Collective motion of torque-dipolar micro-swimmers

We present a model and simulations for micro-swimmers that take 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. The linear analysis of the coarse-grained model shows an instability for a range of parameters, which we summarise in a phase diagram. Lastly, we show large-scale simulations of torque-dipolar micro-swimmers and illustrate the collective behavior in the regions of parameter space indicated by the stability analysis.