Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell

E. Paune; J. Casademunt

doi:10.1103/physrevlett.90.144504

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Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell

E. Paune·J. Casademunt

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Abstract

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast c=(mu_1-mu_2)/(mu_1+mu_2), in a model porous medium defined as a Hele-Shaw cell with random gap b_0+delta b. Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, non-conserved and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number as ell_1 ~ b_0(c Ca)^{-1/2} and ell_2 ~ b_0 Ca^{-1}. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.

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E. Paune, J. Casademunt. 2002-07-29. Kinetic roughening in two-phase fluid flow through a random Hele-Shaw cell. https://doi.org/10.1103/physrevlett.90.144504

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