Einstein's Viscosity Equation for Nanolubricated Friction.

The generalized Einstein equation for the viscosity of a dispersion/suspension, μ = (1 + αfϕ)μ0, where μ0 is the liquid viscosity, ϕ is the solid volume fraction, and αf is a coefficient, is applied to the viscosity of a nanofluid lubricant. The coefficient of lubricated friction in the hydrodynamic regime is proportional to the viscosity of the lubricant. Therefore, an equation for the coefficient of friction with nanofluid lubrication can be formulated. We present such an equation and show its validity for common types of bearings (journal, rolling, and ball bearings). The equation, which may be viewed as one of nanofriction laws, is compared with experimental results for WS2 nanoparticle-enhanced oil lubrication, showing agreement within 7% accuracy.