A lattice gas approach to shock propagation in a clay-like deformable porous medium

A three-component interacting lattice gas model is introduced to study the shock propagation in a porous medium consisting of clay-like pore barriers, fluid particles, and empty sites to represent air and other constituents. An attractive potential between the clay particles is considered to generate a soft porous matrix containing fluid in the pores. The mobility of the clay and fluid particles can be varied as well as their concentrations to capture the details of different porous systems. A collision scheme is implemented with appropriate energy dissipation. We restrict to a square lattice and consider a line of shock. The velocity gradient caused by the shock drives the fluid and clay particles. Unusually superfast power-law behavior is observed for the rms displacements of the fluid and clay particles in this velocity-field-driven system; the power-law exponents seem to depend on details such as mass of the particles and their energy dissipation. We find that the propagation and attenuation of the shock front depend strongly on the type of particles, rigidity of the clay-matrix and its porosity. Various general features are observed such as smearing of the shock front with non-linear propagation and evolution of the velocity and density profiles in both fluid within the pores as well as the clay matrix as the shock propagates.