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The lattice Boltzmann (LB) method is used to study the kinetics of domain growth of a binary fluid in a number of geometries modeling two-dimensional porous media. Unlike methods which solve the Cahn-Hilliard equation, the LB method correctly simulates fluid properties, phase segregation, interface dynamics, and wetting. Our results, based on lattice sizes of up to 40964096, show little evidence to indicate the breakdown of late stage dynamical scaling, and suggest that confinement of the fluid is the key to the slow kinetics observed. Randomness of the pore structure appears unnecessary.
Grunau et al. (Mon,) studied this question.