Bad Idea #2: You can piece together pieces of several different free online essays on the topicIf youve ever watched an online plagiarism detector perform its search, youd know that this is likewise bad advice. Specifically, these programs are designed to crawl millions of webpages to find content that is word-for-word of the text submitted to them. It doesnt matter if the content is pulled from a hundred different sources, plagiarism detection software can find all of themâ€"including short passages of approximately five words.There is also a false assumption that goes along with this one, stating that as long as the copied passages are less than a certain percentage of the original work, its fine to plagiarize. Whether you copy a passage of five words or 500â€"the act (and therefore, the consequence of that act) is the same.Whether you copy a passage of five words or 500â€"its still plagiarism. Photo by Green Chameleon on Unsplash.Bad Idea #3: You can plagiarize since there are no original ideas leftWhile its true that there is nothing new under the sun, this reality doesnt give you an excuse to claim anothers work as your own. When writers and literary scholars mention that there are no original ideas left (another way to state the adage I mentioned above), they are referring to story archetypes that have been used since the dawn of human existence. And sureâ€"most storylines or plots have been done before, in some version, either in movies or books. Characters change and se ttings change, but there are certainly repetitions of conflicts and archetypes in literature that cant be avoided.However, there will always be a way for you to approach the topic with fresh eyesâ€"and with YOUR eyes. Even if your thoughts are similar to others, you will still express them in a unique way because you are a unique individual. There is no one else in the entire world who looks, thinks, and processes ideas exactly like you do. This means that the work you produce, whether it is writing or research or both, should be entirely original in the way it is written and compiled. Since every writer is an individual, it is highly unlikely that he or she will choose word-for-word the exact phrasing of another writer who has broached the topic previously.Bad Idea #4: If the source is obscure enough, no one will know you plagiarizedTechnology is an amazing thing and plagiarism software is part of that emerging technology. While the plagiarism-checker programs have varying abilitie s and scopes of their search, your theft of anothers words could always be discovered with the right one. The question then becomes: Are you willing to run that risk?Even if a source is entirely offline (very few are nowadays) and completely obscure, a professor paying attention will potentially be able to detect plagiarism because the writing style and word choice will be so very different than your own. Many professors hand out in-class assignments and tests that require you to write in class. This means that they have a sample of your writing, which clues them in to your writing style and the extent of your vocabulary. Anything you turn in that is in glaring contrast will immediately be suspected of plagiarism by a professor who is looking for it.Bad Idea #5: You wont get penalized if you accidentally plagiarize somethingAs nice as this would be, it simply isnt true. Many universities have a strict no-plagiarism policy, and any instance of it could be dealt with harshly, includin g expulsion, even if it was accidental. In fact, freelance writers who publish online content often run their work through a plagiarism detector to make sure they havent accidentally plagiarized someone. As a professional writer, this type of accidental plagiarism could still have the same consequences of intentional plagiarism, including lawsuits, losing their job, and loss of credibility in their industry.The fact is: its an easy mistake to make, especially when you read a lot of content about a particular topic. Sometimes, thoughts go through our brains that we assume to be original but are actually thoughts weve read somewhere and simply forgot we had read it (in that exact combination of words).Professors understand this and have likely dealt with the situation in their own research and writing. However, any responsible researcher or writer will take steps to ensure that his or her work is original and that it cites all sources quoted, whether directly or indirectly. This invol ves checking for plagiarism, even of the accidental variety, which is easy to do with all of the free plagiarism-checker websites available. When you submit your work for class or for a writing assignment given to you by your company, you should take these same steps.Bad Idea #6: Everyone does it, so you should tooI think most mothers have a similar reply when their rebellious teenager uses this argument to justify doing something against house rules: If everyone jumps off a bridge, would you follow them?While its a somewhat comedic anecdote, there is truth in it. Just because its widely done doesnt mean its right. And just because other people get away with it doesnt mean you will avoid getting caught, as well. In much the same sense that a police officer or judge will not be inclined to ignore laws broken simply because other people break themâ€"neither will a professor be inclined to excuse plagiarism, simply because he or she has seen it attempted often over the span of their ca reer.Beyond these facts, its important to understand that plagiarism is theftâ€"theft of anothers words and ideas, while claiming them as your own. In the same sense you would not be a thief in other facets of your life, dont be a thief of anothers writing and research.Bad Idea #7: If it isnt copyrighted, you can plagiarize itCopyright law is not as complex as you might think. In fact, once something is published online or as an original hardcopy, it retains an original copyright, whether the author attaches the copyright symbol () to it or not.Obviously, not every author would pursue litigation for copyright infringement, but the possibility is still there. This is especially true if you publish content onlineâ€"whether academic or otherwiseâ€"without attributing it to its original author. Just as there is software to detect plagiarism, there is likewise software for authors and website managers to use that detects if anyone is using their original content online. With this softwar e, they are able to find the website that is using their original content, as well as the websites owner (through information you provided when you registered the website). This means that the threat of lawsuits is always there, particularly if you are publishing online.Even if youre not publishing it online, plagiarism detector software can locate the original content online and mark yours as being plagiarized. And this software is freely available for professors or employers to use.Plagiarism can ruin your reputation and result in expulsion.Bad Idea #8: If you just rewrite another persons paper, it isnt plagiarizingThis is one of the most commonly held myths about plagiarismâ€"thinking that rewriting or rearranging the words of an entire section or paper is somehow not plagiarism. While this method might help you avoid some online plagiarism detectors, depending on the source youre rewriting, it can still be highly visible to your professor that you have done this.The problem with this method of plagiarizing is that it is both underhanded and still not your original thought. There are some cases in which you will need to do this in order to avoid quoting so much, you still need a citation following the rewrite to direct the reader toward the original source.

The Nsa s Foreign Defense - 1287 Words

Bethany Hamilton EGL 101, Dr. Laura Rozakis Know Thy Enemy: Why The NSA’s Foreign Defense Needs to Leave Our Backyards Thomas Jefferson said, â€Å"My reading of history convinces me that most bad government results from too much government.† The National Security Agency (NSA), established by the National Security Act of 1947, exists to safeguard American citizens against terror threats and foreign intelligence.(National Archives) Since the terrorist attack on the Twin Towers on September 11, 2001, the NSA, through the guise of the Patriot Act, has been investigating American citizens who are not suspect of law breaking. President George W. Bush enacted the Patriot Act (Uniting and Strengthening America by Providing Appropriate Tools Required to Intercept and Obstruct Terrorism Act of 2001 [Britannica]) in October 2001, but current President Barack Obama furthered its parameters via Executive Orders such as EO’s 13526 and 13549 (Federal Register). The Agency’s private inve stigations have caused public suspicion. This concern was validated by the revelation of the government’s collection of metadata (phone history), storage of text messages, possession of spy programs, and proof of the wire tapping of two-country related phone calls after Edward Snowden, a former NSA contractor, leaked private information to the public in May/June of 2013. (Britannica) With our country’s focus on the strengthening of military weapons and protection programs against foreign enemies,Show MoreRelatedAnalysis of Defense Intelligence Agency999 Words   |  4 Pagesstarted in 1958. The organizational structure of the DoD and U.S. foreign intelligence came to a new shape with the establishment of DIA. It was Robert McNamara, then Secretary of Defense, who came up with the concept of DIA in 1961. DIA gathers human source intelligence, analyzes technical intelligence, distributes intelligence/reports to the intelligence agencies, provides advice and support to t he Joint Chiefs of Staff with foreign military intelligence, and provides military intelligence to combatantRead MoreAmerican Peoples Privacy Is Being Spied on by the NSA and It Is Wrong703 Words   |  3 Pagesviolated by the NSA. Everyday person today in the USA uses technology to communicate and pleasure use: e-mail, texting, social networks, calling, blogs, forums, instant messaging, Internet and using search engines. The American people personal computer or electronic information is spied on and collect by the NSA this is wrong this is violating the fourth amendment. Who is spying and collecting personal electronic information from American people by the National Security Agency known as NSA. They areRead MoreBarack Obama s Presidential Debates1110 Words   |  5 PagesDuring the Democratic presidential debates on Tuesday, frontrunner Hillary Clinton was backed by her fellow Democratic contenders, most notably, Sen. Bernie Sanders (I-VA), who remarked in response to Clinton s e-mail flap, â€Å"Let me say something that may not be great politics, but I think the secretary is right. The American people are sick and tired of hearing about your damn emails.† http://www.reuters.com/article/2015/10/14/us-usa-election-democrats-idUSKCN0S70B920151014 This was an earlyRead MoreThe Cyber Defenses Of The United States887 Words   |  4 Pagesweekly if not daily and their cyber defenses must be kept up to par otherwise there will be an extreme loss of information and resources. FBI director James Comey can be quoted as saying â€Å"There are two kinds of big companies in the United States. There are those who ve been hacked by the Chinese and those who don t know they ve been hacked by the Chinese† (Comey). Comey can also be quoted as having said that, â€Å"China was seeking to obtain information that s useful to them so they don t haveRead MoreThe National Security Agency1257 Words   |  6 PagesThe National Security Agency (NSA) was created in 1952 and is headquartered in Forte Meade, Maryland. It is under the direction of the Department of Defense and reports to the Director of National Intelligence. Although classified, the NSA has an estimated 37,000 employees (1) and an estimated operating budget of about 11 billio n dollars per year, for comparison the Central Intelligence Agency has an estimated 20,000 employees and an operating budget of about 14 billion dollars per year (2). At theRead MoreNsa, Nsa And The Nsa1181 Words   |  5 Pages Working closely with the NSA, he realized the far reach with the everyday surveillance. While working with Booz Allen he started copying top-secret documents from the NSA. In those documents he realised NSA has been listening and watching most people s conversations and emails after 9/11 to see if â€Å"terrorist were planning to attack and never had to say anything to the people because of the espionage act saying it s ok to spy and not tell the people about it so they couldn t hide. After he hadRead MoreAnnotated Bibliography Of The Usa Patriot Act1349 Words   |  6 PagesBibliography and have found decent information analyzing. What I have been learning recently is that too many Americans are paranoid that the government is constantly looking at their emails and phone calls. Kevin Maney claims that most of the data at NSA sits in storage because no one has time to look at it all (Maney). I strongly agree with him and it seems logical. Yet Americans will be worried either way. Friday November 11th, I saw many articles of history claiming that government surveillance hasRead MorePresident Reagan Signed Into Law A National Security Decision Directive1344 Words   |  6 Pagesdirective placed the National Security Agency (NSA) in charge of the security of all computers and networks, and, for many civil liberations in Congress that went too far. The directive also created a national Telecommunication and Information Systems Manager â€Å"to consider all technical matters† as well as develop procedures for implementing the policy. The NSA director was to become that Manager. Congress had a substantial issue with that because NSA was forbidden from collecting any data on AmericanRead MoreDigital Privacy Concerns Essay1565 Words   |  7 Pagesexpressing his acknowledgement of the issue, failed to discuss an array of other pressing dilemmas regulated by the recently exposed National Security Agency (NSA), especially those involving the mass data stockpiles and the rights of foreigners against immoderate and disproportionate surveillance by the US. Furthermore, the intentions of the NSA still remain unclear; why is the collection and the extended retention of this data useful? Those in power believe that the collection of this informationRead MoreHistory Of Intelligence During The United States1137 Words   |  5 Pagesintelligence  operation.   The efforts were on code  breaking and counterintelligence  operations against Germany and Japan.   After World War 1, the United States Intelligence focused on code breaking. The U.S. infiltrated espi onage networks and arrested any foreign agents.  In 1941, the Peacetime Civilian Intelligence agency was created.   The office of the Coordinator of Information was designed to organize the activities of several agencies.   (The Evolution of the U.S. Intelligence Community-An Historical Overview

