Modeling and simulation of active suspensions containing large numbers of interacting micro-swimmers

• Fast numerical method to compute the colonial dynamics of micro-swimmers.
• Includes long-range interactions and short-range steric effects between swimmers.
• The methodology uses the immersed boundary framework.
• Can efficiently simulate many thousands of interacting motile particles in 3D.
• Can use the method to study many biological and physical phenomena.

We present a mathematical model and simulation method to compute the colonial dynamics of micro-swimmers that interact directly and through the fluid they are suspended in. The model uses the stress generated by each self-motile particle for long-range interactions and includes short-range steric effects between particles. The time-step computational cost is O(N logN + M), with N the total number of mesh points, and M the number of swimmers. This fast method enables us to efficiently simulate many thousands of interacting self-propelling particles in three dimensions and with background flows. We show examples of collective behavior in suspensions of “pusher” and “puller” micro-swimmers.