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

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