Mathematical modeling of deposition and erosion dynamics in a complex branching pore morphology

Deposition and erosion are fundamental processes in fluid dynamics, and they play a crucial role in various natural phenomena and engineered systems. These processes involve the transport of particles by the fluid flow, resulting in erosion of materials from one location and their subsequent deposition at another. In this study, we propose a mathematical model to simulate the deposition and erosion processes occurring in a porous medium represented by an idealized structure composed of bifurcating cylindrical channels, featuring two types of branching: symmetric and asymmetric. The fluid flow within the channels is governed by the Stokes equations, while the transport, deposition and erosion of solid particles are described by an advection-diffusion equation. Furthermore, we investigated the effects of deposition and erosion processes on the evolution of the porous medium internal morphology.