Jane Eyre Character Analysis - 1588 Words

Bertha Mason, Edward Rochester’s first wife, is generally considered the villain in the novel Jane Eyre, although, when taking a closer look at her most diabolical habit, escaping her captivity and setting fires, placing the role of the evil antagonist onto her an incorrect assumption. Jane Eyre is told through the eyes of Jane Eyre herself, in a first person account of her life. Jane, in the most nicely put way, dislikes Bertha, but understandably so. Bertha, in the eyes of the law, has the one thing Jane wants more in the world than anything else, Rochester. Because Bertha and Rochester are still technically married, Jane and Rochester cannot be together. The two lovers made it as far as the aisle before someone bothered to let Jane know†¦show more content†¦Bertha herself doesn’t do anything mad, but it is the perception of what she does that makes her appear insane. It has to be understood that she has been locked away from modern society for years on end, almost to a degree of solitary confinement by today’s standards. In 1951, McGill University signed off on a six-week study on the effects of leaving people in confined cells with moderate sensory deprivation. The study was suspended after just seven days. One week into the experiment and the participants were having visual and sonic hallucinations, and lost the ability to think clearly about anything, for any amount of time. This is what happened to Bertha. On top of that, â€Å"madness† is claimed to be hereditary in Bertha’s family, which is most likely schizophrenia or bipolar disorder, which are both common genetic disorders. Rochester subjected someone, with an already potentially fragile mind, to a state of living for years that would drive the average healthy person to the brink of madness after just one week. Bertha Mason is made the scapegoat for Rochester’s problems and is only as insane and evil as the reader perceives her to be. She most certa inly has her vendettas, but they are targeted at people or ideas, she does not aim to hurt everyone. Bertha has been vengeful toward not only Rochester, but also her family, as evident by her attacking her brother when he comes to visit, for allowing her to be kept in the state she has.Show MoreRelatedJane Eyre Character Analysis950 Words   |  4 PagesJane Eyre is one of many characters in literature that readers can show true empathy to. She is an honorable woman, humble and courageous, kind but strong-willed. While many stories rely on imperfect lead protagonists who fail in order to relate to the downtrodden nature of the human condition, Jane is altogether different. She appeals to the nobler parts of one’s self, a part that is equally common to everyone, but by which one is rarely reminded of. Jane Eyre written by Charlotte Brontà « demonstratesRead MoreJane Eyre Character Analysis1402 Words   |  6 PagesIn her novel Jane Eyre, Charlotte BrontÃ'‘ depicts the ch aracters of Jane Eyre and Bertha Mason as being negatively perceived by society, as they are both treated unfairly and are seemingly undesirable and disregarded. Looked down upon by society, they are made to feel suppressed and as if their thoughts do not matter. Such feelings of oppression seem to drive both Jane and Bertha to madness; Bertha seems to embody the inner rage that Jane tries to control within herself throughout the novel. ThroughRead MoreJane Eyre Character Analysis1064 Words   |  5 PagesCharlotte Bronte’s novel, Jane Eyre is the story of an orphaned ten-year-old girl name Jane Eyre, who overcomes abuse and neglect to discover compassion and love. Jane lives with the Reed family at Gateshead Hall, who was despised Jane, and she is bullied by Mrs. Reed and her son, John. John bullied her when she was reading the book, he threw the book at her head, John tortured Jane mercilessly and cruelly. Jane totally afraid of John, but she didn’t cry and cower un der him. She did try to avoidRead MoreJane Eyre Feminist Analysis1066 Words   |  5 Pagesnature or their intuition. Jane Eyre, a semi-autobiography by Charlotte Brontà «, is an exemplary novel where an untraditional heroine defies societal normality. The female protagonist Jane Eyre exhibits a self-created drive for personal success and a perpetual ambition to learn, characteristics customary of men. After the publication of Jane Eyre, many critics has viewed it through the feminist literary lenses, claiming it to contain biblical feminism. In the literary analysis â€Å"Charlotte Brontà «Ã¢â‚¬â„¢s Religion:Read MoreSummary of Clarkes Brontes Jane Eyre and the Grimms Cinderella1341 Words   |  6 PagesClarke, Micael M. Brontes Jane Eyre and the Grimms Cinderella. SEL: Studies in English Literature 1500-1900. 40.4 (2000): 695-710. Clarke explores the similarities and importance of Brontà «Ã¢â‚¬â„¢s use of the Grimms’ version of Cinderella within the story of Jane Eyre. She outlines how the two stories are parallel and then skillfully explores the symbolism that is present in both. Through her analysis of the ways the two stories are similar, Clarke concludes that the combination ofRead MoreLiterary Analysis : Emily, Wuthering Heights, And Jane Eyre924 Words   |  4 PagesLiterary Analysis The novels Emma, Wuthering Heights, and Jane Eyre were written by women in the 1800’s. The three writers chose to write and publish their novels under a different name from their own. Emma was written by Jane Austen, and published anonymously in 1815 (Behrens and Rosen 361). Emily Brontà « wrote Wuthering Heights, and was published in 1847 under the name Ellis Bell (Behrens and Rosen 368). The author of Jane Eyre, who was also the sister of Emily Brontà «, was Charlotte Brontà «. ThisRead MoreThe Upbringing Of Orphans By Charles Dickens And Jane Eyre1714 Words   |  7 Pagesorphans. The novels Oliver Twist by Charles Dickens 1838 and Jane Eyre by Charlotte Bronte 1847 depicted much of the 19th century working class and illustrated the treatment of orphans with different socio-economic perspectives. The role of the two orphans in the novels (Oliver and Jane) leads the reader through a maze of experiences, encountering life s threats and grasping its opportunities. The no vels show an insight of the two characters with a common childhood who were often treated with disdainRead MoreJane Eyre By Charlotte Bronte1374 Words   |  6 PagesJane Eyre by Charlotte Bronte Within the specter of the Gothic fictions arises the atmosphere of gloom, terror, and mystery with some elements of uncanny challenging reality. One major characteristic function of the Gothic fictions is to open the fiction to the realm of the irrational and perverse narratives, obsessions, and nightmarish terrors that hide beneath the literally civilized mindset in order to demonstrate the presence of the uncanny existing in the world known rationally through experienceRead MoreUse of Gothic Elements in Charlotte Brontes Jane Eyre1740 Words   |  7 PagesUSE OF GOTHIC ELEMENTS IN CHARLOTTE BRONTES ‘JANE EYRE Charlotte Brontes Jane Eyre was published in the middle of the nineteenth century. Bronte was greatly influenced by the Gothic novels that were in fashion before the time of Jane Eyre. The Gothic novel was popularised in the late eighteenth and early nineteenth centuries, and was defined by its use of suspense, supernatural elements, and desolate locations to generate a gloomy or chilling mood. The protagonist of the novel would generallyRead MoreUse of Gothic Elements in Charlotte Brontes Jane Eyre1729 Words   |  7 PagesUSE OF GOTHIC ELEMENTS IN CHARLOTTE BRONTES ‘JANE EYRE Charlotte Brontes Jane Eyre was published in the middle of the nineteenth century. Bronte was greatly influenced by the Gothic novels that were in fashion before the time of Jane Eyre. The Gothic novel was popularised in the late eighteenth and early nineteenth centuries, and was defined by its use of suspense, supernatural elements, and desolate locations to generate a gloomy or chilling mood. The protagonist of the novel would generally

Sentimental Bloke and Australian Culture

Question: Discuss about the Sentimental Bloke and Australian Culture. Answer: Introduction: The Sentimental Bloke is an Australian film that is based on the poems from the Songs of a Sentimental Bloke, a piece done by Dennis C. J. This literary work is a piece that has literary been considered one of the greatest silent film in Australia. The book sets out to depict Bill, the author as one who wants to quit his gambling and drinking addiction. This film tends to mooch along a series of vignettes drawn from the poem. Before this becomes actualized, Bill gets arrested and gets a six-month incarceration after he is found in a gamble. Upon his release, he falls in love with one Doreen who gets her stipend from a pickle factory. The Sentimental Bloke is an affectionately known book that takes pride in its portrayal of naturalism and acts of humor. The literary work is set in Melbourne but later, the author, together with his family relocated to Sydney, a city well known for its toughness and reputable reservation. The violent gangs had since disappeared into thin air just before the city came to light, just in the wake of the continent recovering from the First World War (Conor, 23). This is a story set right in its historical context with vast visits on the happenings of the unforgettable period of war in world history. Being set at a time when the war was at its peak, the book is believed to have derived its popularity from among the war veterans and post-war soldiers of the time. The Sentimental Bloke serves to connect Australia and the Great Britain in the manner in which it won admiration from the public. The Play proved a success in the UK unlike in the United States where it was a flop. The reason why the film was not a hit in the US was its difficult prose which the audience failed to comprehend and internalize. It was not until the Melbourne fire tragedy that the film got some challenges, but this was not to see its end as some parts of the movie had been saved from the inferno and went ahead to be cast at the Sydney Film Festival (Boyd, 3-18). The other connection between Australia and Great Britain is how the author juxtaposes with the foppish Briton soldier who was played by his wife while on duty. The wife who also happens to be in combat is portrayed to have pantomime tights and plumed military cap. According to the author, her characters have been depicted to portray the link between effeminacy and dandy dress. The theme of masculinity and feminism has also been expressed in the film. The fil was a masculine affair. The play presents an expression of heterosexual romantic affair pitting a male character from a male perspective, a fact that is expressed in a self-consciously manly way. In this regard, the play touches a cultural nerve in some way (Bellanta, 1-20). The pre and post war times were marred by the confusion as to what the role of men and women were about romance. The Australian men were supposed to be foot soldiers and while on their return, were expected to nurse and care for their young ones as they turned into caring spouses. The other instance that depicts masculine versus feminine state was the case of the larrikin digger. His celebration was a blatant ridicule to the female rowdies (Lawson, 18-32). In his thought, he strived to express his wish to have the larrikinism affair be an entirely masculine affair as no single female rose to prominence after or during the war. The theme of high culture versus popular culture has been given weight in this film. It is known that the archetypal appearance of the Anzac was one of a drunkard, anti-authoritarian and one that was full of impudent humor as well as nonchalance in the face of many. This was a culture that was first eclipsed in the acts of the Australian servicemen who saw to it that it was prudent to have such self-actualization and self-generation of culture (Edmondson et al. 11). This culture and name calling was viewed to have been derived from their numerous stories and jokes about themselves refereeing to one another as diggers. The film then portrays the digger with all manner of attributes that range from carelessness to being an introvert who thrives in disheveled clothes. Conclusively, the film is a bona fide production that stands the test of time. It an Australian cinema at its best, dramatic, emotionally earnest and funny film that is still intact in the memories of many viewers. This movie should be recommended for anyone who wishes to have a silent cinema with a beautifully narrated story. Works Cited Bellanta, Melissa. "A Masculine Romance: The Sentimental Bloke and Australian Culture in the War-and Early Interwar Years."Journal of Popular Romance Studies4.2 (2014): 1-20. Bellanta, Melissa. "Posts Tagged masculinity." Boyd, David. "The public and private lives of a Sentimental Bloke."Cinema Journal(1998): 3-18. Conor, Liz.The spectacular modern woman: Feminine visibility in the 1920s. Indiana University Press, 2004. Edmondson, Ray, and Andrew Pike.Australia's Lost Films: The loss and rescue of Australia's silent cinema. National Library Australia, 1982. Lawson, Sylvia. "Towards decolonisation: Film history in Australia."Nellie Melba, Ginger Meggs and Friends, Kibble Books, Malmsbury, Vic(1982): 18-32.

