A thermodynamically compliant model for the dynamics of a swarm of microswimmers

The effect of the concentration of swimmers in the dynamics of a swarm of diffusiophoretic microswimmers is analyzed. For that purpose, a Janus dumbbell model inspired by the nonequilibrium thermodynamics of multi-component fluids that undergo chemical reactions is used. One of the beads of the dumbbell is allowed to act as a catalyst for a chemical reaction between the reactants. The entropy balance for the model allows one to check that the entropy production rate stays positive for a given set of parameters [J. Chem. Phys. 152, 194902 (2020)]. The second law of thermodynamics shows that in the typical classification of microswimming mechanisms the Janus dumbbell is a pusher. The flow field produced by a periodic swarm of these pusher dumbbells is found by solving the Stokes equation. A Janus dumbbell in the swarm can swim up to seven times faster than when alone. This occurs in a swarm where the distance between dumbbells is about 3.3 times their length. However, at those higher dumbbell concentrations hydrodynamic interactions produce significant rotational velocities that, after some time of ballistic motion, can cause instabilities in the ordered structure of the swarm.