| A microbicide gel is under development to prevent HIV transmission during sexual intercourse. In order to fulfill the desired function of a microbicide gel, it is important that it coats the entire vaginal wall. Fluid mechanics can contribute to the analysis of the flow of a microbicide gel in vivo. This dissertation offers a model of fluid mechanics which interprets the behavior of a microbicide gel (a non-Newtonian fluid) as a low Reynolds number flow.The flow of a microbicide gel in vivo is analyzed by a numerical method. Firstly, a rheological model and a governing equation for a microbicide gel are derived. The mechanical behavior of a microbicide gel is appropriately considered as a non-Newtonian fluid. A Carreau-like model is adopted as a rheological model for the gel. The Carreau model is modified in order to obtain the Carreau-like model. Due to the geometry, an efficient formulation of the governing equations employs the Reynolds lubrication equation. A Reynolds lubrication equation in terms of the height profile of a vagina is derived from the balance of linear momentum and the continuity equation. In addition, dimensionless numbers and a non-dimensional governing equation are introduced. A numerical method is developed to solve the equations using finite differences. As a practical aid, a relationship between Deborah number, defined as the ratio of the material relaxation time to the time scale of the flow, and computation time step size is established. The influences of two important factors, i.e., a yield stress of the gel and dilution by vaginal fluid, are investigated. In case of a yield stress, the lubrication theory is not strictly applicable to a yield stress fluid, owing to a well-known 'yield stress paradox.' We develop the criteria, under which a lubrication theory is consistent with a yield stress fluid, by a scaling analysis.The numerical model, which is developed in this dissertation, can solve any combination of many factors, e.g., a gravitational force, a compliance of the vaginal walls, Theological properties of the gel, a yield stress, and inhomogeneous dilution by vaginal fluid. This facilitates an analysis of a microbicide gel behavior in vivo and reduces the effort of experiments. Ultimately, this dissertation contributes to the development of safe and effective microbicides to inhibit HIV transmission by providing a tool for use in design of the gel delivery vehicle. |
