Hydrodynamic collision between a microswimmer and a passive particle in a micro-channel

Microswimmers interacting with passive particles in confinement are common in many systems, e.g., spermatozoa encountering other cells or debris in the female reproductive tract or active particles interacting with polymers and tracers in microfluidic channels. The behaviour of such systems is driven by simultaneous, three way hydrodynamic interactions between the microswimmer, the passive particle and the microchannel walls. Therefore, in this work we investigate the hydrodynamic collision between a model microswimmer and a passive particle using three different methods: (i) the point particle approach, (ii) analytical calculations based on method of reflections, and (iii) lattice Boltzmann numerical simulations. We show that the hydrodynamic collision is essentially an asymmetric process - the trajectory of the microswimmer is altered only in an intermediate stage while the passive particle undergoes a three stage displacement with a net displacement towards or away from the microchannel walls. The path of the passive particle is a simple consequence of the velocity field generated by the swimmer: an open triangle in bulk fluid and a loop-like trajectory in confinement. We demonstrate the generality of our findings and conclude that the net displacement of the passive particle due to collision may be capitalised in order to develop applications such as size separation of colloidal particles and deposition of particles in the microchannel interiors.