Hydrodynamics of fluid membranes
We derive the complete covariant, stochastic hydrodynamical equations governing the low frequency and the long wavelength hydrodynamics of fluid membranes. We first use these equations to study how membrane dynamics renormalizes under removal of high wave number degrees of freedom. The complications of this problem in membrane systems are usually not encountered by other stochastic models. We find that even the equilibrium distribution has to be corrected by an extra factor associated with gauge fixing and the compensation for mis-counting degrees of freedom for different configurations of the membrane. This extra factor, with asymmetric high wave number characteristics, modifies the average value of our noise sources and directly affects the dynamical calculations. Besides, the nonlinear dependence of nondissipative couplings and dissipative coefficients on the field variables leads to additional difficulties in this problem. We investigate the statistical properties of our stochastic equations by reformulating them in terms of Poisson brackets. In this derivation, a particular parametrization needs to be specified due to the covariance of our equations. We then derive the Fokker-Planck equation and determine the statistics of the noise sources that ensures that probability distribution decays to the equilibrium distribution at long times. We also solve the two simplified models, the membrane generalization of the Rouse and Zimm models. We find the nontrivial renormalization of the dynamic coefficients in the Rouse model. Finally, we apply our hydrodynamical equations for fluid membranes to study lamellar lyotropic smectics. We predict the new modes at the length scales that cannot be reached by the hydrodynamics of two-component smectic.
Cai, Weicheng, "Hydrodynamics of fluid membranes" (1995). Dissertations available from ProQuest. AAI9543058.