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Remarkable parallels in the behavior of diffusion-limited aggregation and two-fluid displacements in porous media exist; hence, the former can be used to simulate the latter. Both processes can be described by the application of Laplace's equation with similar boundary conditions. Displacements can be stabilized by reversing the flow direction and interfacial tension can be incorporated to broaden dendrites or fingers. Furthermore, diffusion-limited aggregation can be used to simulate flow in anisotropic or inhomogeneous porous media.
Lincoln Paterson (Mon,) studied this question.