On Mathematical Modeling of Erosion and Deposition in Complex Porous Media*

Erosion and deposition are represented as the evolution of solid bodies as colloidal particles get transported within the porous media due to forces exerted by the fluid or air on the solid contact interface. These processes arise in many environmental contexts, industrial applications and are notably complicated and challenging to study in experimental endeavors. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow networks in cylindrical channels undergoing a unidirectional flow, using asymptotic and numerical techniques. Our model captures geometry evolution as particles get eroded from or deposited into the wall of the channels. Consequently, the structure channels' radii expand and shrink, respectively, due to the interplay of erosion and deposition. Previous endeavors to model this phenomenon have revealed three different regimes within a single pore: (i) a dominant-deposition regime, (ii) a dynamic erosion-deposition regime, (iii) and a dominant-erosion regime, leading to equilibrium. In this work, we extend the parametric sweep of the physical parameters within the constructed model to trace the final configuration of the branching structure using a geometrical aspects sweep of the system.