© 1993 by Oxford University Press
AN EXACT SOLUTION TO THE NONLINEAR DIFFUSION-CONVECTION EQUATION FOR TWO-PHASE FLOW
(
1Division of Science and Technology, Griffith University Nathan, Australia
2Mathematical Institute, University of Oxford Oxford OX1 3LB
3Division of Science and Technology, Griffith University Nathan, Australia
)
A new exact solution to the nonlinear diffusion-convection equation
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for two-phase fluid flow in porous media is derived. The solution is sought for Dirichlet boundary conditions and a diffusivity of the form D(
) = Dosol;(1– 
)2. The functional form of the fractional flow function f() is then found from a condition which determines the integrability of the resulting nonlinear ordinary differential equation. This results in an f()-function of the form f() = (F1 + F2 + F32)/(1– ). Asymptotic expansions are derived for the fluid flux across the surface boundary x = 0 as a function of the parameters Do and , and the surface boundary condition. These expansions show that a Buckley-Leverett-type profile can be obtained in the limit of 
1 for a saturated surface boundary condition.