AN INTEGRAL-EQUATION FOR IMMISCIBLE FLUID DISPLACEMENT IN A TWO-DIMENSIONAL POROUS-MEDIUM OR HELE-SHAW CELL

Abstract

AbstractAn integral equation for the normal velocity of the interface between two immiscible fluids flowing in a two-dimensional porous medium or Hele-Shaw cell (one fluid displaces the other) is derived in terms of the physical parameters (including interfacial tension), a Green's function and the given interface. When the displacement is unstable, ‘fingering’ of the interface occurs. The Saffman-Taylor interface solutions for the steady advance of a single parallel-sided finger in the absence of interfacial tension are seen to satisfy the integral equation, and the error incurred in that equation by the corresponding Pitts approximating profile, when interfacial tension is included, is sho..