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Interfacial roughening denotes the nonequilibrium process by which aninitially flat interface reaches its equilibrium state, characterized by thepresence of thermally excited capillary waves. Roughening of fluid interfaceshas been first analyzed by Flekkoy and Rothman [Phys. Rev. Lett. 75, 260(1995)], where the dynamic scaling exponents in the weakly damped case in twodimensions were found to agree with the Kardar-Parisi-Zhang universality class.We extend this work by taking into account also the strong-damping regime andperform extensive fluctuating hydrodynamics simulations in two dimensions usingthe Lattice Boltzmann method. We show that the dynamic scaling behavior isdifferent in the weakly and strongly damped case.

Interfacial roughening in non-ideal fluids: Dynamic scaling in the weak- and strong-damping regime