We study the effect of shear flow on the entropic Helfrich interaction in lyotropic surfactant smectic fluids. Arguing that flow induces an effective anisotropic surface tension in bilayers due to a combination of intermonolayer friction, bilayer collisions and convection, we calculate the reduction in fluctuations and hence the renormalised change in effective compression modulus and steady-state layer spacing. We demonstrate that non-permeable or slowly permeating membranes can be susceptible to an undulatory instability of the Helfrich-Hurault type, and speculate that such an instability could be one source of a transition to multilamellar vesicles.

The effect of strong shear flow on highly fluctuating lamellar systems stabilized by intermembrane collisions via the Helfrich interaction is studied. Advection enters the microscopic equation of motion for a single membrane via a nonlinear coupling. Upon coarse-graining the theory for a single bilayer up to the length scale of the collision length, at which a hydrodynamic description applies, an additional dynamical coupling is generated which is of the form of a wave-vector-dependent tension that is nonlinear in the applied shear rate. This new term has consequences for the effects of strong flow on the stability and dynamics of lamellar surfactant phases.