Shear rheology of concentrated emulsions at finite inertia: a numerical study
University of Delaware
The dynamics and rheology of an emulsion of viscous drops in shear flow is investigated computationally. The simulations are performed using a three-dimensional front tracking method. An emulsion gives rise to an effective non-Newtonian rheology with finite normal stress differences and shear-dependent viscosity. Previous estimates about the bulk properties of emulsions were limited to Stokes conditions under which a positive first normal stress difference and a negative second normal stress difference are predicted. However, the introduction of finite inertia significantly modifies the behaviour of emulsions. The normal stress differences change sign and the emulsion shows a shear-thickening behaviour with inertia. Computed rheological properties (effective shear viscosity and first and second normal stress differences) in conditions close to Stokes limit match well with the existing theoretical and simulated results. The first component of the rheology arising from the interfacial stresses at the drop surface is investigated as functions of particle Reynolds number, capillary number and volume fraction. The sign change is caused by the increase in drop inclination in presence of inertia, which in turn directly affects interfacial stresses due to drops. Increasing volume fraction or capillary numbers increases the critical Reynolds numbers for sign reversals due to increasing alignment of the drops with the flow directions. The Reynolds stresses which form the second component of the stress formulation are also considered in detail. The primary components of the Reynolds stress showed a simple scaling with Reynolds number for moderate values of inertia. They showed a non-linear increase at larger values of Reynolds number. A comparison of the estimated effective viscosity with an established empirical relation is also presented. Presence of finite surface tension results in a characteristic stress relaxation time scale for emulsions. This is investigated for both dilute and concentrated systems and the results are verified against the standard theoretical expressions. Finally, to enhance the capabilities of the current computational method to handle extremely low Reynolds number flows, a parallel version of the Alternate Direction Implicit method is implemented.