An improved conditionally volume averaged viscoelastic two-phase model for simulation of transient droplet deformations under simple shear

In this work we simulate the transient deformation of a Newtonian droplet in a viscoelastic matrix subject to a simple shear flow. The viscoelastic two-phase model was derived in a former work by applying the technique of conditionally volume averaging and subsequent closure modeling (Habla et al., 2013). It was shown that the model requires a sufficient spatial resolution of the interfacial transition region in order to give proper results. As the original model was not capable of keeping the interface thickness constant when simulating problems involving moving interfaces, an intermediate step originally proposed by Olsson and Kreiss (2005) is adopted in this work in order to remedy this shortcoming. The intermediate step is validated by the simulation of a rotating cylinder and it is shown that this step can in fact fix this issue. The adapted model is then used to simulate transient droplet deformations carried out in 2D and 3D. In the 3D simulations we use an adaptive mesh refinement technique in order to guarantee a sufficient interface resolution while keeping the computational costs low. It is shown that the intermediate step keeps the interface thickness constant even in such a complex flow. The evolution of the Taylor deformation parameter is compared to the measurements of Sibillo et al. (2004) and the simulations of Yue et al. (2005) and Habla et al. (2011a) for three different Capillary numbers and finally the steady-state stress and pressure fields as well as the local flow-type parameter ξ are presented.