Active particles on curved surfaces: Equation of state, ratchets, and instabilities

Nikolai Nikola, Alexandre P. Solon, Yariv Kafri, Mehran Kardar, Julien Tailleur, Raphaël Voituriez

Published 2015-12-17Version 1

We study, from first principles, the pressure exerted by an active fluid of spherical particles on general surfaces in two dimensions. We show that, despite the non-uniform pressure along curved surfaces, an equation of state is recovered when a proper spatial averaging of the forces exerted on the wall is taken. This result holds even in the presence of pairwise interactions between particles or when asymmetric walls induce ratchet currents, which are accompanied by a spontaneous shear stress on the wall. For flexible obstacles, the pressure inhomogeneities lead to a modulational instability as well as to the spontaneous motion of short semi-flexible filaments.