2D Squeezing-flow of a Non-Newtonian Fluid Between Viscoelastic Walls: Numerical Simulations

Abstract

Abstract This study is part of a broader research plan to design and develop microbicides to prevent against HIV (Human Immunodeficiency Virus) and other sexually transmitted infections (STIs). A microbicide is a topical compound that contains active ingredients to protect against STIs. The active ingredients are suspended in a delivery vehicle, such as creams and polymeric gels. The efficacy of a microbicidal gel depends on the extent of the spreading, the amount of the epithelial surfaces coated, and the retention on the vulnerable epithelial surfaces. The effectiveness of a microbicidal gel to coat and adhere to the epithelium is affected by several factors, such as the rheological properties of gel, gravity, biomechanical properties of the vaginal tissue, vaginal geometry, effects of the neighbouring tissues, and dilution. This thesis presents an engineering approach to help understand the impact of the viscoelastic characteristics of the vaginal tissue on the spreading of different formulations of a microbicidal gel. This study focuses on the relative effects of the tissue biomechanical properties and gravity on the spreading behaviour of a gel with different rheological properties. In this study, a numerical model was developed to investigate the flow of the gel under different conditions. A 2D numerical flow model (1D spreading) was developed to simulate the flow under the influence of gravity and the squeezing forces due to the biomechanical properties of the vaginal tissue. The gel was modelled as a non-Newtonian fluid using the power-law constitutive model. The viscoelastic characteristic of the soft tissue was represented by the Voigt model. This study is an initial attempt to incorporate the viscoelastic characteristics of the vaginal tissue in the development of a microbicidal drug delivery vehicle. The results of the numerical simulations were analysed based on a series of coupling parametric studies. Based on the results of the parametric studies, the tissue viscoelastic parameters have a different impact on the flow behaviour of the gel depending on the relative magnitudes of the tissue elastic and viscous components. For a higher tissue viscous-coefficient, the tissue viscous effect resulted in less spreading and as the tissue elasticity increased, the impact of the tissue viscous component diminished. The impact of the tissue viscous component depended on the fluid rheological properties. The impact of the tissue viscous-coefficient was more noticeable at a lower fluid consistency and at a higher fluid shear-thinning index. Once applied to the vaginal canal the gel is expected to dilute after it mixes with vaginal fluids. The dilution of the gel would decrease its consistency and increase its shear-thinning index and consequently increase the impact of the tissue viscous component on the spreading of the gel. In conclusion, the results of this study strongly suggest the need to determine the biomechanical properties in vivo. The importance and the significance of measuring the biomechanical properties are two fold; 1) the characterization of the tissue viscoelastic properties would help in developing more accurate and more relevant theoretical models and 2) knowing the biomechanical properties of the vaginal tissue would play a key role in validating the numerical studies and in evaluating the performance of microbicidal gels in a clinical setting. The results of this study would ultimately serve as a tool in the designing and optimizing microbicidal gels.