Reverse Osmotic Effect in Active Matter

Spatially controlling the activity of self-propelling microswimmers has been proposed for a number of interesting applications such as directed transport, self-rectification, and patterning. We present a general theory to describe dilute suspensions of microswimmers with an abrupt spatial variation in their self-propelling or swim speed as well as their translational and rotational diffusivities. We find that the concentration of microswimmers is governed by the swim speed and modulated in amplitude by the diffusivities. The theory shows that the spatial variation in the swim speed generates a fluid pressure distribution that produces a reverse-osmotic flow: the suspending fluid spontaneously flows from regions of high concentration to low.