Modelling the impact of synovial fluid elasticity on tangential stress

TL;DR

This paper investigates how the elasticity of synovial fluid influences tangential stress and friction during oscillatory joint motion, revealing significant effects that differ from Newtonian and standard viscoelastic models.

Contribution

It introduces a modified Oldroyd-B model to analyze the impact of synovial fluid elasticity on joint friction, highlighting fundamental differences in stress predictions.

Findings

Elasticity significantly affects tangential stress in synovial fluid.

Modified Oldroyd-B model predicts different stress scalings than classical models.

Polymer elasticity impacts friction in oscillating joints.

Abstract

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.