A Level Set method for capturing interface deformation in immiscible stratified fluids

Abstract

The interface behavior between two stratified fluids showing a large difference in viscosity was investigated numerically. A three-dimensional numerical method for the simulation of the deformation of the interface in a stirred vessel is presented. In such a systems, the interface is distorted by hydrodynamic stresses and pressure changes. Different regimens of agitation were employed to explore the response of the interface, where the boundary between them is preserved and break up is avoided. The numerical scheme presented explicitly solves the Navier–Stokes equations for an incompressible fluid whilst the convection-diffusion part is treated through a Level-Set method along a moving and deforming interface. The spatial discretization was carried out by implementing a Runge–Kutta method in a second order scheme, along as a Weighted Essentially Non-Oscillatory approach. In addition, surface tension effects were included to observe its influence on the interface response. It was found that due the effect of inertia the interface is reshaped towards the vertical direction, in this process the interface experiences high-pressure gradients, which drag the interface in the upward direction. The numerical methodology was validated by comparison of simulations and experimental measurements of an interface deforming at two low Reynolds number. The results shown that the algorithm is able to resolve accurately the detailed features of the distorted fluid interfaces.