Towards controlling the rheological properties of suspension systems using fully differentiable unsteady Navier-Stokes flow solvers

Variations in the microstructure of freely suspended particles leads to diverse rheological

properties of complex fluids. While the study of suspension flows started more than 100

years ago, we still do not know whether it is possible to precisely

control rheological response by tuning particle types and properties. We show how the recent advances in automatic

differentiation could open the doors for seamless targeting of desired rheological properties. As

a first demonstration, we implement Brinkman penalization method in JAX-CFD code for

simulating non-interacting noncolloidal particles suspended in a Newtonian fluid. By directly

differentiating through the model, we solve multiple canonical optimization problems at low

and moderate Reynolds number flows for both dilute suspensions and structured

porous media. We discuss how such a method provides a generalizable foundation for reverse

engineering of intricate suspension flow problems.