Simplified mathematical model for erosion and deposition in a porous medium

We develop a two-dimensional mathematical model that investigates the processes of erosion and deposition in an elastic porous medium. To simplify, we assume homogeneity and nondimensionalize the parameters, including Darcy velocity, particle concentration, and shear stress before reducing the continuum model via asymptotic analysis by exploiting its small aspect ratio. Our results illustrate the evolution of the medium under a prescribed constant flux of particles, wherein we draw conclusions on how total volume changes based on varying coefficients that dictate the tendency of particles to adhere to or be eroded from the walls of the medium at varying values of shear stress.