Generalized rate-and-state model linking rheology and soft matter tribology

In the present work, a complex fluid lubrication model based on a single state variable named the structural parameter was used to predict steady-state frictional responses for a continuous hydrogel-on-flat contact. The model predicts the steady-state lubrication curve, or steady-state friction versus sliding speed curve, that was only previously predicted by the adsorption friction model, a widely used model for hydrogel lubrication. For the first time, model can predict the analytical solutions of two transition speeds in the steady-state lubrication curve rather than the single critical speed in the adsorption model. Finally, we suggest a physical meaning of the structural parameter based on a comparison with the rate-and-state friction model used for geological events. We posit that it is measure of real contact area mediated by the water intervention. This is the first study to connect various fields including rheology, soft matter tribology, and geological physics.