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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| Veröffentlicht in: | European journal of applied mathematics Jg. 25; H. 4; S. 425 - 447 |
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| Format: | Journal Article |
| Sprache: | Englisch |
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Cambridge, UK
Cambridge University Press
01.08.2014
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| ISSN: | 0956-7925, 1469-4425 |
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| Abstract | 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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| AbstractList | 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. 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. [PUBLICATION ABSTRACT] |
| Author | KHALID, A. H. McDONALD, N. R. VANDEN-BROECK, J.-M. |
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| Cites_doi | 10.1063/1.870112 10.1017/S0956792511000210 10.1017/S0022112072002551 10.1017/S0022112094002144 10.1126/science.1136907 10.1038/059222d0 10.1137/0146003 10.1088/0953-8984/19/46/462101 10.1088/0953-8984/17/28/R01 10.1109/TMECH.2004.828659 10.1098/rspa.1976.0092 10.1017/S0956792500001029 10.1016/S0021-8928(02)00060-6 10.1017/S0956792507006869 10.1016/S0021-8928(96)00117-7 10.1093/qjmam/38.3.343 10.1063/1.2952374 10.1017/S0956792599003964 |
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| SubjectTerms | Applied mathematics Boundary value problems Cusps Delay Electric charge Electric fields Free boundaries Mathematical analysis Mathematical models Point charge |
| Title | Hele-Shaw flow driven by an electric field |
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