Active versus Passive Hard Disks against a Membrane: Mechanical Pressure and Instability

G. Junot,¹ G. Briand,¹ R. Ledesma-Alonso,^1,2 and O. Dauchot^1
1UMR Gulliver 7083 CNRS, ESPCI ParisTech, PSL Research University, 10 rue Vauquelin, 75005 Paris, France
²CONACYT—Universidad de Quintana Roo, Boulevard Bahía s/n, Chetumal, 77019 Quintana Roo, México

Abstract
We experimentally study the mechanical pressure exerted by a set of respectively passive isotropic and self-propelled polar disks onto two different flexible unidimensional membranes. In the case of the isotropic disks, the mechanical pressure, inferred from the shape of themembrane, is identical for both membranes and follows the equilibrium equation of state for hard disks. On the contrary, for the self-propelled disks, the mechanical pressure strongly depends on the membrane in use and thus is not a state variable. When selfpropelled disks are present on both sides of the membrane, we observe an instability of the membrane akin to the one predicted theoretically for active Brownian particles against a soft wall. In that case, the integrated mechanical pressure difference across the membrane cannot be computed from the sole knowledge of the packing fractions on both sides, further evidence of the absence of an equation of state.