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

This study examines the flow dynamics of synovial fluid within a lubricated knee joint during movement, incorporating a linear re-absorption rate of water and nutrients at the synovium. The fluid behavior is modeled using a couple-stress fluid framework which accounts for inertial forces and employing a slip boundary condition, which plays a crucial role in reducing drag and enhancing joint lubrication for the formation of a uniform lubrication layer over the cartilage surfaces. Mathematically, the nonlinear governing equations are transformed into a system of linear partial differential equations using a recursive approach and inverse method is applied to further reduce these equations to a system of ordinary differential equations, which are solved using software Mathematica. The results indicate that synovial fluid flow generates high pressure and shear stress at the synovium 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 joint capsule during activity driven by linear re-absorption and molecular rotation, while transverse flow increases near the synovium due to its permeability. These findings provide critical insights for biomedical engineers to quantify re-absorption rates and stress distributions in synovial fluid under normal physiological conditions.