Study of non-Newtonian synovial fluid flow by a recursive approach

Abstract

This study analyzes the non-Newtonian synovial fluid flow between the joints in a synovitis, which is a diseased condition due to inflammation of synovial membrane. It is assumed in this study that the secretion of synovial fluid through the inflamed synovial membrane is a linear function of the membrane length. The mathematical modeling of synovial fluid through a synovial membrane is made by the non-Newtonian Linear Phan-Thien–Tanner (LPTT) fluid model through a thin conduit having permeable walls. The nonlinear flow of LPTT fluid gives the non-homogeneous complex boundary value problem, and the recursive approach is used to solve the problem. The flow of synovial fluid along and across the membrane is calculated under the inflamed membrane, and results are displayed through graphs. The axial pressure required for the non-Newtonian fluid flow and deformation of synovial fluid that produces the shearing forces near the synovial membrane are also calculated. The purpose of this research is to observe the shear stress on the synovial fluid and inflammation rate on the flow along the membrane at different position and pressure required for the flow of synovial fluid in diseased condition. The mathematical and graphical results for pressure, flow, volume flux, and streamline are calculated and plotted using the software MATHEMATICA. This study is very helpful for the biomedical engineers to measure the compression force and shear stress on the synovial fluid in a diseased condition and can be controlled by the viscosity of the synovial fluid.