Analytical study of tangent hyperbolic fluid flow through permeable cavity: an application to synovial fluid in human joint

The scientific article offers an analytical solution for the model of synovial fluid flow between the cartilage under the influence of load on the cartilage surface, inlet pressure and flux. The tangent hyperbolic fluid model is used in the analogy of spongy cartilage to discuss the rheology of synovial fluid in rectangular slit having permeable boundary. The transverse velocity on the surface of permeable cartilage is measured by the pressure difference, and axial velocity is assumed to be maximum at the centre of slit. The two-dimensional and two-directional flow is produced by the pressure gradient or pressure difference, which is modelled by the physical laws of mass and momentum with the nonhomogeneous boundary conditions in finite domain. The complex system of nonlinear equations is solved by the perturbation technique with the assumption that elastic forces are weaker than the viscous forces. The effect of filtration rate, power-law index, inlet pressure and Weissenberg number on flow properties are observed through graphs, and it is examined that when these emerging parameters rises, then the flow towards the cartilage surface begins to thin. As a result, the viscosity of the synovial fluid near the cartilage become weak but it is strong between the cartilage surfaces that is filled by the synovial fluid. Also, the filtration rate against pressure and permeability is also measured by the formulas calculated in this research and it is concluded that the high filtration rate requires the less pressure and high permeability on the boundary of the cartilage cavity.