Casimir stresses in active nematic films

Abhik Basu,Frank Jülicher,Jean-Francois Joanny,Jacques Prost

doi:10.1088/1367-2630/ab5628

Abstract

We calculate the Casimir stresses in a thin layer of active fluid with nematic order. By using a stochastic hydrodynamic approach for an active fluid layer of finite thickness L, we generalize the Casimir stress for nematic liquid crystals in thermal equilibrium to active systems. We show that the active Casimir stress differs significantly from its equilibrium counterpart. For contractile activity, the active Casimir stress, although attractive like its equilibrium counterpart, diverges logarithmically as L approaches a threshold of the spontaneous flow instability from below. In contrast, for small extensile activity, it is repulsive, has no divergence at any L and has a scaling with L different from its equilibrium counterpart.

Highlights

It is well-known that the zero-point energy of the electromagnetic field inside a cavity bounded by conducting walls is formally diverging, its variation upon displacements of the boundaries remains finite
In nematic liquid crystals confined between two parallel plates, the thermal fluctuations of the director field that describes the nematic order, play the role of the electromagnetic fluctuations in the electromagnetic Casimir effect
We study Casimir forces using a stochastically driven coarse-grained hydrodynamic approach for active fluids [9,10,11], with a nematic order, described by a unit vector polarization field pα, α = x, y, z

Summary

Casimir stresses in active nematic films

Abhik Basu1,3, Jean-Francois Joanny2,4, Frank Julicher3, Jacques Prost2 1Condensed Matter Physics Division, Saha Institute of Nuclear Physics, 1/AF, Bidhannagar, Calcutta 700 064, India, 2Physicochimie Curie (CNRS-UMR168), Institut Curie, Section de Recherche, 26 rue d’Ulm 75248 Paris Cedex 05 France, 3Max-Planck-Institut fur Physik komplexer Systeme, Nothnitzerstr. 38, 01187 Dresden, Germany, 4E.S.P.C.I, 10 rue Vauquelin, 75231 Paris Cedex 05, France (Dated: May 8, 2019)

INTRODUCTION

ACTIVE CASIMIR STRESS

STEAD STATE STRESSES IN A FLUCTUATING ACTIVE FLUID

We first consider the contribution η

Pαz nπ L hnz

This is of the form δCA