Universal Law for the Dispersal of Motile Microorganisms in Porous Media

Dispersal is essential to the plethora of motile microorganisms living in porous environments, yet how it relates to movement patterns and pore space structure remains largely unknown. Here we investigate numerically the long-time dispersal of a run-and-tumble microorganism that remains trapped at solid surfaces and escapes from them by tumbling. We find that dispersal and mean run time are connected by a universal relation, that applies for a variety of porous microstructures and swimming strategies. We explain how this generic dependence originates in the invariance of the mean free path with respect to the movement pattern, and we discuss the optimal strategy that maximizes dispersal. Finally, we extend our approach to microorganisms moving along the surface. Our results provide a general framework to quantify dispersal that works across the vast diversity of movement patterns and porous media.