Unsteady deformations of a free liquid surface caused by radiation pressure

Abstract

We present an analytical model of the time-dependent, small-amplitude deformation of a free liquid surface caused by a spatially localized, axisymmetric, pulsed or continuous, acoustic or electromagnetic radiation pressure exerted on the surface. By exactly solving the unsteady Stokes equation, we predict the surface dynamics in all dynamic regimes, namely inertial, intermediate and strongly damped regimes. We demonstrate the validity of this model in all dynamic regimes by comparing its prediction to experiments consisting of optically measuring the time-dependent curvature of the tip of a hump created at a liquid surface by the radiation pressure of an acoustic pulse. Finally, we present a numerical scheme simulating the behaviour of a fluid–fluid interface subjected to a time-dependent radiation pressure and show its accuracy by comparing the numerical predictions with the analytical model in the intermediate and strongly damped regimes.