Charge Fluctuations and Shear Stress of Thin Films

We consider the effects of lateral charge fluctuations on the linear shear response of thin films. These fluctuations break the in-plane symmetry of the system and at short enough times cause the interaction energy to depend on the relative positions of the top and bottom surfaces of the film. This gives rise to a shear stress which can be significant depending on the time scale of charge reequilibration and on the charge and thickness of the film. The results have implications for the shear of charged membranes as well as the shear and frictional properties of electrolytes between two charged surfaces.