Fluctuations of elastic interfaces in fluids: Theory, lattice-Boltzmann model, and simulation

We study the dynamics of elastic interfaces-membranes-immersed in thermally excited fluids. The work contains three components: the development of a numerical method, a purely theoretical approach, and numerical simulation. In developing a numerical method, we first discuss the dynamical coupling between the interface and the surrounding fluids. An argument is then presented that generalizes the single-relaxation-time lattice-Boltzmann method for the simulation of hydrodynamic interfaces to include the elastic properties of the boundary. The implementation of this method is outlined and it is tested by simulating the static behavior of spherical bubbles and the dynamics of bending waves. By means of the fluctuation-dissipation theorem we recover analytically the equilibrium frequency power spectrum of thermally fluctuating membranes and the correlation function of the excitations. Also, the nonequilibrium scaling properties of the membrane roughening are deduced, leading us to formulate a scaling law describing the interface growth, W-2(L,t) =L-3 g(t/L-5/2), where W, L, and t are the width of the interface, the linear size of the system, and the time, respectively, and g is a scaling function. Finally, the phenomenology of thermally fluctuating membranes is simulated and the frequency power spectrum is recovered, confirming the decay of the correlation function of the fluctuations. As a further numerical study of fluctuating elastic interfaces, the nonequilibrium regime is reproduced by initializing the system as an interface immersed in thermally preexcited fluids.