Using inertia-viscous stress-balances to model the mid-filament dynamics of capillary-thinning of Newtonian and non-Newtonian liquid bridges

The behaviour of complex fluids can be investigated by subjecting them to controlled rheometric flows such as extensional flow. A uniaxial extensional flow is generated at the necking plane of liquid filaments due to surface tension. Simple stress balances are often used to model capillary thinning dynamics at the necking plane, and extract the extensional viscosity of the sample fluid. Previous modelling studies have focussed on liquids where either viscous or inertial effects are dominant. Experimental observations on the other hand are obtained where effects of viscosity and inertia are both important. The failure to account for both effects simultaneously can cause discrepancies in interpreting experimental data. Here a stress-balance that simultaneously incorporates both viscous and inertial effects is used to predict the evolution of the mid-plane radius as a function of time in capillary thinning experiments. The stress-balance is extended to include non-Newtonian stresses, and is used to study the dynamics of slender filaments of polymer solutions and suspensions of motile microbes. The results of modelling the non-Newtonian fluids are used with new micro-structure based constitutive models for non-Newtonian stresses in extensional flow.