Modeling and simulation of conditionally volume averaged viscoelastic two-phase flows

Conditional volume averaging is used to develop a model capable of simulating two-phase flows of viscoelastic fluids with surface tension effects. The study is started with the single-phase mass and momentum balances, which are subsequently conditionally volume averaged. In doing so, we arrive at a set of equations having unclosed interfacial terms, for which closure relations for viscoelastic fluids are presented. The resulting equations possess a structure similar to the single-phase equations; however, separate conservation equations are solved for each phase. As a result, each phase has its own pressure and velocity over the entire domain. Next, our numerical implementation is briefly outlined. We find that a Poiseuille single-phase flow is predicted correctly. The closure terms are examined by considering a two-phase shearing flow and a quiescient cylinder with surface tension. A convergence analysis is performed for a steady stratified two-phase flow with both phases being viscoelastic.