Optimal clearance rates by a model oyster

Oysters are a significant factor in understanding water quality in coastal regions due to their function as filter feeders and their global range. Mathematical studies of bivalve filtration have typically modeled the animals as a pair of siphons, in line with the morphology of species like mussels and clams which have extendable appendages that extend from the body in order to reach into ambient currents. This is not the case with oysters where water is drawn directly in through a distributed opening between the two shells, and then expelled as a more localized jet, passing over the filtering gills in between. As a step towards understanding the filtration effectiveness of oysters, we consider the flow created by a single oyster in an otherwise motionless tank. For simplicity, we adopt a two-dimensional annular geometry in which the oyster and tank are taken to be the circular inner and outer walls; a prescribed radial velocity at the inner wall (the oyster) drives Stokes’ flow within the annulus. The transport arising from the resulting flow pattern is then gauged by solving an advection-diffusion equation for a passive scalar where concentration is held fixed at the outer wall (the tank) but set to zero at inflow or outflow to the oyster, assuming that filtration occurs immediately on entry. We investigate how different pumping arrangements and scalar diffusivities (Peclet numbers) impact the clearance rate of the passive scalar.