Hele-Shaw flow driven by an electric field

The behaviour of two-dimensional finite blobs of conducting viscous fluid in a Hele-Shaw cell subject to an electric field is considered. The time-dependent free boundary problem is studied both analytically using the Schwarz function of the free boundary and numerically using a boundary integral me...

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Bibliographic Details
Published in:European journal of applied mathematics Vol. 25; no. 4; pp. 425 - 447
Main Authors: KHALID, A. H., McDONALD, N. R., VANDEN-BROECK, J.-M.
Format: Journal Article
Language:English
Published: Cambridge, UK Cambridge University Press 01.08.2014
Subjects:
Applied mathematics
Boundary value problems
Cusps
Delay
Electric charge
Electric fields
Free boundaries
Mathematical analysis
Mathematical models
Point charge
Hele-Shaw flows
Free boundary problems
Complex variable methods
ISSN:0956-7925, 1469-4425
Online Access:Get full text
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Summary:The behaviour of two-dimensional finite blobs of conducting viscous fluid in a Hele-Shaw cell subject to an electric field is considered. The time-dependent free boundary problem is studied both analytically using the Schwarz function of the free boundary and numerically using a boundary integral method. Various problems are considered, including (i) the behaviour of an initially circular blob of conducting fluid subject to an electric point charge located arbitrarily within the blob, (ii) the delay in cusp formation on the free boundary in sink-driven flow due to a strategically placed electric charge and (iii) the stability of exact steady solutions having both hydrodynamic and electric forcing.
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ISSN:0956-7925
1469-4425
DOI:10.1017/S0956792513000351