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

A nonlocal interface equation is derived for two-phase fluid flow, with arbitrary wettability and viscosity contrast, c = ( μ 1 − μ 2 ) / ( μ 1 + μ 2 ) , in a model porous medium defined as a Hele-Shaw cell with random gap b 0 + δ b . Fluctuations of both capillary and viscous pressure are explicitly related to the microscopic quenched disorder, yielding conserved, nonconserved, and power-law correlated noise terms. Two length scales are identified that control the possible scaling regimes and which scale with capillary number Ca as ℓ 1 ∼ b 0 ( c C a ) − 1 / 2 and ℓ 2 ∼ b 0 C a − 1 . Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments