Non-Markov Model for Self-Propelling Droplets

Active droplets and particles make an experimentally-tractable model systems for autophoretic micro-swimmers that interact with their own and each other’s trails through the concentration gradient they leave behind. Here, a non-Markov model is derived to describe their collective motion. The model is shown to capture experimental features, such as the enhancement of diffusion as the fuel concentration is decreased. It also explains the paradoxical observation that the lower the microscopic diffusivity of the swimmers, the higher their effective diffusion coefficient at long times.