Sheared capillary waves on nanometer scales

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In bulk fluids hydrodynamic Navier-Stokes equations are proven to be valid down to the nanometer scale. However, at interfaces it was shown recently that the interplay of substrate potentials and thermal noise can lead to qualitative different behaviour on laterally much larger scales up to microns. Based on a stochastic version of the hydrodynamic equations this proposal aims at the theoretical modelling of fluid flow at interfaces, where recent experiments indicate an influence of thermal noise on fluid flow: (i) droplet coalescence and interfacial flow in sheared colloidal dispersions; (ii) capillary waves on a nanometer scale; (iii) fluid flow in thin liquid films. We will apply non-linear stochastic hydrodynamic equations and time-dependent density functional theory, in combinations with geometric techniques such as normal coordinates. We expect to elucidate (i) the role of thermal capillary waves on the coalescence event; (ii) the dependence of dispersion relations and damping factors on molecular interactions; (iii) the discrepancies between experiments and simulations - discovered recently in thin film flow.