Enhanced efficiency of feeding and mixing due to chaotic flow patterns around choanoflagellates

The motion of particles and feeding currents created by micro-organisms due to a flagellum are considered. The calculations are pertinent to a range of sessile organisms, but we concentrate on a particular organism, namely Salpingoeca amphoridium (SA) (a choanoflagellate), due to the availability of experimental data (Pettitt, 2000). These flow fields are characterized as having very small Reynolds numbers, which implies that viscous forces dominate over inertial ones consistent with using the Stokes flow equations. The flow generated by the flagellum is modelled via the consideration of a point force known as a stokeslet. The interaction between the boundary, to which the organism is attached, and its flagellum leads to toroidal eddies, which serve to transport particles towards the micro-organism, promoting filtering of nutrients by the microvilli which constitute the cell's collar (the filtering mechanism in SA). It is our conjecture that the interaction of multiple toroidal eddies will lead to chaotic advection and hence enhance the domain of feeding for these organisms. The degree of mixing in the region around SA is investigated using chaotic and statistical measures to study the influence the flagellum has on the surrounding fluid. The three-dimensional particle paths around such organisms are also considered with the aim of showing that the plane within which they are situated is an attractor.