Computational Model for the Generalised Dispersion of Synovial Fluid

The metabolic function of synovial fluid is important to understand normal and abnormal synovial joint motion, especially if one seeks some leading causes of the degenerative joint disease. The concentration of hyaluronic acid molecules and other high molecular weight substances in the synovial fluid may be responsible to disperse the nutrients into the cartilage. The theoretical study of the convective diffusion mechanism occurring in the knee joint is presented. A flow model has been analyzed for better understanding of the convective diffusion of the viscous flow in between the articular surfaces. The governing system of partial differential equations has been solved for the Newtonian fluid with suitable matching and conditions. The analytical solution for the unsteady dispersion problem has been obtained for the better understand the phenomena of nutritional transport to synovial joint. The contributions of (convection + diffusion) on the dispersion of nutrients are investigated in detail. The dispersion coefficient has been computed for different values of the viscosity parameter. The results show that the average concentration has a negative correlation with the axial distance and the time. Keywords—Synovial Fluid; Articular Cartilage; Unsteady diffusion coefficient; Computational model