Numerical Simulation of Non-Newtonian Multiphase Flows

A finite element code based on the level-set and distributed Lagrange multiplier/fictitious domain methods is developed for simulating multiphase flows in two- and three-dimensions. The method is used to study the flow of solid particles and gas bubbles in liquids. For simulating the motion of rigid particles suspended in Newtonian and viscoelastic liquids we use the distributed Lagrange multiplier/fictitious domain method (DLM). The two-fluid interface in our code is tracked by the level-set method. Using our code we have studied deformation of drops in simple shear and pressure driven flows and that of bubbles in gravity driven flows over a wide range of dimensionless capillary (Ca) and Deborah numbers (De). For a Newtonian bubble rising in a quiescent viscoelastic liquid we find that there are limiting values of the parameters De and Ca, above which the bubble assumes a characteristic shape with a cusp-like trailing edge. In a pressure driven flow the drop is stretched such that its front, which is closer to the channel center, remains round, and the trailing edge, which is closer to the channel wall, becomes sharp. These numerical results are in agreement with the experimental observations.

Top of Page