Kinetic Roughening in Two-Phase Fluid Flow through a Random Hele-Shaw Cell

Eduard Pauné, Jaume Casademunt
2003 Physical Review Letters  
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
more » ... gimes 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.
doi:10.1103/physrevlett.90.144504 pmid:12731922 fatcat:5c4qswkktfgahooyvkc5huaw64