title: Non-Darcy behavior of two-phase channel flow.
abstract: We study the macroscopic behavior of two-phase flow in porous media from a phase-field model. A dissipation law is first derived from the phase-field model by homogenization. For simple channel geometry in pore scale, the scaling relation of the averaged dissipation rate with the velocity of the two-phase flow can be explicitly obtained from the model which then gives the force-velocity relation. It is shown that, for the homogeneous channel surface, Dacry's law is still valid with a significantly modified permeability including the contribution from the contact line slip. For the chemically patterned surfaces, the dissipation rate has a non-Darcy linear scaling with the velocity, which is related to a depinning force for the patterned surface. Our result offers a theoretical understanding on the prior observation of non-Darcy behavior for the multiphase flow in either simulations or experiments.
authors.affiliation: LSEC, Institute of Computational Mathematics and Scientific/Engineering Computing, NCMIS, AMSS, Chinese Academy of Sciences, Beijing 100190, China.
authors.forename: Xianmin
authors.initials: X
authors.lastname: Xu
authors.affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China.
authors.forename: Xiaoping
authors.initials: X
authors.lastname: Wang
mesh_terms: D008962:Models, Theoretical; D009038:Motion; D010539:Permeability; D016062:Porosity