The contributions of Richard Wright and Gwendolyn Brooks to the civil rights movement

For the longest time in the history of the American society, black people faced severe discrimination from the white community. They were denied of their basic rights and they faced segregation, marginalization, maltreatment as well as poor working conditions.Advertising We will write a custom essay sample on The contributions of Richard Wright and Gwendolyn Brooks to the civil rights movement specifically for you for only $16.05 $11/page Learn More Other than these, slave trade which involved the dehumanizing sale of African Americans thrived and black men were also denied the right to vote. This provoked a fight for civil rights through the Civil Rights Movement which fought for the African Americans rights a ccording toFinlayson (11). This essay delves deeply into the contributions of Richard Wright and Gwendolyn Brooks to the Civil Rights Movement which played a great role in redeeming the black people from this discrimination. However, on the ground this was not the case as the African Americans were segregated, marginalized, maltreated, and subjected to poor working conditions. They also lacked opportunities and access to public amenities according to Levy (7-10). This saw the blacks come together in churches through song, literature, businesses, homes, families, poems and books all with the goal to fight against discrimination by the whites. Among these were Richard Wright and Gwendolyn Brooks who used literary works to voice out their displeasure on the discrimination against blacks as well as portray a humanitarian point of view on the plight of the African Americans in the 20th century (Marshall Cavendish Corporation 4). Richard Wright was among the young Americans born in the period when segregation and discrimination was at its peak. During this period, blacks were not supposed to contradict a white person but take in the segregation happily, cheerfully and humbly (Rowley 5).Advertising Looking for essay on ethnici ty studies? Let's see if we can help you! Get your first paper with 15% OFF Learn More Wright’s father abandoned their family when he was young and went to a segregated high school and was deeply hurt by the poor conditions that African Americans were living in. He published his first short story in 1924 and during the great depression; he did a variety of jobs and joined the communist party. He also wrote articles for the Daily Worker. He later moved to New York where he wrote a collection known as â€Å"Uncle Tom’s Children† which won him an award whose money he used to finish his famous book, â€Å"The Native Son† (Williams and Beard 358). Wright’s writing was mainly influenced by the prejudice and suffering he saw the black people go through as well as his own personal life. He was very outspoken on the injustices of racism and discrimination. His first book â€Å"Tom’s children† was soft and brought many to tears. To him however this was a failure in conveying his message as he wanted his audience to be shocked by the realities of racism which he was able to do in â€Å"The Native Son†. The book â€Å"Native Son† brought about racism in a very harsh and unmasked manner especially in the last chapter, â€Å"the trial†. It is the story of a man who kills two women; a white woman by accident and his black girlfriend purposely out of frustration and anger. He is caught and taken to trial but he is only convicted of one murder; that of the white girl which he committed accidentally. The murder of his black girlfriend is completely ignored and went unpunished showing the white community’s extent of their racism (Fraile 151). In the â€Å"Native Son†, Wright relies on naturalism and symbolism to bring out his key themes which include injustice, racism, violence and oppression. The bigger one is the representative of America’s racial hatred.Advertising We will write a custom essay sample on The contributions of Richard Wright and Gwendolyn Brooks to the civil rights movement specifically for you for only $16.05 $11/page Learn More The names of the characters also hint at the themes, for example, â€Å"Mr. Max† to represent Marxism and Clara â€Å"Mears† to mean a merely exploited black woman (Nelson 500). Wright also brings light to how discrimination affects black men as providers in their families in his play â€Å"Man of all work†. The play also reflects his experience with his father who was not willing to work hard to provide for the needs of their family. In this play, he uses symbolism and irony to show how black men are forced to do all sorts of work sometimes even having to pretend to be women to provide for their families. In another play called â€Å"Man ain’t God like that†, Wright explores western cultural imperialism. It also explores the effects of merging Christi anity with traditional African beliefs. Also in this play, he uses irony to hold the story and bring out its themes (Nelson 498-500). The other significant writer into the fight for civil rights is Gwendolyn Brooks. Gwendolyn Brooks unlike Richard Wright was a poet cum reporter and thus used poetry in her contributions to the fight for civil rights. Brooks had an eye for the discrimination of the blacks and their oppression by the white people. She saw a world filled with poverty, violence and loyalty. In the midst of this was humanity with a strong prideful persistence that was indifferent to oppression of that other group which surrounded and threatened it. Her poetry therefore not only represented this bleak world but also her personality as a strong black woman. Her books include, â€Å"A Street in Bronzeville† which portrays the frustration of a World War 2 veteran with American racism and the â€Å"Maud Martha†.Advertising Looking for essay on ethnicity studies? Let's see if we can help you! Get your first paper with 15% OFF Learn More Among her famous poems is â€Å"Annie Allen† a poem on the life of the black woman, â€Å"The Bean eaters† which talks about the civil rights movement and â€Å"In the Mecca†, a poem on the Black Nationalism. Other literary works include â€Å"Man of the middle class†, â€Å"The Chicago defender† and â€Å"The loveliest lyncher is the Lord† which tries to understand and represent the ordinariness of white life (Wright 36). In her poems, Brooks employs various styles to bring out her themes. In her poem â€Å"Annie Allen† for example, Brooks employs a realistic tone. Her tone evokes bitterness without invoking any tendencies towards violence or separatism. The poem follows Annie through different stages that open her eyes to the various realities of life around her. Annie starts her quest in childhood where she desires to break from the norms of her mother in the notes of childhood and girlhood. She is then exposed to the realities of marriage and love in the â€Å"Anniad† and finally chooses her identity in the womanhood. The poem strives to bring out the theme of equality and the demolishing of all forms of racial discrimination. She uses stylistic devices such as a contrast milk- glass, fruit -bowl, jelly- jar, and old peach cans to show different worlds. Also, the juxtaposition between dreams and reality, rhyming couplets, similes such as like a candle and set against the weeds of disappointment among others (Saber 36). In conclusion, both writers made significant contributions to the fight for civil rights. Through their literary works, they were able to bring out the intricacies and suffering that came with racial discrimination. Their blunt depiction of the lives of the African Americans in the 20th century forced the white people to view their actions as they were. This awakened them from their ignorance and showed the world as a whole the plight of the African Americans. Works Cited Finlayson, Reg gie. We shall overcome: The history of the American civil rights movement. USA: Twentieth Century Books, 2003. Print. Fraile, Ana. Richard wrights Native son. London: Rodopi International, 2007. Print. Levy, Peter. The civil rights movement. USA: Green Wood Publishing, 1998. Print. Marshall Cavendish Corporation. America in the 20th century. USA: Marshall Cavendish, 2003. Print. Nelson, Emmanuel. African American Dramatists. UK: ABC-CLIO, 2004. Print. Rowley, Hazel. Richard Wright: The life and times. USA: University of Chicago Press, 2008. Print. Saber, Yomna. â€Å"Brave to be involved: shifting positions in the poetry of Gwendolyn Books.† Peter Lang Journal (2010): 5-9. Print. Williams, Horace and Ben, Beard. This Day In civil rights history. USA: Newsouth Books, 2009. Print. Wright, Stephen. On Gwendolyn Brooks: Reliant contemplation. USA: University of Michigan Press, 2001. Print. This essay on The contributions of Richard Wright and Gwendolyn Brooks to the civil rights movement was written and submitted by user Soft Deer to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.

personal statement Essay Example

personal statement Essay Example personal statement Essay personal statement Essay personal statement BY kit-li96 Prompt #1 Step back, relax, and I will you take on a Journey. A Journey into the past, of which made me the person I am today. A childhood not so bright, but one of a very promising future. There have been times of struggle, sacrifices, and hardships, but at the end of the day What doesnt kill us can only make us stronger This name carries generations of family history and culture, NigistiAzeb Retta Adane Retta Kesaun Yelow Selassie. I was born on September 22, 1996, in Black Lion Hospital (Ethiopia). The daughter of Kiros Meresa, and Retta Adane, I was born into a olitical family, with relations to the last Emperor Haile Selassie. Most of my life I had no clue to who my dad really was. I met him for the first time when I moved to America, in 2001 with my mother. My father had an affair and contracted HIV, and died 7 years later. But, the first six months coming into the country, we were left with little money, and no place to live. The first few months the church placed us in women shelters, which allowed me to start going to school. Even though I was young I knew I had to learn English as soon as possible to teach my mother. I am academically hardworking and I don’t slink off from school work. I like analyzing and train myself to possess regular survey wonts. I believe this diligence is really of import particularly when seeking to guarantee my ain personal development every bit good as the advancement of the community I am in. I am besides adept in human dealingss and interpersonal communicating and I believe that this will assist me utilize diverseness to my ain advantage and development. I am cognizant that as an international pupil from Vietnam there will be jobs with accommodation in the beginning ; but I am ready and willing to travel through the alterations in the involvement of academic excellence. Possibly. other than merely the interaction that I could offer to the other pupils of the University. I can besides portion my civilization and Asiatic heritage to enrich others. This manner. I can besides promote credence and apprehension among assorted civilizations and nationalities presently taking up classs at UCF. My household owns a part concern in Vietnam and since I major in concern disposal – selling. I am trusting that my first manus experiences in the selling and forces dealingss division of our household concern would besides be deserving sharing to my other co-workers. I am besides dedicated to the public assistance of communities and of college pupils. I joined Vietnamese Student Associations in the yesteryear to protect and contend for the rights of pupils from my ain state. I besides value the spirit of volunteerism ; in fact. I was besides a voluntary for the African Community in Seattle. I can personally guarantee the UCF community that I would be an plus to the University should I be given the opportunity. I will seek my really best to stand out in my surveies to farther hike the already esteemed name of the college. I will seek chances where I could be of aid to the full community and where I could lend what cognition I already possess to the other pupils of the University. I am a house truster of interaction and inter-personal relationships and so I will affect myself in activities that would non merely be enriching for myself but besides for the other pupils whom I interact with. The diverseness of environment in UCF makes me enthusiastic about future chances for personal development and authorization ; but most of all. I would wish to be the sort of pupil who non merely thinks about oneself but besides considers the public assistance of other pupils every bit good as of the University.

Elizabeth Taylor Greenfield

Elizabeth Taylor Greenfield   Overview Elizabeth Taylor Greenfield, known as â€Å"The Black Swan,† was considered the most well-known African-American concert performer of the 19th Century. African-American music historian James M. Trotter lauded Greenfield for her remarkably sweet tones and wide vocal compass. Early Childhood The exact date of Greenfield’s date is unknown yet historians believe it was in 1819. Born Elizabeth Taylor on a plantation in Natchez, Miss., Greenfield moved to Philadelphia in the 1820s with the mistress, Holliday Greenfield. After relocating to Philadelphia and becoming a Quaker, Holliday Greenfield freed her slaves. Greenfield’s parents migrated to Liberia but she stayed behind and lived with her former mistress. The Black Swan Sometime during Greenfield’s childhood, she developed a love of singing. Soon after, she became a vocalist at her local church. Despite a lack of musical training, Greenfield was a self-taught pianist and harpist. With a multi-octave range, Greenfield was able to sing soprano, tenor and bass. By the 1840s, Greenfield began performing at private functions and by 1851, she performed in front of a concert audience. After travelling to Buffalo, New York to see another vocalist perform, Greenfield took the stage. Soon after she received positive reviews in local newspapers who nicknamed her â€Å"African Nightingale† and â€Å"Black Swan.† Albany-based newspaper The Daily Register said, â€Å"the compass of her marvelous voice embraces twenty-seven notes each reaching from the sonorous bass of a baritone to a few notes above even Jenny Lind’s highs.†   Greenfield launched a tour that would make Greenfield the first African-American concert singer to be recognized for her talents. Greenfield was best known for her renditions of music by George Frideric Handel, Vincenzo Bellini and Gaetano Donizetti. In addition, Greenfield sang American standards such as Henry Bishop’s â€Å"Home! Sweet Home!† and Stephen Foster’s â€Å"Old Folks at Home.† Although Greenfield was happy to perform at concert halls such as Metropolitan Hall, it was to all white audiences. As a result, Greenfield felt compelled to perform for African-Americans as well. She often performed benefit concerts for institutions such as the Home of Aged Colored Persons and the Colored Orphan Asylum. Eventually, Greenfield traveled to Europe, touring throughout the United Kingdom. Greenfield’s acclaim was not met without disdain. In 1853, Greenfield was set to perform at Metropolitan Hall when a threat of arson was received. And while touring in England, Greenfield’s manager refused to release funds for her expenses, making it impossible for her stay. Yet Greenfield would not be dissuaded. She appealed to abolitionist Harriet Beecher Stowe who arranged for patronage in England from the Duchesses of Sutherland, Norfolk and Argyle. Soon after, Greenfield received training from George Smart, a musician with ties to the Royal Family. This relationship worked in Greenfield’s benefit and by 1854, she was performing at Buckingham Palace for Queen Victoria. Following her return to the United States, Greenfield continued to tour and perform throughout the Civil War. During this time, she made several appearances with prominent African-Americans such as Frederick Douglas and Frances Ellen Watkins Harper. Greenfield performed for white audiences and also for fundraisers to benefit African-American organizations. In addition to performing, Greenfield worked as a vocal coach, helping up and coming singers such as Thomas J. Bowers and Carrie Thomas. On March 31, 1876, Greenfield died in Philadelphia. Legacy In 1921, entrepreneur Harry Pace established Black Swan Records. The company, which was the first African-American owned record label, was named in honor of Greenfield, who was the first African-American vocalist to achieve international acclaim.

