Phase Distribution in a Sheared High-Viscosity Two-Fluid Immiscible Mixture*

Mixing immiscible fluids where the volume fraction of one phase is much lower than for the other phase usually results in a mixture where the low volume fraction phase consists of drops or bubbles dispersed in a contiguous phase. When the volume fractions are comparable, however, the structure of the phase boundary is much more complex, often resulting in a co-continuous mixture. Understanding the structure of a mixture of immiscible fluids is important for many reasons, including the formation of polymer mixtures, which motivates the present study. The effect of volume fraction on the mixing and phase distribution in a sheared high viscosity immiscible mixture of two Newtonian fluids is examined by fully resolved numerical simulations. The densities of the phases are the same, but one is more viscous than the other. The results show that when the volume fraction of the phases is different, the low-volume fraction phase consists of drops dispersed in the high-volume fraction phase, but when the volume fraction of the phases are the same, the distribution is co-continuous. We show how the various measures of the mixture change with volume fraction and viscosity contrast. Preliminary results for more complex non-Newtonian material models are also discussed.