Reverse osmotic effect in active matter

In nonequilibrium active matter systems, a spatial variation in activity can lead to a spatial variation in concentration of active particles satisfying, at steady state, the condition nU = const [Schnitzer, Phys. Rev. E 48, 2553 (1993); Tailleur and Cates, Phys. Rev. Lett. 100, 218103 (2008)], where n is the number density and U is the active (swim) speed. We show that this condition holds even when the variation is abrupt and when thermal Brownian motion is present provided that the Péclet number is large. This spatial variation in swim speed and concentration produces a fluid pressure distribution that drives a reverse osmotic flow—fluid flows from regions of high concentration to low.