Skip to main content Accessibility help
×
Home
Hostname: page-component-78dcdb465f-bcmtx Total loading time: 0.518 Render date: 2021-04-14T21:11:24.222Z Has data issue: true Feature Flags: { "shouldUseShareProductTool": true, "shouldUseHypothesis": true, "isUnsiloEnabled": true, "metricsAbstractViews": false, "figures": false, "newCiteModal": false, "newCitedByModal": true }

Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers

Published online by Cambridge University Press:  14 October 2013

Ory Schnitzer
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Itzchak Frankel
Affiliation:
Department of Aerospace Engineering, Technion – Israel Institute of Technology, Haifa 32000, Israel
Ehud Yariv
Affiliation:
Department of Mathematics, Technion – Israel Institute of Technology, Haifa 32000, Israel
Corresponding
E-mail address:

Abstract

In Taylor’s analysis of electrohydrodynamic drop deformation by a uniform electric field (Proc. R. Soc. Lond. A, vol. 291, 1966, pp. 159–166) inertia is neglected at the outset, resulting in fluid velocities that scale as the square of the applied-field magnitude. For large (i.e. millimetric) drops, with increasing field strength the Reynolds number predicted by this scaling may actually become large, suggesting the need for a complementary large-Reynolds-number investigation. Balancing viscous stresses and electrical shear forces in this limit reveals a different velocity scaling, with the $4/ 3$ -power of the applied-field magnitude. For simplicity, we focus upon the flow about a spherical gas bubble. It is essentially confined to two boundary layers propagating from the poles to the equator, where they collide to form a radial jet. The transition occurs over a small deflection region about the equator where the flow is effectively inviscid. The deviation of the bubble shape from the original sphericity is quantified by the capillary number given by the ratio of a characteristic Maxwell stress to Laplace’s pressure. At leading order the bubble deforms owing to: (i) the surface distribution of the Maxwell stress, associated with the familiar electric-field profile; (ii) the hydrodynamic boundary-layer pressure, engendered here by centrifugal forces; and (iii) the intense pressure distribution acting over the narrow equatorial deflection zone, appearing on the bubble scale as a concentrated load. Remarkably, the unique flow topology and associated scalings allow the obtaining of a closed-form expression for the deformation through the mere application of integral mass and momentum balances. On the bubble scale, the concentrated pressure load is manifested in the appearance of a non-smooth equatorial dimple.

Type
Rapids
Copyright
©2013 Cambridge University Press 

Access options

Get access to the full version of this content by using one of the access options below.

References

Batchelor, G. K. 1967 An Introduction to Fluid Dynamics. Cambridge University Press.Google Scholar
Baygents, J. C. & Saville, D. A. 1989 The circulation produced in a drop by an electric field: a high field strength electrokinetic model. In Drops & Bubbles, Third International Colloquium, Monterey 1988 (ed. Wang, T.), vol. 7, pp. 717. AIP Conference Proceedings.Google Scholar
Feng, J. Q. 1999 Electrohydrodynamic behaviour of a drop subjected to a steady uniform electric field at finite electric Reynolds number. Proc. R. Soc. Lond. A 455 (1986), 22452269.CrossRefGoogle Scholar
Feng, J. Q. & Scott, T. C. 1996 A computational analysis of electrohydrodynamics of a leaky dielectric drop in an electric field. J. Fluid Mech. 311, 289326.CrossRefGoogle Scholar
Lac, E. & Homsy, G. M. 2007 Axisymmetric deformation and stability of a viscous drop in a steady electric field. J. Fluid Mech. 590, 239264.CrossRefGoogle Scholar
Landau, L. D. & Lifshitz, E. M. 1987 Fluid Mechanics: Course of Theoretical Physics. Pergamon.Google Scholar
Melcher, J. R. & Taylor, G. I. 1969 Electrohydrodynamics: a review of the role of interfacial shear stresses. Annu. Rev. Fluid Mech. 1, 111146.CrossRefGoogle Scholar
Moore, D. W. 1963 The boundary layer on a spherical gas bubble. J. Fluid Mech. 16 (2), 161176.CrossRefGoogle Scholar
Salipante, P. F. & Vlahovska, P. M. 2010 Electrohydrodynamics of drops in strong uniform dc electric fields. Phys. Fluids 22, 112110.CrossRefGoogle Scholar
Saville, D. A. 1997 Electrohydrodynamics: the Taylor–Melcher leaky dielectric model. Annu. Rev. Fluid Mech. 29, 2764.CrossRefGoogle Scholar
Sherwood, J. D. 1988 Breakup of fluid droplets in electric and magnetic fields. J. Fluid Mech. 188, 133146.CrossRefGoogle Scholar
Stewart, M. B. & Morrison, F. A. 1979 Small Reynolds number electrohydrodynamic flow around drops and the resulting deformation. J. Appl. Mech. 46 (3), 510512.CrossRefGoogle Scholar
Stewartson, K. 1958 On rotating laminar boundary layers. In Boundary Layer Research, Freiburg, Germany, 1957 (ed. H. Görtler), pp. 59–71. IUTAM Symposium, Springer.Google Scholar
Taylor, G. 1966 Studies in electrohydrodynamics. I. The circulation produced in a drop by electrical field. Proc. R. Soc. Lond. A 291 (1425), 159166.CrossRefGoogle Scholar
Torza, S., Cox, R. G. & Mason, S. G. 1971 Electrohydrodynamic deformation and burst of liquid drop. Phil. Trans. R. Soc. A 269 (1198), 295319.CrossRefGoogle Scholar
Yariv, E. & Rhodes, D. 2013 Electrohydrodynamic drop deformation by strong electric fields: slender-body analysis. SIAM J. Appl. Math. (in press).Google Scholar
Zholkovskij, E. K., Masliyah, J. H. & Czarnecki, J. 2002 An electrokinetic model of drop deformation in an electric field. J. Fluid Mech. 472, 127.CrossRefGoogle Scholar

Full text views

Full text views reflects PDF downloads, PDFs sent to Google Drive, Dropbox and Kindle and HTML full text views.

Total number of HTML views: 0
Total number of PDF views: 65 *
View data table for this chart

* Views captured on Cambridge Core between September 2016 - 14th April 2021. This data will be updated every 24 hours.

Send article to Kindle

To send this article to your Kindle, first ensure no-reply@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about sending to your Kindle. Find out more about sending to your Kindle.

Note you can select to send to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers
Available formats
×

Send article to Dropbox

To send this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Dropbox.

Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers
Available formats
×

Send article to Google Drive

To send this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your <service> account. Find out more about sending content to Google Drive.

Deformation of leaky-dielectric fluid globules under strong electric fields: boundary layers and jets at large Reynolds numbers
Available formats
×
×

Reply to: Submit a response


Your details


Conflicting interests

Do you have any conflicting interests? *