Erosion and deposition

Erosion and deposition are prevalent and integral phenomena in natural and industrial settings such as agriculture, dam construction, and fluid filtration, among others. As such, we develop a mathematical continuum model that exhibits the behavior of these processes in an idealized two- dimensional porous medium and that allows for predictions of values and limitations of parameters such as porosity, shear stress, particle concentration, and porous medium deformation. By exploiting established governing equations such as the Darcy, advection-diffusion-reaction, and Navier-Cauchy equations, and then simplifying calculations via nondimensionalization and asymptotic analysis based on the small aspect ratio of the medium, we successfully model from a macroscale perspective how the erosion and deposition processes alter the internal morphology of an elastic porous medium. The essence of our results, beyond displaying how the medium evolves subject to the complex interplay among multiple parameters, covers how the total volume of the medium changes as we vary quantities of coefficients that measure the tendency of particles to erode or become deposited based on the physical properties of those particles and of the fluid and medium in which they travel.

Deposition and erosion processes have significant effects on the environment, industrial applications, and porous media. In this work we study the deposition and erosion of solid particles at the microscale level and their direct consequences on the internal structure of porous media with complex internal morphology. We formulate a mathematical model to investigate these phenomena in a porous medium with branching structure consisting of axisymmetric channels, undergoing a unidirectional flow. The flow and the transport of solid particles are modeled with the Hagen-Poiseuille law and advection-diffusion-reaction equations, respectively. As a consequence of deposition and erosion, those channels tend to shrink or expand, respectively, based on some key parameters which are discussed in this paper. This is modeled by threshold laws: the fluid-solid interface erosion and deposition occur when the total shear stress is, respectively, greater or lower than some specified critical values, depending on the solid material. Depending on the gradients of initial pore radii and layer thicknesses, substantial differences in the branching evolution under erosion and deposition are observed. Therefore, we characterize the evolution of the internal morphology of the porous medium using geometric parameters.

Erosion and deposition are represented as the evolution of solid bodies due to the forces exerted by the fluid or air on the contact surfaces, which both often lead to reconfiguration and change of the topology and structure of the porous media. These processes are notably very complicated and challenging to study. In this work, we formulate simplified 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 the advection-diffusion equation for solid transport, we propose a model to construct a complete analysis of both the erosion and deposition. 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 or lower than some specified critical values, depending on the solid material. As a consequence of the erosion and deposition, the radii of the channels in the structure expand and shrink, respectively, due to several key parameters, which we find and investigate in this paper. We also perform a parametric study to quantify the correlation between these threshold values and the particle concentration in the flow. A comprehensive parametric study of the constructed model reveals that the final configuration of the structure can be predicted from the system parameters.