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On a generalized two-fluid Hele-Shaw flow

Published online by Cambridge University Press:  01 February 2007

V. M. ENTOV  and
P. ETINGOF
V. M. ENTOV
Affiliation:
Institute for Problems in Mechanics RAS, prospekt Vernadskogo 101-1, 119526, Moscow, Russia email: [email protected]
P. ETINGOF
Affiliation:
Department of Mathematics, Massachussets Instutute of Technology, Cambridge MA, USA email: [email protected]
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Abstract

Generalized two-phase fluid flows in a Hele-Shaw cell are considered. It is assumed that the flow is driven by the fluid pressure gradient and an external potential field, for example, an electric field. Both the pressure field and the external field may have singularities in the flow domain. Therefore, combined action of these two fields brings into existence some new features, such as non-trivial equilibrium shapes of boundaries between the two fluids, which can be studied analytically. Some examples are presented. It is argued, that the approach and results may find some applications in the theory of fluids flow through porous media and microfluidic devices controlled by electric field.

Type
Papers
Information
European Journal of Applied Mathematics , Volume 18 , Issue 1 , February 2007 , pp. 103 - 128
Copyright
Copyright © Cambridge University Press 2007

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References

[1]Crowdy, D. (2002) On a class of geometry-driven free boundary problems. SIAM J. Appl. Math. 62 (3), 945–964.CrossRefGoogle Scholar
[2]Dukhin, S. S. & Deryagin, B. V. (1974) Surface and Colloid Sci. In: Matijevich, E., editor, Electrokinetic Phenomena. Wiley.Google Scholar
[3]Entov, V. M., Etingof, P. I. & Kleinbock, D. Ya. (1993) Hele-Shaw flows with free boundaries produced by multipoles. Euro. J. Appl. Math. 4 (2), 97–120.CrossRefGoogle Scholar
[4]Entov, V. M., Etingof, P. I. & Kleinbock, D. Ya. (1995) On nonlinear interface dynamics in Hele-Shaw flows. Euro. J. Appl. Math. 6 (5), 399–420.CrossRefGoogle Scholar
[5]Gakhov, F. D. (1990) Boundary Value Problems. Dover.Google Scholar
[6]Marino, S., Coelho, D., Békri, S. & Adler, P. M. (2000) Electroosmotic phenomena in fractures. J. Colloid & Interface Sci. 223 (2), 292–304.CrossRefGoogle ScholarPubMed
[7]Muskhelishvili, N. I.Singular Integral Equations. Dover.Google Scholar
[8]Ockendon, J. R. & Howison, S. D. (2002) Kochina and Hele-Shaw in modern mathematics, natural science and industry. J. Appl. Math. Mech. 66 (3), 505–512.CrossRefGoogle Scholar
[9]Overbeek, J. Th. G. (1952) Electrochemistry of the double layer. In: Kruyt, H. R., editor, Colloid Science, pp. 115–193. Elsevier.Google Scholar
[10]Richardson, S. (1972) Hele-Shaw flows with a free boundary produced by the injection of fluid into a narrow channel. J. Fluid Mech. 56 (4), 609–618.CrossRefGoogle Scholar
[11]Richardson, S. (2001) Hele-Shaw flows with time-dependent free boundaries involving a multiply connected fluid region. Euro. J. Appl. Math. 12, 571–599.CrossRefGoogle Scholar
[12]Varchenko, A. N. & Etingof, P. I. (1992) Why the Boundary of a Round Drop Becomes a Curve of Order Four. AMS.Google Scholar
[13]Wong, P. K., Wang, T.-H., Deval, J. H. & Ho, C.-M. (2004) Electrokinetics in micro devices for biotechnology applications. IEEE/ASME Trans. Mechanotronics, 9 (2), 366–376.CrossRefGoogle Scholar