A cellular automata convection-diffusion model of flows through porous media

A cellular automata model is proposed for investigating the process of formation and percolation of gas or fluid flows through interstices in solid media. The model is a cellular automata analogy of a convection-diffusion equation in partial derivatives. The advantage of the model is that it allows a simple representation of boundary conditions and, thus, makes it possible to investigate properties of media with a complex pore configuration. Moreover, using probabilistic transition rules makes it possible to adapt to the properties of the boundaries between liquid and solid phases. A formal representation of the model is given. Results of experimental investigation for a medium with hydrophobic, hydrophilic, and neutral pores are presented.