Effects of micro-inertia on average normal stress differences of a concentrated emulsion

A viscous emulsion of drops typically experiences a positive first normal stress difference and a negative second normal stress difference in shear. However, our group has shown that small amount of particle inertia can change their signs (Li & Sarkar 2005, J. Rheol., 49, 1377). The result stems from the inertia induced increase in drop inclination angle. We have performed direct numerical simulation to investigate the phenomenon both in dilute limit and moderate concentration (5-27% volume fraction). The computed rheological properties (effective shear viscosity and first and second normal stress differences) in the Stokes limit match well with previous theoretical (Choi–Schowalter in the dilute limit) and simulated results (for concentrated systems) using the boundary element method. The critical Reynolds number for sign reversal increases with concentration and can be explained by relating it to drop-drop interactions and specifically to the contact pair-distribution function. The functional dependence of excess stresses with Reynolds number, capillary number, viscosity mismatch and volume fraction will be described.