Constitutive relation for the friction between lubricated surfaces

Motivated by recent experiments and numerical results, we propose a constitutive relation to describe the friction beween two surfaces separated by an atomically thin layer of lubricant molecules. Our phenomenological approach involves the development of a rate and state law to describe the macroscopic frictional properties of the system, in a manner similar to that which has been proposed previously by Ruina [J. Geophys. Res. 88, 10 359 (1983)] for the solid on solid case. In our case, the state variable is interpreted in terms of the shear melting of the lubricant, and the constitutive relation captures some of the primary experimental differences between the dry and lubricated systems.