4 1 0 O ct 2 00 1 A nonlinear differential approach to the Saffman-Taylor finger

Abstract

Nonlinear time-dependent differential equations for the Hele-Shaw, Saffman-Taylor problem are derived. The equations are obtained using a separable ansatz expansion for the stream function of the displaced fluid obeying a Dar-cian flow. Suitable boundary conditions on the stream function, provide a potential term for the nonlinear equation. The limits for… (More)

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