Inertial and Linear Re-Absorption Effects on a Synovial Fluid Flow Through a Lubricated Knee Joint

Abstract

This study examines the flow dynamics of synovial fluid within a lubricated knee joint during movement, incorporating the effect of inertia and linear re-absorption at the synovial membrane. The fluid behavior is modeled using a couple-stress fluid framework, which accounts for mechanical phenomena and employs a lubricated membrane. synovial membrane plays a crucial role in reducing drag and enhancing joint lubrication for the formation of a uniform lubrication layer over the cartilage surfaces. The mathematical model of synovial fluid flow through the knee joint presents a set of non-linear partial differential equations solved by a recursive approach and inverse method through the software Mathematica 11. The results indicate that synovial fluid flow generates high pressure and shear stress away from the entry point due to the combined effects of inertial forces, linear re-absorption, and micro-rotation within the couple-stress fluid. Axial flow intensifies at the center of the knee joint during activity in the presence of linear re-absorption and molecular rotation, while transverse flow increases away from the center and near to synovium due to its permeability. These findings provide critical insights for biomedical engineers to quantify pressure and stress distributions in synovial fluid to design artificial joints.