The behaviour of viscoplastic drops during formation and detachment from a capillary nozzle, free-fall, impact on a solid substrate and subsequent spreading are investigated experimentally by high-speed imaging. Drop dynamic behaviour is an integral component of many contemporary industrial processes ranging from fuelinjection systems in combustion engines to spray coating, agrochemical and pharmaceutical delivery, fire extinguishment and ink-jet printing. Yield-stress fluids are commonly used nowadays in products ranging from mayonnaise to hair-gel. It is hoped that through understanding the dynamics of viscoplastic fluids, additional spray applications can be developed that will help to advance and optimise industrial processes. Viscoplastic fluids exhibit shear-thinning behaviour when the applied stress exceeds a certain threshold value, called the yield-stress. Below this threshold however, the fluid behaves like an elastic solid. By comparing the behaviour of viscoplastic drops with both Newtonian and shear-thinning fluids, yield-stress is shown to be capable of altering detachment behaviour, drop shape during free-fall, impact morphology and the final sessile shape of drops after spreading. For drops attached to the end of a capillary tube, growth continues until a maximum supportable tensile stress is reached in the drop neck. After this critical point, drops become unstable and detach. The critical break-up behaviour of low yield-stress drops is found to be similar to those of Newtonian and shear-thinning fluids. Above a threshold value however, characterised in terms of the ratio between yield-stress magnitude and capillary pressure, yield-stress forces exceed surface tension forces and the maximum tensile stress achievable in the drop neck at critical stability is governed by the extensional yield-stress, established using the von Mises criterion. This threshold value can also be used to characterise equilibrium drop shapes during free-fall. Whereas Newtonian, shear-thinning and low yield-stress fluids form near spherical equilibrium drop shapes, fluids above a threshold value become increasingly more prolate as the yield-stress increases. Upon impact, viscoplastic drops can exhibit central peaks at the end of inertial spreading. The influence of yield-stress magnitude on impact behaviour is qualitatively established by measuring the size of these peaks. Peaks indicate that deformation during impact is localized and within a threshold radius, shear stresses will not be large enough to overcome the yield-stress, therefore fluid within this region will not deform from the drop shape prior to impact. After impact, spreading will be dependent on the surface energy. Again, the ratio of the yield-stress magnitude to the capillary pressure can be used to characterise the final sessile drop shape. Whilst the equilibrium contact angle of Newtonian, shear-thinning and low yield-stress drops is independent of the yield-stress magnitude, above a threshold value, contact angles vary as a function of yield-stress magnitude. Whilst the research presented in this thesis highlights how fluid yield-stress can influence drop dynamics, some results are only qualitative. To establish more quantitative results, computational fluid dynamics methods should be used to examine viscoplastic drop dynamics. This research should focus primarily on impact behaviour, an aspect that has not received much attention previously. Modelling shear-thinning and viscoplastic fluid behaviour can be achieved by incorporating the relevant rheological models into the flow equations and examining impact morphology using a volume of fluid method. Numerical results can then be directly compared with the experimental results. Useful further experimentation could examine the relaxation behaviour of diamagnetically levitated viscoplastic drops. The results from this work could provide further insight into what rheological model best describes viscoplastic behaviour for shear-stresses below the yield-point.

L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters