2D Thin-Film Flow of a Non-Newtonian Fluid Between Elastic Boundaries

Abstract

This thesis presents a numerical technique to optimize the efficacy of anti-HIV vaginal drug delivery systems known as microbicides. A microbicide is a topical, prophylactic agent that acts as a barrier from transmission of HIV and other sexually transmitted infections (STIs). A microbicidal formulation consists of an anti-HIV active ingredient within a drug delivery vehicle such as a polymeric gel. For a microbicide to be effective it must be able to perform its function by adhering to the epithelial surface. The effectiveness of the gel depends on the gel's rheological properties as well as the vaginal tissue properties, vaginal geometry, external forces like gravity and other factors like dilution, etc. As a next step in the design of a microbicidal delivery vehicle, this thesis primarily focuses on the combined effect of gravity, tissue elasticity, and rheological properties and their influence on the gel distribution. A 2D numerical model for the flow a non-Newtonian fluid between elastic boundaries is presented. The following models are considered: * Power-law fluid model with linear elastic boundary condition, * Ellis fluid model with linear elastic boundary condition, * Power-law fluid model with non-linear elastic boundary condition. The equations describing the evolution of the gel shape were solved numerically using implicit finite difference method along with Newton's search method for the non-linear system of equations. A parametric and sensitivity analysis of coating behavior to changes in non-Newtonian fluid properties for different elasticities combined with gravity was presented. The results of the parametric study showed that the combined effect of tissue elasticity and gravitational forces greatly influenced the gel coating. A higher tissue elasticity resulted in greater spreading length, faster spreading rates and dominance over gravitational force. The gel consistency had greater impact on gel coating compared to shear-thinning index; a higher consistency resulted in slower spreading rates. The shear-thinning index is relatively of less importance; however, it may be important for long spreading times. Sensitivity analysis for 10% changes in consistency and shear-thinning index showed high sensitivity for synergistic change in both parameters. The sensitivity of spreading length for changes in consistency were greater compared to changes in shear-thinning index. In conclusion, the relative importance of each parameter has been determined. These results will ultimately help in determining optimal gel properties for microbicidal gel in groups of women with different tissue elasticities. Thus, this work will help in designing better microbicides.