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Abstract

Oysters are suspension feeders which rely on actively moving fluid into and through themselves for sustenance. This investment of energy suggests a benefit to pumping fluid and consequently presents the question: To what degree it improves filtration rates. To investigate this, we develop a simplified model of the animal where the inner boundary of an annulus represents the oyster and the outer boundary represents a wall. The fluid flow is generated by a prescribed radial velocity condition on the inner boundary and material interaction with the model animal is modulated by a matching boundary condition in concentration. We show, through analysis of the model, that the material flux into the model animal is invariant under reversing the direction of flow and particular reflections of the geometry when the flow is in steady-state. In numerical simulations, we explore both the low and high Reynolds number limits for the flow. The low Reynolds number model (Stokes flow) produces material fluxes closest to the full model and the high Reynolds number model (potential flow) shows more similar optimal configurations; including both viscosity and inertia in the flow results in the highest amount of material capture as turbulence mixes the domain more effectively. Despite their limitations, Stokes flow and potential flow facilitate an adjoint formulation. In these cases, we use gradient-based optimization using the adjoint to find the boundary conditions that maximize material capture.