Modelling the impact of synovial fluid elasticity on tangential stress

The rheological properties of synovial fluid have been observed to substantially impact its lubricating behaviour. While numerous studies have illustrated the importance of its shear-dependent viscosity, the impact of synovial fluid elasticity for oscillatory joint motion is far less characterised. Hence we consider how elasticity impacts the tangential stress, and thus friction, exerted on confining surfaces in rheological models of synovial fluid on the length and time scales of oscillatory joint motion, though in a simplified setting rather than considering the full complexity of a joint. Minor changes in the elastic constitutive equation from a canonical upper convected Oldroyd-B model lead to fundamentally different scalings and predictions for tangential stress compared to either a Newtonian fluid and an Oldroyd-B fluid. In particular, polymer elasticity within physiological fluids is predicted to have a profound effect on friction both within the oscillating joint and more generally, in turn suggesting further examination of synovial fluid elasticity in experimental and modelling studies.