The collective dynamics of self-propelled particles

We have proposed a method for the dynamic simulation of a collection of self-propelled particles in a viscous Newtonian fluid. We restrict attention to particles whose size and velocity are small enough that the fluid motion is in the creeping flow regime. We have proposed a simple model for a self-propelled particle, and extended the Stokesian Dynamics method to conduct dynamic simulations of a collection of such particles. In our description, each particle is treated as a sphere with an orientation vector $\te{p}$, whose locomotion is driven by the action of a force dipole at a point slightly displaced from its centre. In isolation, a self-propelled particle moves at a constant speed in the direction of $\te{p}$. When it coexists with many such particles, its hydrodynamic interaction with the other particles alters its velocity and, more importantly, its orientation. As a result, the motion of the particle is chaotic. Our simulations are not restricted to low particle concentration, as we implement the full hydrodynamic interactions between the particles, but we restrict the motion of particles to two dimensions to reduce computation. We report the statistical properties of a suspension of self-propelled particles, such as the distribution of particle velocity, the pair correlation function and the orientation correlation function, for a range of the particle concentration.