Significance of swimming and feeding currents for nutrient uptake in osmotrophic and interception-feeding flagellates

We introduce 2 simple models for the flow generated by a self-propelled flagellate: a sphere propelled by a cylindrical flagellum and one propelled by an external point force. We use these models to examine the role of advection in enhancing feeding rates in 3 situations: (1) osmotroph feeding on dissolved molecules, (2) interception feeding on non-motile prey particles, and (3) interception feeding on motile prey (such as bacteria). We show that the Sherwood number is close to unity for osmotrophic flagellates, as suggested by most previous models. However, a more correct representation of the flow field than that predicted by a naive sinking sphere model leads to substantially higher clearance rates for interception-feeding flagellates. We find that a short flagellum is favourable for interception feeding, but at the cost of an increase in the drag on the body of the swimming unicell. We finally demonstrate that prey motility significantly enhances prey encounter rates in interception-feeding flagellates and is, in fact, often much more important for food acquisition than the feeding current.