Dynamics of Newtonian and non -Newtonian drops and bridges

Dynamics of drops forming from capillaries and nozzles and that of stretching liquid bridges are not only fundamentally important scientific problems but they also lie at the heart of many applications including inkjet printing, biochip arraying, spray coating, filament-stretching rheometry, and gravure coating where the working fluid is often non-Newtonian. A major goal of this thesis is to develop accurate and efficient computational methods to predict the dynamics and breakup of drops and bridges of non-Newtonian liquids. The theoretical approach consists of Galerkin/finite element analysis of the full two-dimensional (2-d) set of equations and a one-dimensional (1-d) approximation based on slender jet theory governing the dynamics. A comparison of predictions made with the 1-d and 2-d algorithms in the case of Newtonian and shear-thinning liquid bridges is presented here for the first time and at the outset in order to establish when the 1-d theory is accurate. The thesis then goes on to tackle a number of increasingly more difficult situations using slender jet theory. The 1-d algorithm is used here for the first time to follow not only the creation of satellite droplets but whether they persist or get eliminated by merging with the primary drop. Unlike previous studies, this work also examines the effect of both simple and complex non-Newtonian rheology on the physics of interface rupture. First a generalized Newtonian fluid model accounting for shear thinning and strain hardening and then a more complex and fully viscoelastic fluid model that treats the polymer molecules as so-called FENE dumbbells are utilized. The 1-d algorithm is also utilized to put on firm theoretical footing the century-old drop weight method for measuring surface tension. Experimental observations based on high-speed digital imaging are utilized to motivate and support the theoretical studies. While such studies are important in their own right, they also point out deficiencies in existing theoretical models and aid in the development of a new technique for the measurement of extensional viscosity of viscoelastic fluids. A filament stretching rheometer based on a liquid bridge design is built here in order to probe extensional properties of polymer solutions