Direct numerical simulations of droplet emulsions in sliding bi-periodic frames using the level-set method

We present a direct numerical simulation technique for droplet emulsions of Newtonian–Newtonian system in simple shear flow. The Lees–Edwards type boundary condition has been incorporated with the sliding bi-periodic frame of Hwang et al. [W.R. Hwang, M.A. Hulsen, H.E.H. Meijer, Direct simulation of particle suspensions in sliding bi-periodic frames, J. Comput. Phys. 194 (2004) 742] for the continuous flow field problem and the level-set method with the continuous surface stress (CSS) formulation has been used for accurate description of the sharp interfaces. Based on the standard velocity–pressure formulation of the finite-element method, we use the mortar element method for the implementation of the sliding periodicity and employ the discontinuous Galerkin (DG) method for the stabilization of the interface advection equation. We present numerical results on the morphological development for a single, two and multiple drops in sliding bi-periodic frames for the demonstration of the feasibility of the present method in investigation of the relationship between the morphology and the bulk material responses such as the shear viscosity and the first normal stress difference.