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Simplified mathematical model for erosion and deposition in a porous medium

Amy María Sims*, Sai Kunnatha*, Emeka Peter Mazi, Priyanka Joseph, Kulsum Saber, Daniel Hwang, and Pejman Sanaei†

  • *These authors contributed equally to this work.
  • †Contact author: psanaei@gsu.edu
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Phys. Rev. Fluids 9, 124306 – Published 19 December, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.124306

Abstract

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 Darcy's law, 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.

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Outline

Information

Phys. Rev. Fluids 9, 124306– Published 19 December, 2024
  • Received 18 August 2024
  • Accepted 2 December 2024
Article part of CHORUS
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