Dispensing of rheologically complex fluids: The map of misery

Rheological effects may complicate the dispensing of complex fluids, when compared to their Newtonian counterparts. In this work, fluids with tailored rheological properties have been studied using high-speed video-microscopy. The level of viscosity, the degree of shear thinning, and the elasticity have been varied independently. At low-flow rates, droplets are formed that pinch off. The drop volumes, breakup mechanisms, and times have been identified. At higher-flow rates, a continuous jet is observed, with the transition depending on the rheology of the dispensed fluid. The relevant nondimensional groups are the Ohnesorge, Deborah, and elasto-capillary number, for when viscosity, inertia, or elastic forces dominate flow. In each of these cases, the transition between dripping and jetting dispensing occurs, controlled by a critical Weber, capillary, and Weissenberg number, respectively. This set of six nondimensional groups can be used to construct an operating space and map out areas of potential problems