Torque-dipolar micro-swimmers: modeling, circling behavior and large-scale simulations

We present a new model for micro-swimmers that takes into account the counter-rotation of the body and flagella, as seen in motile bacteria or spermatozoa. The disturbance fluid flow of one such swimmer now contains a torque-dipole singularity in addition to the well-known force-dipolar singularity. We show that this head-and-flagella counter-rotation gives rise to clock-wise circling at no-slip walls just as observed in experiments of bacteria on surfaces. We discuss the scattering behavior of spermatozoa in a forest of cylindrical pillars, confirmed also by new experiments. Last, we show large scale and fast simulations of thousands of such swimmers that interact with each-other through direct collisions as well as through the fluid.