Stretching liquid flowsjets, drops and liquid bridges. Experiments and one-dimensional modelling of linear and non-linear phenomena in laminar capillary flows

Resumen

The present PhD Thesis deals with several linear and nonlinear phenomena present in extensional laminar capillary flows, such as jets, drops and liquid bridges. When dispensing liquid from a vertical injector in the presence of gravity, drops grow at the outlet until the surface tension forces can no longer balance their weight and the pinch-off occurs. This dripping regime does not exists above a critical flow rate, at which an abrupt transition to jetting takes place. The parameters governing this transition are the liquid properties, the injector radius and the liquid flow rate. In this Thesis, experiments and global linear stability analysis are employed to obtain the critical flow rate below which a liquid jet stretched by gravity is no longer steady. The theoretical description, based on the one-dimensional mass and momentum equations retaining the exact expression of the interfacial curvature, accurately predicts the onset of jet self-excited oscillations experimentally observed for wide ranges of liquid viscosity and nozzle diameter. The analysis reveals the essential stabilizing role played by the axial curvature of the jet, being this effect especially relevant for injectors with a large enough diameter. The results obtained allow to conclude that, surprisingly, the size of the steady threads produced at a given distance from the exit can be reduced by increasing the nozzle diameter. Detailed descriptions of the rich dynamics of both the dripping regime and the transition to jetting are available in the literature, but only for small injector sizes. Therefore, new experiments on the dripping dynamics and jetting transition for a wide range of both liquid viscosities and injector diameters are presented in this work. The results reveal the existence of new regimes of dripping, which had not been observed before. In addition, the hysteresis present in the dripping-jetting transition, previously measured only for the case of water, is quantified for a liquid of higher viscosity for the first time. The detailed characterization of the necking and pinching dynamics of drops is often studied through the thinning proccess of an axially stretched liquid bridge. In this context, recent works on the capillary break-up of particulate suspensions show how the presence of particles modifies the expected thinning behaviour of a liquid bridge. Nevertheless, in this kind of experiments the final stage close to the pinch-off is not well understood yet. In this dissertation, the different thinning velocities present near the pinch-off of particle suspensions in a Newtonian matrix are modelled. To that end, the liquid trapped between two end particles of finite diameter is considered as a stretching Newtonian liquid bridge with a non-uniform prescribed motion of the boundaries. The model, based on the one-dimensional mass and momentum conservation equations, shows quantitative agreement with the experimental thinning and final pinching behavior of suspending medium between individually monitored particles in the suspension. Comparison of the model predictions with experiments of suspensions with different particle sizes, volume fractions and matrix viscosities confirms that the developed model constitutes an excellent tool to improve the understanding of the detailed pinch-off mechanism of particle suspensions and, importantly, allows to conclude that the description of the final stages does not require non-Newtonian modelling.