Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number

Abstract

Restricted accessMoreSectionsView PDF ToolsAdd to favoritesDownload CitationsTrack Citations ShareShare onFacebookTwitterLinked InRedditEmail Cite this article Feng James Q. 1999Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds numberProc. R. Soc. Lond. A.4552245–2269http://doi.org/10.1098/rspa.1999.0402SectionRestricted accessResearch articleElectrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number James Q. Feng James Q. Feng Xerox Corporation, Wilson Centre for Research and Technology, 800 Phillips Road, Webster, NY 14580, USA Google Scholar Find this author on PubMed Search for more papers by this author James Q. Feng James Q. Feng Xerox Corporation, Wilson Centre for Research and Technology, 800 Phillips Road, Webster, NY 14580, USA Google Scholar Find this author on PubMed Search for more papers by this author Published:08 June 1999https://doi.org/10.1098/rspa.1999.0402AbstractThe electrohydrodynamic flow associated with a fluid drop in an electric field is a consequence of the tangential electric stress at the fluid interface. The tangential viscous stress due to the electrohydrodynamic flow arises to just balance the tangential electric stress at the fluid interface so that the traction boundary condition is satisfied. Influenced by both the local electric stress and viscous stress, the drop interface may exhibit various shapes. The presence of fluid flow also leads to charge convection phenomena. The relative significance of the charge convection effect is usually measured in terms of the electric Reynolds number, ReE, defined as the ratio of the timescales of charge convection by flow and that for charge relaxation by ohmic conduction. This work presents a quantitative analysis of the charge convection effects in a framework of the leaky dielectric model at finite ReE, which has not been considered in previous investigations. Axisymmetric steady flows driven by an applied uniform electric field about a deformable fluid drop suspended in an immiscible fluid are studied by computational means of the Galerkin finite–element method with supplementary asymptotic analysis. The results of finite–element computations are in general agreement with the prediction by the asymptotic analysis for spherical drops at vanishingly small ReE. A common effect of charge convection is found to reduce the intensity of electrohydrodynamic flow. As a consequence, oblate drops are predicted to be less deformed in an electric field when charge convection is taken into account. The prolate drops are often associated with an equator–to–pole flow, which convects charges toward the poles to form a charge distribution resembling that in a highly conducting drop immersed in an insulating medium. Therefore, charge convection tends to enhance the prolate drop deformation. In many cases, charge convection effects are found to be significant even at apparently small ReE, corresponding to the charge relaxation time–scale about 10−3s, suggesting that many experimental results reported in the previous publications could have been influenced by charge convection effects. 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This Issue08 June 1999Volume 455Issue 1986 Article InformationDOI:https://doi.org/10.1098/rspa.1999.0402Published by:Royal SocietyPrint ISSN:1364-5021Online ISSN:1471-2946History: Published online08/06/1999Published in print08/06/1999 License: Citations and impact Keywordselectric Reynolds numberfluid drop deformationselectrohydrodynamicscharge convection