Ion-Induced Swelling Behavior of Articular Cartilage due to Non-Newtonian Flow and Its Effects on Fluid Pressure and Solid Displacement

In this study, we examine the behavior of articular cartilage equilibrated in a salt (NaCl) solution during non-Newtonian fluid flow that follows an Ostwald–de Waele model. A linearly elastic and isotropic rectangular strip of cartilage is considered for analysis. A continuum theory of mixtures has been employed to develop a coupled system of partial differential equations for the solid displacement and the fluid pressure by considering the important factor of the ion concentration by assuming the cartilage as a deformable porous media. The coupled system of partial differential equations is solved using the numerical method named method of lines. In most cases, shear-thinning fluid is compared to the shear-thickening fluid to magnify the difference. Graphical results show that shear-thickening fluids bring more solid deformation and shows less fluid pressure in comparison to the shear-thinning fluids.