Computational rheology of a non-Newtonian fluid dripping onto a Substrate*

The Dripping-on-Substrate (DoS) technique is a conceptually-simple, but fluid dynamically complex, probe of the extensional rheology of low-viscosity, non-Newtonian fluids. In this technique, a single drop is left to flow from a syringe pump onto a partially-wettable solid substrate and stimulates the capillary-driven thinning of a liquid bridge. Monitoring the filament thinning process allows the extensional viscosity and relaxation time of the sample to be measured with a high degree of accuracy. Here, we present a computational rheology approach for understanding and optimising the operation of DoS, using an axisymmetric volume-of-fluid approach. The numerical simulations are performed with the open-source Eulerian code Basilisk in which the interface is captured accurately via an adaptively-refined grid. First, we study the effect of gravity and solid substrate wettability on the filament thinning and pinch-off. Furthermore, we examine the role of viscosity on the transition from initial inertia-capillary dynamics to the characteristic nonlinear elasto-capillary thinning of a viscoelastic fluid. We also investigate the role of polymer finite extensibility for weakly-elastic fluids and propose a fitting methodology based on the analytical solution for FENE-P fluids developed by Wagner et al. (2015) for improved determination of the relaxation time of the test fluid. Finally, we explore via simulations of DoS flow configurations the changes in the filament thinning profiles and pinch-off dynamics for strongly shear-thinning fluids such as Xanthan gum solutions.