Student Presenter(s): Hamad El Kahza
Faculty Mentor: Pejman Sanaei
Department: Mathematics
School/College: College of Arts and Sciences, New York City

Erosion and deposition, in the environmental context, is represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surface, which both often lead to reconfiguration and change of the topology of the geological structures and porous media. These processes are notably very complicated and challenging to study in reality. In this work, we formulate novel and idealized mathematical models to examine the internal evolution of flow-networks in the setting of cylindrical channels, undergoing a unidirectional flow, by using asymptotic and numerical techniques. Starting from the Stokes equations combined with an advection-diffusion solid transport, we propose a model to construct a complete analysis of both the erosion and deposition in geological structures and porous media. The considered approach is of the form of threshold laws: the fluid-solid interface erosion and deposition occur when the total shear stress is, respectively, greater and lower than some specific critical values, depending on the solid material. As a consequence of the erosion and deposition, the structure channels' radii expand and shrink, respectively. Throughout this study, we investigate the networks' evolution, which hinges on a parametric research on specific types of membrane properties and their influence on the reconfiguration regime within the channel.