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Engineering of polydisperse porous media for enhanced fluid flows through systematic topology tuning via differentiable direct numerical simulation

Mohammed G. Alhashim1,2,* and Michael P. Brenner1,†

  • 1School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
  • 2Research and Development Center, Saudi Aramco, Dhahran 31311, Saudi Arabia

  • *mga32@seas.harvard.edu; hashimmg@aramco.com
  • †brenner@seas.harvard.edu
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Phys. Rev. Fluids 9, 054103 – Published 10 May, 2024

DOI: https://doi.org/10.1103/PhysRevFluids.9.054103

Abstract

While predicting the flow behavior for a well-defined particulate microstructure is fairly tractable, systematic tailoring of the particle properties to yield desired flows remains illusive. For example, we still do not know how to precisely control rheological response by tuning particle types and properties or how to tailor porous media for filtration applications. Here we show that the recent advances in automatic differentiation provide a platform for methodologically addressing such questions. We optimize the packing of a polydisperse system of periodically arranged circular rods to maximize flow rate in the direction of applied pressure gradient. We show that the optimum topology of the structured porous medium depends on the solid volume fraction and approaches a staggered square with the particles' diameter ratio of 2−1 as the solid volume fraction reaches π/4[1+(2−1)2]. Regardless of the porous medium topology, the divergence exponent of the pressure gradient is universal and is equal to 5/2, as one finds from lubrication theory for a simple square lattice. These results are independent of the flow's Reynolds number and can provide a foundation to study inverse problems for suspension systems.

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Phys. Rev. Fluids 9, 054103– Published 10 May, 2024
  • Received 25 June 2023
  • Accepted 28 March 2024
Article part of CHORUS
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