Week 2 response papers Essay Example | Topics and Well Written Essays - 500 words

Week 2 response papers - Essay Example sidering that controlling people’s values and temperance is difficult, this may not be the ultimate solution to the current and impending environmental problems. In agreement with the student post, teaching people and making them aware of the consequences of their actions can play a lot in changing people’s negative behavior. As the student notes, people may end up being less wasteful as they understand the kind of situation that may result due to their actions or inactions. While laws help in bringing sanity, they alone too reduce people’s freedoms as noted by the student. A world with numerous freedoms taken away is not a healthy world in my personal view. The world would indeed be a better place if sustainability was upheld without necessarily imposing prohibitions or restrictions to such things as procreation as noted by Dasgupta (2007). As suggested b the student, it would be a noble idea to start teaching people about the issues of sustainability and environmental conservation at a tender age, giving them the opportunity to make informed choices about their preferences and actions. The second student has presented very strong and interesting ideas. The notion that there are already too many laws, regulations and prohibitions is only the truth. However, these laws are broken every so often; even by the very same people who enact them, in some cases. Furthermore, individual freedoms are reduced or altogether abolished with almost every single law that is enacted. Considering the above facts, education seems to be a better option in dealing with issues related to sustainability. When people are educated, they are in a better position to use their common senses to solve or avoid problems (Heal, 2009). Yet another commendable suggestion by the student is the idea that experimental tests should not be conducted in the atmosphere but under simulated conditions. It is common for scientists to simulate how things would work under certain circumstances

Starbucks Research Proposal Example | Topics and Well Written Essays - 3750 words

Starbucks - Research Proposal Example This has resulted in the shifting of the power balance from the sellers to the consumers. While consumers are getting more and more demanding in nature, because of their high access to information related to various products and services around the world, the sellers are getting under intense pressure to cater to the needs of the masses. This is resulting in connecting economic policy based developments with regards to political movements of many new and emerging regions, which is thus resulting in the emergence of new economies. Talking from the sellers’ point of view, it is important to mention that because of the high level of connectivity, the world of business has transformed itself into a single connected entity. Needless to say, because of the existence of a single connected world, gaining access to foreign and newer markets has become relatively easy as compared to the previous times. This is resulting in providing the boost to the companies and business organizations, in regards to the process of gaining information to the newer markets. It can be said that because of the easy access to information, the organizations are increasingly focusing on the process of entering new markets. This is resulting in the spiking of the level of competition in regards to the new markets, as in the recent times the more developed and well established markets of the West is facing a situation of stagnancy and low growth because of the multiple economic challenges. Because of the high amount of competition faced in the marketplaces of both the developed as well as the developing economies, the focus has increasingly shifted towards the multiple variables of marketing like product, place, promotion and price. For this project, it is important to mention that the company that has been selected is Starbucks. The entire project will highlight about the various issues related to the company of Starbucks as well as its related services in the various markets around the world. History of Starbucks It can be said that the company Starbucks was founded in the year 1971 in Seattle in America. The company opened with just a single store in the historic area of Pike Place Market and has entered into a mode of high growth and fast development. It is important to mention that the first chairman, president and chief executive of the company is Howard Schultz, who joined the organization in the year 1982. It has to be said that the first top level executive of the company had the vision of bringing the tradition of Italian coffee to the US. He also had the dream of building an image of a place for human interaction as well as community sense over a cup of coffee. Hence, the focus from the very beginning was not only on the product but was also on developing a feeling for the product as well. The mission of the company is to inspire and develop the spirit associated with a cup of coffee for a person at a single neighbourhood at any time. As of the recent day , the company Starbucks operates in over 62 countries, which are spread in various developing as well as the developed economies (Starbucks, â€Å"Our Heritage†). Product of Starbucks It is of considerable importance to mention the

The Legalization of Drugs: Just Say No Essay -- Con-Legalization of Dr

  Ã‚  Ã‚  Ã‚  Ã‚  The idea of legalizing drugs is as bad as the drugs itself. Some drugs are though to have positive medical use, but that's a though to be untrue considering the contradicting facts. How could drugs that are so addicitve be in any way helpful, specially in a medical manner. Every part of the world that has tried it only brought corruption to their country and made addiction rates even worse.   Ã‚  Ã‚  Ã‚  Ã‚  Although rumors that some drugs can help treat certain diceases have been stated they are not true, the fact is that false beliefs don't accumulate to the real facts. The repeutic treatment of heroin is said to alleviate cancer pain, this drug can also create other problems increasing the risk of diversion. In other words, it would encourage patients to sell their heroin on the black market. Another example is Glaucoma, which is a fluid pressure dicease to the eye. The THC that is found in marijuana decreases intraocular pressure. However, while marijuana may decrease intraocular pressure, it also decreases blood pressure making blood flow to the eye. Marijuana is also thought to be useful with treating pain caused by AIDS. Unfortunately, marijuana actually exacerbates the health risks associated with AIDS. Drugs wouldn't only physically be negative, it can also give you mental problems regarding the control towards drugs.   Ã‚  Ã‚  Ã‚  Ã‚  Legalizing would only increase the addiction rates of the already high standards and statistics regardless. For example, cocaine locks all of th...

