Fluid dynamics of non-Newtonian thin films: Squeezing flow, film rupture and contact line instability

HIV is a global pandemic that affects millions of lives every year. Vaginal gel formulation has been touted as an effective strategy to fight sexually transmitted diseases (STD) by acting as a physical barrier, and also by delivering active pharmaceutical agents at the intended location. Microbicidal gels can act as a low cost, self-administered method to prevent HIV and other STD's. The overall long term goal of our research group is to rationally design these delivery vehicles by optimizing their rheological properties for their specific applications. In that regard, there has been an ongoing effort in our group to mathematically model the flow of thin films in order to understand the dynamics and stability of these films, so that we can understand/predict the behavior of the gel during their applications. In my dissertation, I have used thin film lubrication theory to develop mathematical models of (a) boundary elasticity-driven squeezing flow of yield stress fluids, (b) rupture/dewetting of Ellis-type shear-thinning liquid films, and (c) contact line instability of Ellis-type shear-thinning liquid films. Our investigations showed that yield stress can improve the control over the spreading characteristics of liquids, and also possibly aid in the retention of liquid in place. We have demonstrated an optimization framework that can be used to estimate the rheological properties of microbicidal gels for different combinations of tissue elasticity, initial bolus volume, and deployment time. Numerical models of the rupture and dewetting of Ellis-type thin films showed that the shear-thinning rheology could accelerate the rupture process which could create dry spots earlier than Newtonian fluids. Dry spots are usually unwanted for both functional and aesthetic purposes. Numerical models of contact line instability have shown that the shear-thinning rheology increases the finger growth rate for vertical inclines but shows a more complex behavior for flatter inclines. For flatter inclines, the most unstable mode shifts to larger wavelength but the finger growth rate is dependent on the degree of shear-thinning. Fluids with low degree of shear-thinning suppress the fingering but fluids with the highest degree of shear-thinning show an increased growth rate despite the shift in the most unstable mode to larger wavelength. This behavior possibly occurs due to the decrease of apparent viscosity far beyond contact line, especially for fluids with a narrow range for the Newtonian plateau. Lubrication theory can be applied in the modeling of numerous biological and industrial applications. The models developed here are not limited to any specific application, and can easily be modified to study other applications that involves non-Newtonian fluids.