A Study of Fluid Flow Through Deformable Porous Material and Tissue Using Mixture Theory Approach
This dissertation is an attempt to analyze the phenomenon involved in the flow of various fluids through deformable porous media. In particular, problems are modeled using continuum mixture theory approach. First, our focus would be on the study of compression molding process. A mathematical model has been developed to study non-Newtonian fluid flow through preimpregnated pile. The governing equation for solid volume fraction is solved numerically to highlight the rheological effects of fluid flow. Graphical illustrations indicate that shear-thinning and shearthickening fluids induce the increase in solid volume fraction. But, final state of solid volume fraction is homogeneous for shear-thickening fluid as compared to the shear-thinning fluid. Furthermore, ion-induced deformation of articular cartilage due to non-Newtonian fluid flow is investigated. Ionic effects are incorporated with solid stress for biphasic modeling of tissue. Normalized quantities are used to non-dimensionalize the equations for ion-concentration, fluid pressure and solid displacement. First, analytical solution for ion-concentration has been presented. Coupled system of equations for solid displacement and fluid pressure produces complexity. This complexity is handled using numerical technique; Method of Lines. Numerical results indicate that the shear-thickening fluid induces more solid deformation but less fluid pressure as compared to the shear-thinning fluid. In addition to this, a mathematical model has been developed to study rheological effects on compressive stress-relaxation behavior of soft biological tissue. Biphasic mixture theory is incorporated with strain-dependent permeability. Suitable quantities are used to non-dimensionalize the coupled system of equations of solid displacement and fluid pressure. Numerical results show that the solid deformation increases with increase in power-law index. Results also indicate that linear permeability induces more deformation as compared to the strain-dependent nonlinear permeability. Finally, based on the geometry of previous problem, a mathematical model has been developed to study deformation of the biological tissue due to flow of electrically conducting fluid from it. In the presence of Lorentz forces, biphasic mixture theory is incorporated with strain-dependent permeability. Complexity of governing equations is treated numerically. Graphical illustrations show that solid displacement decreases but fluid pressure increases by increasing the strength of magnetic parameter. These results are more profound for the fast rate of compression as compared to the slow rate of compression.