The Taylor Melcher Leaky Dielectric Model

Annu. Rev. Fluid Mech. 1997. 29:27–64 Copyright c 1997 by Annual Reviews Inc. All rights reserved ELECTROHYDRODYNAMICS: The Taylor-Melcher Leaky Dielectric Model Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. D. A. Saville Department of Chemical Engineering, Princeton University Princeton, New Jersey 08544 KEY WORDS: electri? ed drops and jets, suspensions, interface charge, bulk charge ABSTRACTElectrohydrodynamics deals with ? uid motion induced by electric ? elds. In the mid 1960s GI Taylor introduced the leaky dielectric model to explain the behavior of droplets deformed by a steady ? eld, and JR Melcher used it extensively to develop electrohydrodynamics. This review deals with the foundations of the leaky dielectric model and experimental tests designed to probe its usefulness. Although the early experimental studies supported the qualitative features of the model, quantitative agreeme nt was poor.Recent studies are in better agreement with the theory. Even though the model was originally intended to deal with sharp interfaces, contemporary studies with suspensions also agree with the theory. Clearly the leaky dielectric model is more general than originally envisioned. INTRODUCTION The earliest record of an electrohydrodynamic experiment is in William Gilbert’s seventeenth century treatise de Magnete, which describes the formation of a conical shape upon bringing a charged rod above a sessile drop (Taylor 1969).Nineteenth-century studies of drop dynamics revealed how radially directed forces stemming from interfacial charge offset surface tension (Rayleigh 1882), but until the 1960s most work focused on the behavior of perfect conductors, (mercury or water) or perfect dielectrics (apolar liquids such as benzene). This began to change following studies on poorly conducting liquids—leaky dielectrics—by Allan & Mason (1962). Another branch of el ectrohydrodynamics, electrokinetics, deals with the behavior of charged particles in aqueous electrolytes (Saville 1977, Russel et al 1989). However, there are signi? ant differences between the behavior of electrolytes and leaky dielectrics. In electrolytes, electrokinetic phenomena are dominated by effects of interface 27 0066-4189/97/0115-0027$08. 00 28 SAVILLE charge derived from covalently bound ionizable groups or ion adsorption. Near a surface charged in this fashion, a diffuse charge cloud forms as electrolyte ions of opposite charge are attracted toward the interface. A concentration gradient forms so that diffusion balances electromigration. Then, when a ? eld is imposed, processes in this diffuse layer govern the mechanics. In electrokinetics, applied ? ld strengths are small, a few volts per centimeter, whereas in electrohydrodynamics the ? elds are usually much larger. With perfect conductors, perfect dielectrics, or leaky dielectrics, diffuse layers associated with equ ilibrium charge are usually absent. Accordingly, development of the two subjects proceeded more or less independently. Nevertheless, the underlying processes share many characteristics. Most obvious is that electric charge and current originate with ions; therefore, charge may be induced in poorly conducting liquids even though equilibrium charge is absent.The Cardiovascular SystemThe different treatments began to merge with the appearance of Taylor’s 1966 paper on drop deformation and Melcher & Taylor’s review of the topic (1969). Applications of electrohydrodynamics (EHD) abound: spraying, the dispersion of one liquid in another, coalescence, ink jet printing, boiling, augmentation of heat and mass transfer, ? uidized bed stabilization, pumping, and polymer dispersion are but a few. Some applications of EHD are striking. For example, EHD forces have been used to simulate the earth’s gravitational ? ld during convection experiments carried out during a space sh uttle ? ight (Hart et al 1986). In this application, combining a radial electric ? eld with a temperature gradient between concentric spheres engenders polarization forces that mimic gravity. One of the more unusual appearances of EHD involves the blue haze found above heavily forested areas. BR Fish (1972) provides experimental evidence to support his proposition that the haze derives from waxy substances sprayed into the atmosphere from the tips of pine needles by high ? elds accompanying the overhead passage of electri? d clouds during thunderstorms. This review concentrates on what has come to be known as the leaky dielectric model to elucidate its structure and describe its experimental foundations. For insight into other aspects of EHD, one or more of the many reviews or monographs1 may be consulted (Arp et al 1980, Melcher 1972, 1981, Tobazeon 1984, Crowley 1986, Chang 1987, Bailey 1988, Scott 1989, Ptasinski & Kerkhof 1992, Castellanos 1994, Atten & Castellanos 1995). In its most elementary form the leaky dielectric model consists of the Stokes equations to describe ? id motion and an expression for the conservation of current employing an Ohmic conductivity. Electromechanical coupling occurs only at ? uid-? uid boundaries where charge, carried to the interface by 1 Depending on the keywords used, computer literature surveys turn up hundreds of papers on EHD since the 1960s. Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. ELECTROHYDRODYNAMICS 29 Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11.For personal use only. conduction, produces electric stresses different from those present in perfect dielectrics or perfect conductors. With perfect conductors or dielectrics the electric stress is perpendicular to the interface, and alterations of interface shape combined with interfacial tension serve to balance t he electric stress. Leaky dielectrics are different because free charge accumulated on the interface modi? es the ? eld. Viscous ? ow develops to provide stresses to balance the action of the tangential components of the ? eld acting on interface charge.This review is organized as follows: First the model is outlined to identify approximations and potential pitfalls. Then experimental and theoretical results for two prototypical geometries—drops and cylinders—are surveyed. This discussion will establish the status of the leaky dielectric model where forces are con? ned to a sharp boundary. In closing, recent results on motion produced by EHD body forces are surveyed to indicate how the model has been extended to new situations. BALANCE LAWS The differential equations describing EHD arise from equations describing the conservation of mass and momentum, coupled with Maxwell’s equations.To establish a context for the approximations inherent in the leaky dielectric model, it is necessary to look on a deeper level. Then the leaky dielectric model arises naturally through a scale analysis. As noted earlier, the hydrodynamic model consists of the Stokes equations without any electrical forces; coupling to the electric ? eld occurs at boundaries, so forces from the bulk free charge must be negligible. Moreover, the electric ? eld is solenoidal. The next section examines how to establish conditions under which these approximations are appropriate. Scale Analysis and the Leaky Dielectric ModelUnder static conditions, electric and magnetic phenomena are independent since their ? elds are uncoupled (Feynman et al 1964). Insofar as the characteristic time for electrostatic processes is large compared to that for magnetic phenomena, the electrostatic equations furnish an accurate approximation. When external magnetic ? elds are absent, magnetic effects can be ignored completely. From Maxwell’s equations, the characteristic time for electric pheno mena, ? c ? â€Å"†o / , can be identi? ed as the ratio of the dielectric permeability2 (â€Å"†o ) and conductivity3 ( ).For magnetic phenomena the characteristic time, ? M ?  µÃ‚ µo `2 , is the product of the magnetic permeability,  µÃ‚ µo , conductivity, and the square of a characteristic length. Transport process time-scales, ? P , arise rationalized Meter-Kilogram-Second-Coulomb (MKSC) system of units will be used. conductivity will be de? ned explicitly in terms of properties of the constituent ions. For the present note simply that conductivity has the dimensions of Siemans per meter, i. e. , C2 -s/kg-m3 . 3 The 2 The 30 SAVILLE Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. nnualreviews. org by Brown University on 08/07/11. For personal use only. from viscous relaxation, diffusion, oscillation of an imposed ? eld, or motion ? M . The of a boundary. Slow processes are de? ned as those where ? P ? C second inequality can be rearranged to (â€Å" / µ)1/2 â€Å"o / `( µo â€Å"o )1/2 , and since ( µo â€Å"o ) 1/2 is equal to the speed of light, 3 ? 108 m/s, `( µo â€Å"o )1/2 is very small for our systems. For the electrostatic approximation to apply on a millimeterscale, the electrical relaxation time, â€Å"†o / , must be longer than 10 12 s. The inequality is satis? d easily because the conductivity is seldom larger than one micro-Siemans per meter for liquids of the sort under study here. Accordingly, the electrical phenomena are described by r  · â€Å"†o E = ? e and r ? E = 0. (2) (1) E is the electric ? eld strength, and ? e is the local free charge density. Boundary conditions derived from Equations 1 and 2 using the divergence theorem and a pill-box system spanning a portion of a boundary show that the tangential components of E are continuous and the normal component jumps by an amount proportional to the free charge per unit area, q, that is, k†Ã¢â‚¬ o Ek  · n = q. 3) Here k( ·)k denotes the jump, â€Å"outside–inside,† of ( ·) across the boundary, and n is the local outer normal. Electrostatic phenomena and hydrodynamics are coupled through the Maxwell stress tensor. A simple way of seeing the relationship between Maxwell stresses and the electrical body force is to suppose that electrical forces exerted on free charge and charge dipoles are transferred directly to the ? uid. For a dipole charge Q with orientation d the force is (Qd)  · rE. With N dipoles per unit volume, the dipole force is P  · rE; P ? N Qd de? nes the polarization vector. The Coulomb force due to ree charge is ? e E, so the total electrical force per unit volume is ? e E + P  · rE. This force can be transformed into the divergence of a tensor, r  · [â€Å"†o EE 1 â€Å"†o E  · E ], using Equations 1 and 2. The tensor 2 becomes the Maxwell stress tensor, M , ? ? ? 1 ? @† â€Å"†o 1 â€Å"†o EE E ·E , 2 † @? T upon in serting the isotropic in? uence of the ? eld on the pressure (Landau & Lifshitz 1960). ELECTROHYDRODYNAMICS 31 Using the expression for the electrical stress produces the equation of motion for an incompressible Newtonian ? uid of uniform viscosity, Du (4) = rp + r  · M +  µr 2 u.Dt Alternatively, upon expanding the stress tensor the electrical stresses emerge as body forces due to a non-homogeneous dielectric permeability and free charge, along with the gradient of an isotropic contribution, ? ? ? 1 @† Du = r p â€Å"o ? E ·E ? Dt 2 @? T ? 1 (5) â€Å"o E  · Er† + ? e E +  µr 2 u. 2 For incompressible ? uids, the expression in brackets can be lumped together as a rede? ned pressure. EHD motions are driven by the electrical forces on boundaries or in the bulk. The net Maxwell stress at a sharp boundary has the normal and tangential components [ [ M M Annu. Rev.Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. 1 â€Å"†o (E  · n)2 2  · n]  · ti = qE  · ti  · n]  · n = â€Å"†o (E  · t1 )2 â€Å"†o (E  · t2 )2 (6) after absorbing the isotropic part of the stress into the pressure as noted above. It is understood that ti represents either of two orthogonal tangent vectors embedded in the surface. Denoting a characteristic ? eld strength as E o and balancing the tangential electrical stress in Equation 6 against viscous stress yields a ve2 locity scale of q`E o / µ = â€Å"o `E o / µ.The same scale appears when the normal 2 stress or the bulk electrical forces are used. With â€Å"o E o as a scale for pressure, Equation 5 can be cast in dimensionless form as ?  µ @u + Re u  · ru = ? P @t rp 1 E  · Er† + [r  · (â€Å"E)]E + r 2 u. 2 (7) Here the symbols represent dimensionless variables with lengths scaled by ` and 2 time by the process scale ? P ; Re is a Reynolds number, ? `u o / µ ? ?†o `2 E o / µ2 , when the electrohydrodynamic velocity scale is used for u o . Choosing ? = 103 kg/m3 ,  µ = 1 kg/m-s, ` = 10 3 m, and E o = 105 V/m gives Re ? 10 4 and a viscous relaxation time, ? ? `2 ? / µ, of 1 ms approximately. For a dielectric constant of 4 and a conductivity of 10 9 S/m the electrical relaxation time, â€Å"†o / , is 35 ms. Equation 1 shows how the ? eld is altered by the presence of free charge. In liquids, charge is carried by ions, so species conservation equations must be 32 SAVILLE included to complete the description. Free charge density and ion concentration are related as X ez k n k . (8) ? e = k Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only.Here e is the charge on a proton and z k is the valence of the k th species whose concentration is n k . Note that some of the species may be electrically neutral, that is, z k = 0. Molecules and ions are carried by the ? ow and mo ve in response to gradients in the electrochemical potential. If we denote the mobility of the k th species by ! k , the species conservation equation is @n k +u ·rn k = r  ·[ ! k ez k n k E+! k k B T rn k ]+r k , @t k = 1, . . . , N . (9) Here k B is Boltzmann’s constant, and T is the absolute temperature. The ? rst term on the right represents ion migration in the electric ? ld, the second describes transport by diffusion, and the third denotes production due to chemical reactions since the neutral species act as a source for ions in the bulk. With a single ionic species, N = 1 and r 1 = 0; for a binary, z-z electrolyte, N = 3. In the ? rst case, ions are produced by reactions at electrodes—this is called unipolar injection. With a z-z electrolyte, ions are produced at the electrodes and by homogeneous reactions within the ? uid. Here attention is focused on liquids with charge from a single 1-1 electrolyte so that there are two homogeneous reactions.A forward re action producing positive and negative ions from dissociation of the neutral species as (neutral species, k = 1, z 1 = 0) ! (cation, k = 2, z 2 = 1) + (anion, k = 3, z 3 = 1) (10a) with a rate per unit volume, k+ n 1 , proportional to the concentration of species 1. The recombination reaction is (cation, k = 2, z 2 = 1) + (anion, k = 3, z 3 = ! (neutral species, k = 1, z 1 = 0) 1) (10b) with a rate of k n 2 n 3 . The rate constants k+ and k are speci? c to the ions, neutral species, and solvent; the rate of production of cations or anions is k+ n 1 k n 2 n 3 .Thus, r 1 = r 2 = r 3 = k+ n 1 k n 2n 3 (11) This situation contrasts sharply with that for strong electrolytes where neutral species are dissociated fully and reaction terms absent. Because ionic reactions ELECTROHYDRODYNAMICS 33 Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. are fast, it is convenient to imagine that the reactions are almo st at equilibrium. At equilibrium, the local rate of reaction is zero, so K ? k+ /k = n 2 n 3 /n 1 .This complicates matters because at equilibrium one of the conservation laws must be discarded to avoid an overdetermined system. To scale the problem consistently, note that the concentrations of the two ionic species will be much smaller than the concentration of the neutral constituent. Accordingly, it is convenient to use different concentration scales. Neutral species concentrations are p scaled with a bulk concentration denoted as n 0 and ionic concentrations with n 0 K . Using ! 