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=(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, 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) approximately b(0)(cCa)(-1/2) and l(2) approximately b(0)Ca-1. Exponents for forced fluid invasion are obtained from numerical simulation and compared with recent experiments.
Departament d'Estructura i Constituents de la Matèria, Universitat de Barcelona, Avinguda Diagonal, 647, 08028 Barcelona, Spain.
Eduard
E
Pauné
Jaume
J
Casademunt