We model porous medium as a random pore network and focus on the influence of the medium internal structure on its flow and adsorptive behavior, see Figure 1.  A particular focus is modeling suspension flow, where the particles adsorb on the pore walls.  We first formulate the governing equations of fluid flow on a general network. Then, we model adsorption by imposing an advection equation with a sink term on each pore and study the influence of network parameters on the flow and transport; see the papers below for examples of our recent works. The talk will focus on developing better understanding of the connection between the topology of the medium (pore network) and the flow properties. The challenging aspect of understanding and quantifying evolving pore network topology is addressed by using topological methods that allow for simplified network descriptions, both regarding their static and their dynamic properties. For this purpose, we use tools based on persistent homology. These tools enable us to connect topology, transport, and adsorption as the essential step toward designing porous media of desired properties.

References: Gu, Kondic, Cummings, SIAM J. Appl. Math. 82, 950 (2022); J. Mem. Sci. 657, 120668 (2022); Phys. Rev. Fluids 8, 044502 (2023)