The investigation of fluid flow in cartilage contact gap

Synovial fluid flow in articular joint capsule plays an important role during mixed mode lubrication. However, the actual fluid flow behaviour during cartilage contact has not been fully understood so far. This is due to the difficulties in measuring the gap permeability using conventional experimental techniques. The problem becomes further complicated with consideration of the cartilage surface roughness. Here a validated numerical study was developed to quantify the gap permeability of lateral synovial fluid flow. Both macro- and micro-scale gap flow models were created based on Darcy's law at the macro-scale and the Navier-stokes equation at the micro-scale. To generate model inputs, the cartilage topography was numerically synthesised based on the experimental measurements of bovine medial tibia cartilage surface roughness using Dektak Stylus Profilers. The experimental results show that the average roughness height R_a is 1.97 μm and root-mean-square roughness height R_q is 2.44 μm, while the correlation lengths of the secondary and tertiary undulations are round 100 μm and 20 μm, respectively. The numerical results indicate that the contact gap height and fluid pressure gradient are two critical parameters which significantly affect the gap permeability. As the contact gap closes, there is a decrease in gap permeability, and most importantly, the gap permeability is also very sensitive to the fluid pressure gradient. Furthermore, with gap closure, the permeability of the contact gap gradually approaches that of the cartilage tissue, at which point the contact gap is functional closed. This occurs at a contact gap height around 1 μm and fluid pressure gradient below 5 × 10⁵ Pa/m in this study.