0 as a mobility scale (any one of the three mobilities) and k+ n 0 as a reaction rate scale produces the conservation law for the neutral species, ?D @n 1 + Peu  · rn 1 = ! 1 r 2 n 1 ? P @t and for each ionic species, Da[n 1 n2n3] (12a) ? D @n k + Peu  · rn k = r  · [ z k n k ! k E] ? P @t r n0 1 k 2 k + ! r n + Da n 2 n 3 ], k = 2 , 3. (12b) [n K The new symbols represent a characteristic diffusi on time, ? D ? `2 /! 0 k B T ; 2 a Peclet number, Pe ? `u o /! 0 k B T ? `2 â€Å"o E o / µ! 0 k B T (the ratio of the rates of ion transfer by convection to diffusion); a dimensionless ? eld strength, ? ` eE o /k B T ; and a Damkoler number, Da ? k+ `2 /! 0 k B T (the ratio of a characteristic diffusion time to a characteristic reaction time).The reaction term can be eliminated from Equation 12b using Equation 12a to obtain † # † # r r n0 1 n0 1 ? D @ nk + n + Peu  · r n k + n ? P @t K K † # r n0 1 k k k 2 k k 1 n , k = 2, 3. (12c) = r  · [ z n ! E] + r ! n + ! K To compute local concentrations for systems in local reaction equilibrium, Equation 12c is used with k = 2 and k = 3, along with the equation for reaction equilibrium obtained from Equation 12a for Da 1. Equations 12c for k = 2 and k = 3 can be combined to furnish an expression for the dimensionless charge density, ? e = (n 2 n 3 ), ? D @ e ? + Peu  · r? e ? P @t = r  · [ (n 2 ! + n 3 ! 3 )E] + r 2 [! 2 n 2 + ! 3 n 3 ]. (13) 34 SAVILLE Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. From Equations 1 and 13 the characteristic charge relaxation time can now be identi? ed (in dimensional form) as â€Å"†o /e2 (! 2 n 2 + ! 3 n 3 ) ? â€Å"†o / . To guide simpli? cation of these equations, the magnitudes of the various groups are estimated for small ions with a characteristic radius4 , a, of 0. 25 nm using the Stokes-Einstein relation, (6?  µa) 1 , for the mobility. Then Pe ? 105 , ? 03 , and the diffusion time ? D ? 106 s. Estimating the size of the other dimensionless groups will require knowledge of the dissociation-recombination reactions. The equilibrium constant, K , is estimated from the Bjerrum-Fouss theory of ion association (Fouss 1958, Moelwyn-Hughes 1965, Castellanos 1994) as in ? 3? e2 K = 3 exp . (14) 4a 8? a†Ã¢â‚¬ o k B T while the recombination rate con stant (Debye 1942) k = 4? e2 (! 2 + ! 3 ) â€Å"†o (15) gives a forward rate constant of k+ = k K . (16) Using the data already introduced, K ? 1017 m 3 and k ? 10 18 m3 /s so k+ ? 10 1 s. Accordingly, Da ? 105 .To estimate the concentration of charge carriers, we use an expression for the conductivity of a solution with monovalent ions derived from a single 1-1 electrolyte = e2 (! 2 n 2 + ! 3 n 3 ). (17) For a conductivity of 10 9 S/m with 0. 25 nm ions, n 2 = n 3 = 1020 m 3 ( ? 10 7 moles/liter), so n 1 = 1024 m 3 ( ? 10 3 mol/liter). Thus, n 0 /K ? 107 and p Da n 0 /K ? 107 . To complete the simpli? cation we need to know the charge density. Equation 1 in dimensionless form is (18) 3r  · E = ? e = z(n 2 n 3 ); p 3 ? â€Å"†o E o /e ` n 0 K . Using the numerical values already de? ned, 3 ? 10 4 , suggesting the ? id is electrically neutral on the millimeter length scale. For 4 For comparison, the radius of a sodium ion in water is 0. 14 nm. The size of the charge c arrying ions in apolar liquids is largely a matter of speculation, but the presence of traces of water makes it likely that the charge carriers are larger than the bare ions. ELECTROHYDRODYNAMICS 35 3 ? 1 Equation 13 yields the classical Ohm’s law approximation in dimensionless form, r  · [(z)2 n 2 (! 2 + ! 3 )]E = 0 (19) Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11.For personal use only. as long as Pe3/ ? 1. With the numerical magnitudes given thus far, Pe3/ ? 10 2 , prompting the approximation expressed by Equation 19. To complete the description, charge conservation at the interface must be investigated. Here it is convenient to start with Equation 9 and integrate across an interface with the provision that there are no surface reactions. Using the s-subscript to denote surface concentrations and operators, and ignoring any special transport processes such as lateral surface diffusion, leads to @n k s + u  · r s n k = n k n  · (n  · r)u + s s @t ! ez k n k E + ! k k B T rn k  · n. k = 2, 3. (20) rs  · ( ) is the surface divergence, and n k are surface concentrations. The terms s on the right stand for changes in concentration due to dilation of the surface and transport to the surface by electromigration and diffusion. Adding the two equations, weighing each by the valence and the charge on a proton, gives @q + u  · rs q = qn  · (n  · r)u + k e2 (! 2 n 2 + ! 3 n 3 )Ek  · n @t + k B T r(e! 2 n 2 e! 3 n 3 )  · n. (21) Next Equation 21 is put in dimensionless form using â€Å"o E o as a surface charge scale ? c ? c @q + [u  · rs q ?P @t ? F qn  · (n  · r)u] 1 kr(! 2 n 2 ! 3 n 3 )k  · n. (22) = k (! 2 n 2 + ! 3 n 3 )Ek  · n + A new time scale, the convective ? ow time ? F ? `/u F , appears here. For 1, the diffusion term can be ignored and conduction balanced against charge relaxation and convection. For steady motion, charge convection balances conduction when ? C /? F is O(1). Summary Equations for Leaky Dielectric Model To summarize, the leaky dielectric electrohydrodynamic model consists of the following ? ve equations. The derivation given here identi? es the approximations in the leaky dielectric model.Except for the electrical body force terms, 36 SAVILLE it is essentially the model proposed by Melcher & Taylor (1969). ? µ @u + Reu  · ru ? P @t = Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. rp 1 E  · Er† + r  · (â€Å"E)E + r 2 u & r  · u = 0 2 (70 ) (190 ) r · E=0 ? c @q ? c + [u  · rs q ? P @t ? F k†Ek  · n = q [ [ M M qn  · (n  · r)u] = k Ek  · n (220 ) (30 ) 1 â€Å"(E  · n)2 2  · n]  · ti = qE  · ti  · n]  · n = â€Å"(E  · t1 )2 â€Å"(E  · t2 )2 (6) Note that the equations are written in dimensionless variables using the scales de? ned in the text.The equation of motion is for no nhomogeneous ? uids with electrical body forces. The hydrodynamic boundary conditions, continuity of velocity and stress, including the viscous and Maxwell stress, are assumed. Primes denote dimensionless forms of the parent equations. Electrokinetic Effects Although Equation 19 may be adequate for p millimeter-length scales, it would P fail if free charge on the Debye scale, ? 1 ? â€Å"†o k B T /e2 (z k )2 n k , produces important mechanical effects. As noted earlier, charged interfaces attract counterions in the bulk ? uid and repulse co-ions on the Debye length scale.Electric and hydrodynamic phenomena on this scale are responsible for the ubiquitous behavior of small particles in electrolytes, so it is natural to ask whether similar effects might be important here. In fact, Torza et al (1971) suggested that such effects could be responsible for the lack of agreement between the theory and their experiments on ? uid globules. To see whether the lack of agreement is due to electrokinetic effects we can use the numerical data already put forth. This leads to the following estimates: p = ? 1 ? 10 7 m, 3 ? 1, Pe3 ? 10 3 , Da ? 10 4 , Da n 0 /K ? 10 1 and 10 1 .Accordingly, on the Debye scale the relation between charge and ? eld is represented by Equation 18 while the species conservation equations 12 ELECTROHYDRODYNAMICS 37 become ? D @n 1 = ! 1 r 2 n 1 ? P @t ? D @n k = r  · [ z k n k ! k E] + ! k r 2 n k ? P @t r n0 1 + Da n 2 n 3 ], k = 2, 3. [n K (23a) (23b) Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. These equations are clearly more complex than those for Ohmic conduction, which omits entirely any accounting for individual species. Is this complexity necessary?In the following sections, experimental and theoretical results based on the leaky dielectric model are reviewed for several prototypical problems so as to assess the model’s effectiveness and the extent to which more detailed treatments taking account of diffuse layer effects are warranted. To date, none of the experimental studies show major electrokinetic effects despite the indications of the scale analysis. FLUID GLOBULES Drop Motion in External Fields Allan & Mason (1962) encountered paradoxical behavior when non-conducting drops suspended in non-conducting liquids were deformed by a steady electric ? ld. Conducting drops became prolate, as expected, but non-conducting drops often adopted oblate con? gurations. Oblate shapes were completely unexpected since analyses of static con? gurations predict prolate deformations, irrespective of the drop conductivity. Drop deformations can be analyzed with several methods. O’Konski & Thacher (1953) used an energy method; Allan & Mason (1962) balanced electrical and interfacial tension forces. For small deformations of conducting drops in dielectric surroundings, either procedure gives D= 2 9 a†Ã¢â‚¬ o E 1 . 16 (24) Here E 1 is the strength of the applied ? ld, a is the drop radius, and is interfacial tension. The deformation, D, is the difference between the lengths of the drop parallel and transverse to the ? eld divided by the sum of the two. Given that the drop is a conductor, it is easy to see why the shape is prolate since the pressures inside and outside the drop are uniform, initially, with the difference balanced by interfacial tension and the sphere’s curvature, 2 /a. Therefore, non-uniform electric stresses must be balanced by interfacial tension on the 38 SAVILLE deformed surface. Since the sphere induces a dipole into the incident ? ld, charge on the sphere’s equipotential surface varies as cos #; # being measured from the direction of the ? eld. The ? eld normal to the surface varies in a similar fashion. Accordingly, the electric stress at the surface varies as cos2 #, pulling the drop in opposite directions at its poles. Dielectric drops in dielectric surround ings also become prolate in steady ? elds, irrespective of the dielectric constants of the two ? uids, that is, 2 † 9 a†Ã¢â‚¬ o E 1 (? â€Å")2 (25) 16 (? + 2†³)2 † with circum? exes denoting properties of the drop ? uid (O’Konski & Thacher 1952, Allan & Mason 1962).Here deformation results from polarization forces since free charge is absent and the electric stresses are normal to the surface. Allan & Mason’s (1962) anomalous results led Taylor (1966) to discard the notion that the suspending ? uids could be treated as insulators. Although the suspending ? uids were poor conductors ( < 10 9 S/m) Taylor recognized that even a small conductivity would allow electric charge to reach the drop interface. With perfect dielectrics, the interface boundary condition (see Equation 3) sets the relation between the normal components of the ? eld to ensure that there is no free charge.For leaky dielectrics, charge accumulates on the interface to adjust the ? eld and ensure conservation of the current when the conductivities of the adjacent ? uids differ. The action of the electric ? eld on surface charge provides tangential stresses to be balanced by viscous ? ow. Taylor used the charge calculated from a solenoidal electric ? eld to compute the electric forces at the interface of a drop and then balanced these stresses with those calculated for Stokes ? ow. This procedure led to a discriminating function to classify deformations as prolate or oblate: 2M + 3 . 26) 8 = S(R 2 + 1) 2 + 3(S R 1) 5M + 5 Here S ? â€Å"/? , R ? ? / , and M ?  µ/ µ. Prolate deformations are indicated † ? when 8 > 1, and oblate forms are indicated when 8 < 1. Qualitative agreement between theory and experiment was found in nine of the thirteen cases studied by Allan & Mason (1962). In the other four (prolate) cases, ambiguities in electrical properties hampered a test of the theory. According to Taylor’s leaky dielectric model, tangential el ectric stresses cause circulation patterns inside and outside the drop. As further con? mation of the theory, McEwan and de Jong5 photographed tracer particle tracks in and around a silicone oil drop suspended in a mixture of castor and corn oils. Toroidal circulation patterns were observed, in agreement with the theory. Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. D= 5 McEwan & de Jong’s photos are presented in an addendum to Taylor’s paper (1966). ELECTROHYDRODYNAMICS 39 For a steady ? eld, Taylor (1966) gives the deformation as D= 2 9 a†Ã¢â‚¬ o E 1 8, 16 27) Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. so it is possible to test the theory quantitatively by measuring the length and breadth of drops for small deformations. However, Taylor did not publish a comparison between theory an d experiment. The ? rst quantitative tests were reported by Torza et al (1971), who extended the leaky dielectric model to deal with oscillatory ? elds. The deformation (0 < D < 0. 1) and burst of 22 ? id pairs were studied in steady and oscillatory (up to 60 Hz) ? elds. In steady ? elds, oblate deformations were observed in eight systems, in qualitative accord with the theory. Although the qualitative aspects of the theory were vindicated, the quantitative agreement was very disappointing. The deformation always varied linearly 2 with a E 1 , but the proportionality factor exceeded the theoretical value in all but one case, and the slopes were larger by a factor of two in more than half the systems. In one case, the measured slope was four times the theoretical value.In none of the systems was the measured slope less than the theoretical value, suggesting that the deviations are due to factors other than normal experimental errors. Alternating ? elds offer additional insight into l eaky dielectric behavior. As 2 expected with alternating ? elds where forces vary as a E 1 cos2 (! t), the deformation consists of steady and oscillatory parts (Torza et al 1971) D = D S + DT . 8S = 1 (28) The steady part, Ds , has the same form as Equation 27, but the 8-function is S 2 R(11+14M)+15S 2 (1+M)+S(19+16M)+15R 2 S? 2 ! (M+1)(S+2) , 5(M+1)[S 2 (2+R)2 +R 2 ? 2 ! 2 (1+S)2 ] (29) where ! is the angular frequency, and ? represents a hybrid electrical relaxation time â€Å"o â€Å"/ ? . According to Equation 29 the steady part of the deformation vanishes at a certain frequency and may shift from one form to the other with changes in frequency. Torza et al (1971) measured the steady part of the deformation for all 22 systems in 60-Hz ? elds and obtained results similar to those for 2 steady ? elds. The deformation was proportional to a E 1 , and in ? ve cases theory and experiment were in quantitative agreement.With the other systems the measured slopes exceeded the theoretic al values by substantial margins. The transition from oblate to prolate deformation was reported for one system—a 40 SAVILLE silicone oil drop in sextolphthalate with S ? â€Å"/? ? 2. 2 and R ? ? / < 0. 07. † However, the observed transition frequency (1. 6 Hz) was considerably lower than predicted (2. 5 Hz), although the two could be brought into agreement by lowering S to 1. 