Approximate closed-form solution of the synovial fluid film force in the human ankle joint with non-Newtonian lubricant

The aim of this paper is to propose an approximate closed form lubrication model of the human ankle joint by taking into account the porosity of the cartilage matrix and the non-Newtonian behaviour of the synovial fluid. The model is based on the theory of squeeze lubrication and introduce an original modified Reynolds equation obtained modelling the synovial fluid as a couple-stress fluid and the synovial fluid transport across the articular cartilage by using a modified Darcyʹs equation. This approach gives the advantage to obtain an analytical expression of the synovial pressure field and of the non-stationary fluid film force acting in the synovial joint during the squeeze motion in terms of couple-stress parameter, film thickness, and porosity parameter.