Fully implicit interface tracking for a viscous drop under simple shear

Abstract

In this article we present a novel 3D implicit interface tracking method for sharp interfaces with interfacial tension in the creeping flow regime, employing the finite element method. The interface nodes are allowed to move only in the normal direction and thus remeshing can be avoided, most of the times. The implicit method allows us to overcome certain time step limitations imposed by the mesh capillary time. To validate our method, we use a fairly simple and very well understood problem of a single viscous drop suspended in a viscous matrix that deforms under an applied shear rate. This problem was first studied by Taylor [1] and has been extensively reviewed by Rallison [2] and Stone [3]. The second moment of inertia tensor was used to compute the deformation parameter D and the inclination angle θ and the results are compared to the theory for small deformations of Taylor [1].