8. In this context the authors state: â€Å"This suggests that accurate measurements of the dielectric constants of the phases are crucial to a quantitative test of [the theory]. This observation will be revisited shortly. Some of the disagreement about oscillatory ? elds could be ascribed to the omission of temporal acceleration. Torza et al (1971) used a quasi-steady approximation, tantamount to ignoring ? @u/@t in the equations of motion. Upon including this acceleration, Sozou (1972) found qualitatively different behavior at high frequencies. For example, the steady part of the stress tends to zero, so this part of the deformation vanishes. With the quasi-steady approximation (see Equation 29), the deformation remains ? nite.Although this observation might account for some of the differences between theory and experiment in oscillatory ? elds, it does not resolve the low-frequency dif? culties. Torza et al’s study (1971) provides additional con? rmation of the qualitative aspects of the leaky dielectric model, but the lack of quantitative agreement is disconcerting. Even with water drops whose conductivity is ? ve orders of magnitude larger than the suspending ? uid, deviations between theory and experiment are substantial. Several reasons for the discrepancies were suggested.Lateral motion of charge along the interface due to surface conduction and convection of surface charge were ruled out since they ought to make the relation 2 between deformation and a E 1 nonlinear. Other possibilities were suggested: unspeci? ed deviations from the boundary conditions, s pace charge in the bulk, and diffuse charge clouds due to counterion attraction (cf Equations 23a,b). In an effort to address the boundary conditions issue, Ajayi (1978) employed perturbation methods to account for nonlinear effects in the deformation. This 2 analysis represents the shape using a power series in a†Ã¢â‚¬ o E 1 / .By carrying the analysis through the second order in the small parameter, Ajayi found that P2 (cos #) and P4 (cos #) are required to represent the surface and the deforma2 tion is no longer directly proportional to a†Ã¢â‚¬ o E 1 / . Considering nonlinear effects helps to an extent, but Ajayi observed that â€Å"[the method] cannot remove the discrepancy between theory and experiment. † Another possibility advanced as a source of disagreement involves electrokinetic effects (Torza et al 1971). Given the results of the earlier scale analysis, this theory appeared worth investigating further.Baygents & Saville (1989) addressed the matter us ing asymptotic methods to account for the in? uence of a diffuse layer arising from coulomb interactions between current carrying ions and the surface charge. Three layers were identi? ed where different processes dominate. A diffuse layer adjacent to the surface is separated from an outer region, where the leaky dielectric model applies, by an intermediate region. In Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. ELECTROHYDRODYNAMICS 41 he diffuse layer, electrokinetic processes due to space charge are relevant. The intermediate region is electrically neutral, and charge transport by diffusion, electromigration, and convection are equally important. In the outer region, the electrohydrodynamic equations prevail. Solving the differential equations involved matched asymptotic expansions, and because of the altered structure of the problem, the distributions of velocity and stress differ from those derived using the leaky dielectric model. Nevertheless, the ? nal expression for drop deformation is identical to that derived by Taylor (1966).Electrokinetic effects don’t appear to contradict conclusions drawn from the leaky dielectric model, which, based on this analysis, appears to be an exact lumped parameter description. Since none of the theoretical extensions appeared to resolve the divergence between theory and experiment, further experiments were undertaken. Following Torza et al’s (1971) suggestion regarding the need for accurate dielectric constants and other properties (see above), Vizika & Saville (1992) paid careful attention to direct measurement of physical properties.They studied eleven different drop-host systems in steady ? elds; oscillatory ? elds were employed with ? ve systems. The systems exhibited either prolate or oblate deformations. To increase the deformation, a non-ionic surfactant, Triton, was used in some cases to lower the interfacial tension. Generally speaking, agreement between theory and experiment improved over the earlier study. Figure 1 shows some 2 results with steady ? elds. In all cases, D varied linearly with a E 1 . Vizika & Saville (1992) observed time-dependent effects in some cases, especially with the surfactant. Evidently the ? ids were not completely immiscible, and mass transfer occurred between phases. In these cases it was necessary to remeasure the properties after time had elapsed to permit equilibration. Moreover, in cases where the conductivities of the two phases were comparable, ? eld-dependent effects were often observed. In oscillatory ? elds, the steady part of the deformation was measured at 2 different ? eld strengths; D S always varied linearly with a E 1 . The agreement between theory and experiment for the steady part of the deformation was generally better than with the same systems in a steady ? ld. With water in castor oil, for example, the calculated and measured slopes diff ered by 34% in a steady ? eld; in a 60-Hz ? eld the two agreed. Figure 2 summarizes results with four systems. Another interesting aspect of the leaky dielectric model concerns the effect of frequency. Torza et al (1971) showed, for example, that a drop that assumes an oblate deformation at low frequencies becomes prolate as the fre2 quency increases, that is, Ds /a E 1 increases with frequency. This behavior was measured with silicone drops suspended in castor oil; results are shown in Figure 3.The qualitative agreement between theory and experiment was Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. 42 SAVILLE Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. adequate, but as the ? gure indicates, the behavior is quite sensitive to the drop conductivity. Vizika & Saville (1992) compared theory and experiment for the oscillatory part of the deformation with one system; excellent agreement was obtained.Further encouraging comparisons between theory and experiment were reported by Tsukada et al (1993), who studied deformations with the castor oil–silicone oil system. Castor oil drops in silicone oil gave prolate deformations, oblate deformations were found with the ? uids reversed. In addition to experimental work, a ? nite element technique was employed to calculate deformations in steady ? elds. Except for the inclusion of ? nite deformations and (a) Figure 1 Deformation measurements for ? uid drops (Vizika & Saville 1992).Drops are prolate or oblate depending on whether D > 0 or D < 0. The dashed lines represent calculations made with the leaky dielectric model using measured ? uid properties; solid lines are least-squares representations of the experimental data. In Figure 1b the theoretical line for the upper set of data is not shown since it falls on the regression line for the l ower data; for this system the difference between theory and experiment is large. ELECTROHYDRODYNAMICS 43 Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11.For personal use only. (b) Figure 1 (Continued) inertial effects, the standard leaky dielectric model was employed. At small deformations, numerical results agreed with those from Taylor’s linear theory. With larger deformations, substantial differences appeared. Most of the differences between the ? nite element calculation and the linear theory were due to interface deformation since the Reynolds number in the calculations was always small. For prolate drops, the numerical results and Taylor’s theory agreed with the experimental data for 0 < D < 0. 07.With larger deformations, for example, for D ? 0. 2, the ? nite element solution was better than the linear theory but still predicted smaller deformations than those observed. In addition, the agreement be tween Taylor’s theory and the experiment for oblate drops exhibited a puzzling feature, that is, for large deformations the linear theory was closer to the experimental results than the nonlinear ? nite element calculation. These three studies constitute the most comprehensive test of the theory wherein interface charge arises from conduction across an interface.The agreement between theory and experiment is encouraging, and there seems little doubt that, insofar as drop deformation is concerned, the theory does a satis- 44 SAVILLE Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. Figure 2 The steady part of the drop deformation in oscillatory ? elds (Vizika & Saville 1992). factory job. Nevertheless, only a limited number of ? uids have been studied, and even in these cases, conductivities have not been controlled. Questions as to ? ite amplitude effects or charge convection due to interface motion remain to be investigated. In situations discussed thus far, charge convection has been ignored since ? C /? F ? 1. To investigate the in? uence of charge convection, the HadamardRybczynski settling velocity for a spherical drop can be studied. Although no experimental studies exist, calculations with the model indicate a substantial in? uence. First note that the velocity will be unaltered if a steady ? eld is imposed because, as long as charge convection is negligible, the net charge is zero and the ? ld exerts no net force on the drop. However, an asymmetric charge distribution creates a net force; charge convection due to sedimentation generates the necessary asymmetry. The relevant boundary condition is Equation 220 rewritten for steady ? ow, ? c rs  · (uq) = k Ek  · n. (30) ? F ELECTROHYDRODYNAMICS 45 Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. Figure 3 The unsteady part of t he drop deformation as a function of frequency for silicone drops in castor oil (Vizika & Saville 1992).Torza et al’s (1971) theoretical result is shown for two values of the drop conductivity; other parameters correspond with measured values. 2 Here the ? ow time will be a/u o =  µ/†Ã¢â‚¬ o E 1 , so ? C /? F = (â€Å"†o E 1 )2 / µ  · 1 ? C /? F ? 0. 1 for † = 4,  µ = 10 N-m, = 10 9 S/m, and E 1 = 105 V/m, so a linearized treatment is appropriate (Spertell & Saville 1976). Solving the equations shows the settling velocity is retarded or increased depending on the electrical relaxation times in the two ? uids, that is, 3Ust U = 3 + 2M . (31) (â€Å"†o E 1 )2 + F(R, S, M) 1+ M  µUst is the Stokes settling velocity for a rigid sphere and F(R, S, M) = 6M 2 [3S(R + 1) 1][RS 1] . 5(1 + M)2 S 2 (3 + 2R)(2 + R)2 (32) Also, with charge convection, drop deformation is no longer symmetric with respect to the midplane. These results show clearly that charge convection has different effects, either enhancing or retarding sedimentation, depending on the charge relaxation times in the two ? uids. 46 SAVILLE Given that interface charge induced by the action of an electric ? eld in leaky dielectrics has important effects on quasi-static motions, the next task is to inquire as to its effects on drop stability.Drop Stability and Breakup To provide a context to study the role of tangential stresses it is helpful to recall work on perfect conductors and dielectrics. Studies of drop dynamics6 and stability began with Rayleigh’s celebrated 1882 paper â€Å"On the equilibrium of liquid conducting masses charged with electricity. † His analysis pertains to instantaneous charge relaxation inside an isolated drop, and the relation7 between the frequency, ! , interfacial tension, , and drop charge, Q, is ? Q2 ! 2 = n(n 1) (n + 2) 3 (33) ? a 16? 2 â€Å"o ? a 6 for axisymmetric oscillations of an inviscid drop of radius a and dens ity ?.Here n denotes the index of the Legendre polynomial Pn (cos #). For perfectly conducting ? uids, the electric stress is wholly normal to the interface. Instability occurs for n = 2 when the charge increases to a level where the expression in brackets vanishes. Because a linearized, spheroidal approximation is used, either oblate or prolate deformations are included. Although the Rayleigh limit pertains strictly to small oscillations, dimensional analysis shows that the criterion for instability will still be of the form Q2 â€Å"o a 3 > C, (34) Annu. Rev. Fluid Mech. 1997. 9:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. but the constant C will depend on the properties of the surrounding ? uid. An EHD model of a leaky dielectric drop oscillating in an insulating ? uid addresses effects of charge relaxation inside the drop through a boundary condition for the conservation of interfacial charge, q. Accordingly, the model c onsists of linearized8 equations of motion for incompressible ? uids inside and outside the drop, ?  µ @u = rp + r 2 u, ? p @t r  · u = 0, (35) relations between the ? ld and the current in each phase, r  · E = 0, r ? E = 0, (36) 6 Rayleigh’s Theory of Sound (1945) contains many fascinating accounts of early work on drops and cylinders. 7 Recall that the rationalized MKSC system is used here. In Rayleigh’s notation, † = 1/4? . o 8 The linearization is based on the size of the deformation relative to the undeformed drop. ELECTROHYDRODYNAMICS 47 and boundary conditions. The relation between ? eld and charge is given by the dimensionless form of Equation 3, k†Ek  · n = q, (37) with charge scaled on the charge density on the undeformed drop, Q/4? a 2 .The scale for the electric ? eld, E o , is Q/4? â€Å"o a 2 . Charge on the interface is conserved, and for 1 the balance is Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. ?c @q ? c + [u  · rs q ? P @t ? F qn  · (n  · r)u] = (! 2 n 2 + ! 3 n 3 )E  · n. (38) To conserve charge, ion mobilities in the outer ? uid must be zero so that the current on the right-hand side represents conduction from the interior. For Rayleigh’s perfectly conducting drop, the local charge balance is unnecessary because: (a) the ? ld is nil inside the drop, and (b) charge transport is instantaneous so that the convection and relaxation terms vanish. The remaining boundary conditions are continuity of velocity and stress, and the kinematic condition. These equations have been solved to investigate how relaxation alters Rayleigh’s results (Saville 1974). Both viscous forces and charge relaxation effects were included, but general conclusions were obscured by the awkward transcendental form of the characteristic equation. However, asymptotic methods can be used to identify the salient features. The resul t for a slightly viscous drop in the absence of a suspending ? id is rather surprising in as much as Rayleigh’s result (see Equation 33) is recovered as the stability criterion. Even when charge relaxation by conduction is slow, charge convection still redistributes charge so rapidly that the oscillation frequency is given by Equation 33. A similar explanation was proposed by Melcher & Schwartz (1968) in their study of planar interfaces. Although EHD effects fail to alter the oscillation frequency, damping rates are affected. If the damping rate is denoted as , then )t]; ! R represents the the amplitude of the oscillation decays as exp[(i! R Rayleigh frequencies from Equation 33.First, note that with instantaneous relaxation the damping is volumetric and Rayleigh’s theory gives 1 ? 