Equilibrium and non-equilibrium dynamics of the dilute lamellar phase

A model for the dynamics of the sterically stabilized dilute lamellar phase is constructed and studied. The model consists of a stack of flexible fluid sheets, with excluded volume, separated by macroscopic layers of solvent. The dynamics of small fluctuations of the sheets about their mean positions is found to have two distinct short-wavelength regimes in which the frequency ω depends on the wavenumber q in an unusual manner. One is a single-membrane Zimm mode, ω ≈ −iq3, while the other is a “red-blood-cell mode”, ω ≈ −iq6. These modes give rise to fluctuation corrections for the viscosities of the system, going as ω−13 and ω−23, respectively. In addition, it is shown that a sufficiently rapid shear flow with velocity and gradient in the plane of the layers causes a transition into a state where regions of reduced layer spacing co-exist with regions devoid of any layer material. The critical shear-rate for this transition should go as (layer spacing)−3. Possible experimental tests of these predictions are discussed.