Fluctuating hydrodynamic interfaces: Theory and simulation

The hydrodynamics and statistical mechanics of fluctuating fluid interfaces, both in and out of equilibrium, are studied theoretically and by computer simulation. Theoretically, we show how uncorrelated stresses in the fluids give rise to a correlated force on the interface, i.e., how a Markovian hydrodynamic description with many degrees of freedom reduces to a non-Markovian description of the interface with fewer degrees of freedom. As a key part of this description, we obtain a fluctuation-dissipation theorem that relates the correlations in this thermal force to the hydrodynamic response function of the interface. Simulations are performed with a two-dimensional momentum-conserving lattice-gas model. Results show that an initially flat interface roughens in a manner that satisfies dynamical scaling. Specifically, the time-dependent root-mean-square width W(L, t) of an interface with an initial length L grows like L(1/2)f(t/L(3/2)), where f is a scaling function such that W(t) similar to t(1/3) at early times and W(L) similar to L(1/2) at late times. Except for a logarithmic correction in the static behavior of large-L simulations, both scaling laws are found to to be in good agreement with predictions based on the fluctuation-dissipation theorem. Also, as an independent validation of the simulation method, the equilibrium power spectrum of the interface height is computed and found to be well described by the theory.