2 a ? 1 (39) ? (2n + 1)(n 1) 2 for a 2 for a drop with kinematic viscosity ?. When electrohydrodynamic effects are included and the oscillation time is comparable to the conduction time, th at is when â€Å"†o ! o / ? O(1), damping is slower: ? (40) ? (2n 3)(n 1) 2 . a 48 SAVILLE Other interesting effects can be identi? ed, including modes involving rapid 2 damping in a thin boundary layer where the rate is proportional to (a / 2 ) 3 . Rayleigh’s criterion also applies to very viscous drops with rapid charge a , has a relaxation. In contrast, slow charge relaxation, that is, â€Å"†o / substantial effect on highly viscous systems. Here the criterion for stability is altered to Q2 16? 2 a 3 â€Å"o † > 40? + 180†³ † 10? + 9†³ † (41) Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. for a viscous drop with dielectric constant † and viscosity  µ in a ? uid with † ? ? 1 and  µ where  µ ?  µ and (a /? ? 2 ) 2 ? 1. The next topic concerns behavior beyond the range where a linear treatment is acceptable.To form a simple mo del, the breakup of isolated drops or drops in external ? elds can be treated by approximate methods. A spheroidal approximation (Taylor 1964) yields an accurate expression for the stability of an isolated charged drop or an uncharged drop in an external ? eld. More recent work9 shows that prolate shapes evolving below the Rayleigh limit are unstable to axisymmetric perturbations while oblate shapes above the limit are stable to axisymmetric perturbations but unstable to nonaxisymmetric perturbations. Thus, the Rayleigh limit turns out to be the absolute limit of stability.Dimensional analysis indicates that the criterion for instability of a conducting drop immersed in a gas and stressed by an external ? eld has the form 2 a†o E 1 > C. (42) Taylor’s spheroidal approximation (Taylor 1964) gives C = 2. 1 ? 10 3 for D = 0. 31, in good agreement with experiments on soap ? lms. The limiting deformation corresponds to a drop with an aspect ratio of 1. 9. Above this point the drop is seen to throw off liquid as a ? ne jet. Taylor (1964) analyzed the region near the spheroidal tip, which becomes conical (a â€Å"Taylor cone†) at the limit of stability. For a cone with a vertex angle of 98. , electric stresses on a conducting surface are balanced exactly by surface tension. It turns out that conical tips also exist as static solutions when one perfect dielectric is immersed in another and S ? â€Å"/? ? 17. 6 (Ramos † & Castellanos 1994a). At the limit the vertex angle is 60 . For S < 17. 6, two solutions exist. One has a vertex angle larger than 60 ; the other is smaller. At S = 0 the vertex angles are 0 and 98. 6 , the latter corresponding to Taylor’s solution for an equipotential cone. 9 Pelekasis et al (1990) and Kang (1993) provide useful summaries of the dynamical stability of perfectly conducting drops.ELECTROHYDRODYNAMICS 49 More extensive analyses of the static behavior of drops disclose behavior consistent with this picture: Sherwood (1988, 1991) studied free drops; Wohlhuter & Basaran (1992) and Ramos & Castellanos (1994b) analyzed drops pinned to an electrode. According to the various computations, a dielectric drop immersed in another perfect dielectric elongates into an equilibrium shape as the ? eld increases when S > S1 . For S > S2 > S1 the drops become unstable at turning points in the deformation-? eld strength relation.In the range S1 > S > S2 there is hysteresis; drops are stable on the lower and upper branches of the relation and unstable in between. Values of S2 calculated by various methods are close to the value identi? ed as the maximum value for the existence of a cone. Wohlhuter & Basaran (1992) and Ramos & Castellanos (1994b), who studied pendant and sessile drops between plates, delineate other quantitative effects due to contact angle, drop volume, and plate spacing. How do EHD phenomena modify this picture? Interestingly, solutions for a leaky dielectric cone immersed in another l eaky dielectric ? id exist for R ? ? / > 17. 6, independent of the dielectric constants (Ramos & Castellanos 1994a). Because of tangential stresses, the ? uids are in motion (Hayati 1992). As before the cone angle is less than 60 , and two solutions exist as long as the conductivity ratio is large enough. The balance between electrical stress and interfacial tension determines the cone angle, and the normal component of the viscous stress is zero. As required, the tangential electric stress along the periphery of the cone is balanced by viscous stress. A circulation pattern exists inside and outside the cone with ? id moving toward the apex along the interface and away from it along the axis. One might conjecture that a certain level of conductivity is necessary for the formation of a sharp point and the ensuing micro-jet (see below). Allan & Mason (1962) and Torza et al (1971) observed three modes of drop deformation and breakup at high ? eld-strengths: (a) water drops in oil defor med symmetrically, and globules pinched off from a liquid thread; (b) castor oil drops in silicone oil deformed asymmetrically with a long thread pulled out toward the negative electrode; and (c) silicone oil drops in castor oil ? ttened and broken up unevenly. For modes a and b the initial deformation was prolate; for mode c it was oblate. The breakup of oblate drops in steady ? elds involved a complex folding motion with a doughnut-like shape. In an oscillatory ? eld, small drops were ejected from part of the periphery. Sherwood (1988) dealt with symmetric deformations (mode a) using a boundary integral technique. Perfect conductors or perfect dielectrics deform into prolate shapes in steady ? elds. With perfect conductors, the tips have a small radius of curvature, and Sherwood’s algorithm predicts breakup at the tip with critical ? ld-strengths close to those found by Taylor (1964) and Brazier-Smith (1971). Perfect dielectrics display similar overall behavior, and the max imum Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. 50 SAVILLE aspect ratio is near that predicted by energy arguments. With the leaky dielectric model, drops elongate and take on a shape with fattened ends connected by a thin neck. Since the calculation is quasi-static, transient behavior can be followed in cases where breakup occurs.Here the leaky dielectric model depicts drop elongation followed by breakup into individual droplets, behavior consistent with experimental results. In a leaky dielectric, electrohydrodynamic stresses ? atten the almost-conical tips formed in perfect dielectrics or conductors. Sherwood de? nes two sorts of drop breakup: the electrostatic mode where a conical tip develops and breakup is via tip-streaming, and the EHD mode following instability of the elongated thread. Because of the numerical algorithm’s structure it was not possible to study the other mode of breakup identi? d by Torza et al (1971), which remains a subject for future study along with effects of viscosity. Curiously, conical tips of the sort identi? ed by Ramos & Castellanos (1994a) were not found in Sherwood’s calculation. Following tip geometry much beyond the point of instability has not been possible although Basaran et al (1995) report detecting embryonic jets. Their computation includes dynamic effects with ? uid inertia balanced against interfacial tension and electrostatic forces. Although the focus is on perfect conductors and inviscid ? uids, small jets were identi? d emanating from the tips. Inasmuch as electrohydrodynamic effects appeared to suppress conical tip formation (Sherwood 1988), much more effort will be required to resolve the issue of jet creation. In calculations to date, perfectly conducting, inviscid drops produce (immature) jets; viscous, leaky dielectric drops do not. Predicting the onset and structure of the thin jet emerging from a Ta ylor cone is dif? cult, but EHD processes are clearly involved. Observations of liquid drops emerging from a small capillary make this conclusion abundantly clear.Drops become smaller as the potential is raised, and when the potential reaches a certain level, the drops emerge in a pulsating fashion. With further increases in the potential, the drop develops a Taylor cone that has a jet emerging from its tip. According to Hayati et al (1986, 1987a,b) and Cloupeau & Prunet-Foch (1990), effective atomization is possible only when the liquid conductivity lies in a certain range. To ? rst order, the ? ow pattern inside the cone can be approximated by superimposing ? ow into a conical sink onto the conical ? ow driven by a tangential electric stress varying as r 2 .The tangential stress arises from charge conduction to the interface. Charge accumulation stems from differences between the conductivity of the interior and exterior ? uids. The ? ow pattern has a somewhat counterintuitive str ucture: Liquid is supplied to the jet from the surface of the cone, while a recirculating eddy moves ? uid down the axis of the cone toward the supply. Of course this analysis omits details of the jet, whose characteristics are submerged in the singularity at the cone tip. Accounting for charge convection on the surface of the cone, which clearlyAnnu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. ELECTROHYDRODYNAMICS 51 becomes important near the apex (Ramos & Castellanos 1994b, Fernandez de la Mora & Loscertales 1994), has eluded analysis to date. FLUID CYLINDERS Stability of Charged Cylinders (Free Jets) Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. Here ? ? 2? a/ , a is the radius, Im ( ) and K m ( ) denote modi? d Bessel functions of order m with the prime sign denoting differentiation, and E 1 is the (radial) ? eld strength at the surface. When the inequality fails, the cylinder oscillates. The quantity on the left of Equation 42 is proportional to the growth rate when the cylinder is unstable and to the oscillation frequency when it is stable. For an uncharged cylinder, instability is indicated when ? < 1, that is, when > 2? a. Electric charge expands the range of unstable 2 wave numbers and increases growth rates. For a†o E 1 / = 1, the range is approximately 0 < ? < 1. 35 ( > 1. ? a). Interestingly, charge destabilizes non-axisymmetric deformations that are otherwise stable; the relation for these modes may be obtained from Equation 42 by equating the index of the Bessel functions with the mode for the angular deformation, cos(m#), and changing 1 ? 2 to 1 ? 2 m 2 . Viscous effects dampen the motion, but their effect is such as to make some non-axisymmetric motions relatively more unstable (Saville 1971a). The theory for charged cylinders is in qualitative accord with Huebnerâ⠂¬â„¢s (1969) ? nding of non-axisymmetric modes of breakup with highly charged water jets.Similar behavior exists with highly viscous cylinders, where, in addition to destabilizing non-axisymmetric modes, the presence of charge lowers the wavelength of the most unstable mode. Charge relaxation on an initially uniformly charged jet does not appear to have been studied, although given the importance this process has with axial ? elds, the topic is of considerable interest. Taylor (1964) observed that â€Å"induced charge has a very powerful effect in preventing the break up of jets into drops under certain circumstances and an equally powerful effect in causing violently unsteady movements ultimatelyShortly after Rayleigh’s pioneering paper (Rayleigh 1882), Bassett (1894) showed how charge destabilizes a cylinder by a mechanism similar to that found earlier with drops. Nevertheless, the process is more complex because a cylinder may be unstable even in the absence of electrica l forces. If the wavelength of a corrugation exceeds the circumference, then a varicose surface may have a smaller area than a circular cylinder and be unstable because it has a lower (free) energy. By studying the dynamics of a charged, inviscid cylinder, Bassett showed that an axisymmetric disturbance of wavelength will grow if ? 0 2 ? a†o E 1 K 0 (? ) ? Io (? 2 1 ? 1+? o > 0. (43) Io (? ) K o (? ) 52 SAVILLE Annu. Rev. Fluid Mech. 1997. 29:27-64. Downloaded from www. annualreviews. org by Brown University on 08/07/11. For personal use only. disintegrating the jet into drops in others. † Taylor was referring to the effects of a ? eld aligned with the axis of a water jet. Raco’s (1968) experiments with poorly conducting liquids also show a strong stabilizing effect. These results produce a quandary of sorts. Axial ? elds promote stability with dielectric jets (Nayyar & Murthy 1960) because of the action of the normal component of the electric ? eld on the deforme d interface. But the required ? ld strengths are much larger than those encountered by Taylor, and the dual nature of electric forces noted by Taylor does not appear to be consistent with the behavior of perfect dielectrics. The role of electric stress can be appreciated by imagining an axisymmetric deformation of the surface of the form 1 + ? (z, t). The normal component of the electric stress on the interface of a perfect dielectric due to axial ? eld is 2 a†Ã¢â‚¬ o E 1 where the dielectric constants of the cylinder and outer ? uid are denoted by † and ? â€Å". Thus protrusions are pushed inward and depressions outward irrespective of the wavelength of the disturbance.In contrast, the normal stress on a charged, conducting cylinder is 2 ? ? K 1 (? ) a†Ã¢â‚¬ o E 1 1 (z, t), (45) K o (? ) so this stress resists deformation only when the term in brackets is positive, that is, for ? < 0. 6. Moreover, with perfectly conducting ? uids some wavelengths are made mor e unstable. Although axial ? elds are seen to promote stability with dielectrics, large wavelengths (small ? , s) remain unstable. Since the stresses with perfect conductors or dielectrics are normal to the interface, the situation should be different with leaky dielectric materials due to tangential EHD stresses.The leaky dielectric equations have been solved for a viscous cylinder immersed in another viscous liquid under conditions where the current is continuous at the interface, that is, ignoring charge transport by relaxation, convection, and dilation of the surface. In terms of the dimensionless parameters in Equation 220 , ? C ? ? P & ? F . If, for example, we choose the process time to be the hydrodynamic time and identify it as that for a relatively inviscid mate? ? rial, (? a 3 / )1/2 , then † â€Å"o / ? (? a 3 / )1/2 ? 1. For distilled water, the electrical ? elaxation time is less than a millisecond and the hydrodynamic time for a 1-mm water jet is over a second; for apolar liquids of the sort mentioned earlier, the relaxation time may be longer ( ? 35 ms). In either case ? C ? ? P , so the approximation is appropriate. With leaky dielectrics the normal stress differs from that noted with perfect dielectrics, and there is also a tangential (1 † /†)2 ? (z, t), Io (? )K 1 (? ) + † /† Io (? )K 1 (? ) ? (44) ELECTROHYDRODYNAMICS 53 stress due to induced charge. Before deformation the surface is free of charge since the ? eld is parallel to the surface.Upon deformation