Dynamics of non-Newtonian synovial fluid through permeable membrane with periodic filtration

Abstract

This research measures the flow of synovial fluid through permeable membrane. It is assumed in this study that the ultrafiltration of blood plasma is a continuous function and repeatedly forms the action to keep synovial fluid normal in the joints. The novelty of this research is to analyze the rheology of synovial fluid under the periodic filtration rate within the membrane. To estimate the pressure and shear stress which are essential for the flow of synovial fluid between the synovial joints, mathematical modeling has been made for the synovial fluid flow through permeable membrane by the laws of mass and momentum and viscoelastic LPTT fluid model. The LPTT fluid has the viscoelastic effects in the presence of relaxation time, therefore for synovial fluid the present fluid model represents the best rheological properties. To find the analytical results for the rheology of the synovial fluid, a method proposed by Langlois is used. This research concludes that the pressure difference and transverse velocity are high when the periodic filtration is cosine type whereas the shear stress on the wall is high for sine type of filtration.