Editors: Will be set by the publisher SIMULATION OF SELF-PROPELLED CHEMOTACTIC BACTERIA IN A STOKES

Abstract. We present a method to simulate the motion of self-propelled rigid particles in a two-dimensional Stokesian fluid, taking into account chemotactic behaviour. Self-propulsion is modelled as a point force associated to each particle, placed at a certain distance from its gravity centre. The method for solving the fluid flow and the motion of the bacteria is based on a variational formulation on the whole domain, including fluid and particles: rigid motion is enforced by penalizing the strain rate tensor on the rigid domain, while incompressibility is treated by duality. This leads to a minimization problem over unconstrained functional spaces which can be easily implemented from any finite element Stokes solver. In order to ensure robustness, a projection algorithm is used to deal with contacts between particles. The particles are meant to represent bacteria of the Escherichia coli type, which interact with their chemical environment through consumption of nutrients and orientation in some favorable direction. Our model takes into account the interaction with oxygen. An advection-diffusion equation on the oxygen concentration is solved in the fluid domain, with a source term accounting for oxygen consumption by the bacteria. In addition, self-propulsion is deactivated for those particles which cannot consume enough oxygen. Finally, the model includes random changes in the orientation of the individual bacteria, with a frequency that depends on the surrounding oxygen concentration, i