Viscoelastic Effects on the Unsteady Convective Diffusion in a Synovial Fluid of Human Joints

A generalized dispersion model is used to obtain exact solution for unsteady convective diffusion in a synovial fluid of human joints. In this paper, synovial fluid is represented by viscoelastic fluid. Analytically the problem is formulated as a two region namely diffusion and flow model. Flow and diffusion between approaching cartilage surfaces and within the porous cartilages. The non-linear momentum equations in a fluid film region have been solved by perturbation technique. Exact solution of diffusion equation in fluid film region with mixed boundary condition has been obtained with the help of Gill & Sankarsubramaniam [29]. It has been observed that increase in viscoelastic parameter decreases the ratio of axial velocity and average axial velocity. It is also observed that the axial velocity decreases with increase in intra-articular gap. It has been observed that mean concentration distribution increases with increase in the viscoelastic parameter. It has also been noted that mean concentration decreases with increase in time and axial distance. The results are also obtained for diffusion coefficients versus time. It has been observed that when time increases then diffusion coefficient increases. It should also be noted that when viscoelastic parameter increases then diffusion coefficients decreases.