The role of disorder in flow-induced channelization in porous media

Flow-induced channelisation in porous media emerges from a dynamic interplay between erosion, deposition, and flow. Mild spatial inequalities in porosity and erosion resistance might get amplified, leading to the formation of main streamlines. In this work, we derive a continuum model for the coupled velocity and porosity fields from a capillary model. Both the microscopic and continuum models are based on the lattice Boltzmann method. We show that, with uneven erosion resistance, there is a discontinuous transition in the flow localisation, where permanent channelisation is observed for disorder above a critical value. We also show that, even for uniform erosion resistance, a weak disorder in porosity suffices to trigger permanent channelisation. References: [1] A. F. V. Matias, R. C. V. Coelho, H. A. Carmona, J. S. Andrade Jr., and N. A. M. Araujo. “The role of disorder in flow-induced channelization in porous media”. In preparation. [2] A. F. V. Matias, D. F. Valente-Matias, N. R. Neng, J. M. F. Nogueira, J. S. Andrade Jr., R. C. V. Coelho, N. A. M. Araujo, Physics of Fluids 35, 123611 (2023) [3] A. F. V. Matias, R. C. V. Coelho, J. S. de Andrade Jr., N. A. M. Araujo, Journal of Computational Science 53, 101360 (2021). [4] M. Sedahmed, R. C. V. Coelho, H. A. Warda, Phys. Fluids 34, 023102 (2022)