Numerical simulation of drop impact on a liquid-liquid interface with a multiple marker front-capturing method

The gravity-driven motion of a droplet impacting on a liquid–liquid interface is studied. The full Navier–Stokes equations are solved on a fixed, uniform grid using a finite difference/front-capturing method. For the representation of fluid–fluid interfaces, a coupled Level-Set/Volume-Of-Fluid method [M. Sussman, E.G. Puckett, A coupled Level-Set and Volume-of-Fluid method for computing 3D and axisymmetric incompressible two-phase flows, J. Comp. Phys. 162 (2000) 301–337] is used, in which we introduce the novel approach of describing separate interfaces with different marker functions. As a consequence, we prevent numerical coalescence of the droplet and the liquid–liquid interface without excessive (local) grid refinement. To validate our method, numerical simulations of the drop impact event are compared with experiments [Z. Mohamed-Kassim, E.K. Longmire, Drop impact on a liquid–liquid interface, Phys. Fluids 15 (2003) 3263–3273]. Furthermore, a comparison is made with the numerical results of [A. Esmaeeli, G. Tryggvason, Direct numerical simulations of bubbly flows. Part 2. Moderate Reynolds number arrays, J. Fluid Mech. 385 (1999) 325–358] for an array of rising bubbles. The investigation shows that the multiple marker approach successfully prevents numerical coalescence of interfaces and adequately captures the effect of surface tension. 2009 Elsevier Inc. All rights reserved.