Dynamical coarse-graining of highly fluctuating membranes under shear flow

Abstract

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.

Rheology of Giant Vesicles: A Micropipette Study

“…Also, our findings are consistent with a linear dependence on shear rate of the relative excess area, different from the quadratic predictions for steady shear flow [17]. In related membrane systems such as smectic lyotropics and sponge phases, suppression of fluctuations has been experimentally reported [18] and theoretically discussed within the framework of phase transitions, as recently reviewed by Marlow and Olmsted [19,20]. For ordered stacks, these effects depend on experimental conditions such as the orientation with respect to the flow or flow gradient directions, or the details of the coupling between hydrodynamic flow and membrane deformation, but share a common feature: fluctuations with average lifetimes larger than the typical shear rate are convected by the flow and effectively suppressed from the fluctuation spectrum.…”

Nonequilibrium fluctuations of an interface under shear

“…Note that equations similar to Eq. (9) have been suggested in the context of soft surfaces under shear (see for instance [25][26][27]). As a matter of fact, it belongs to the general class of the Kardar-Parisi-Zhang equation [30] whose derivation is usually based on phenomenological grounds.…”

“…At this point, it should be mentioned that corrections similar to Eq. ( 9) have been suggested in the context of sheared smectic phases (see [25] and references therein), or in the description of coarsening under shear [26,27]. The argument commonly invoked is the following.…”

Block Copolymers Under Shear Flow

“…Effect of flow on highly fluctuating many-component layered surfactants (or membranes) was thoroughly studied in a theoretical work by Marlow and Olmsted. [85] They considered the flow disturbance of the balance of layer spacing governed by the interplay between the long-range steric interaction, known as Helfrich interaction, and the bending elasticity of the bilayers, and took into account the flow perturbation of the layer microstructure. They demonstrated that flow induces the dynamical suppression of fluctuations that resembles a wave-vector dependent tension.…”