Shape Optimization of Peristaltic Pumps Transporting Rigid Particles in Stokes Flow

This paper presents a computational approach for finding the optimal shapes of peristaltic pumps transporting rigid particles in Stokes flow. In particular, we consider that minimize rate energy dissipation while pumping prescribed volume fluid, number particles, and/or distance traversed by over set time period. Our relies on recently developed fast and accurate boundary integral solver simulating multiphase flows through periodic geometries arbitrary shapes. order to fully capitalize dimensionality reduction feature methods, shape sensitivities must ideally involve evaluating physical variables particle or pump boundaries only. We show this can indeed be accomplished owing linearity The forward problem solves motion slip-driven pipe flow adjoint problems our construction solve quasi-static Dirichlet value backwards time, retracing evolution. simply depend solution one (for each functional) problems. validate these analytic derivative formulas comparing against finite-difference based gradients present several examples showcasing under various constraints.