Nonlinear effective properties of unsaturated porous materials

We have investigated the nonlinear responses in terms of effective properties of unsaturated porous materials using a numerical framework. The multiphase microstructure is reconstructed through a random generation-growth method, and the transport governing equations are solved efficiently by a lattice Boltzmann model. After validation, the present framework is used to study the nonlinear behavior of thermal conductivity and electrical permittivity caused by the saturation degree and the phase interaction for multiphase materials. The results show that the effective thermal conductivity of unsaturated porous materials changes with the phase interaction ratio, while the effective permittivity decrease monotonously with the phase interaction. Mechanism analyses indicate that these nonlinear behaviors lie in the role of the liquid phase in the transport. For the thermal conductivity, the liquid phase plays a "bridge" function because its conductivity is between those of the solid and the gas. A better bridge network would enhance the overall effective thermal conductivity. However for the electrical permittivity, the liquid phase acts the leading force for transport and a more effective liquid phase connection will hence lead to a higher effective electrical permittivity of the multiphase system.