Nonlinear Brownian dynamics of interfacial fluctuations in a shear flow

Abstract

Using Brownian dynamics simulations, we investigate the effect of an external flow on the fluctuations of a liquid–liquid interface for a wide range of shear rates. Although the statistics is Gaussian at low shear, we observe a transition to a nonlinear phenomenology above a critical shear rate. In particular, we show that statistical properties at high forcing share striking similarities with Burgers turbulence. An energy criterion allows us to predict the onset of non-Gaussian statistics. It also provides a simple explanation for the development of shock singularities through the exchange of kinetic energy from regions with positive to negative gradients in the shear direction.