Einstein's Viscosity Equation for Nanolubricated Friction

Alexander Breki; Michael Nosonovsky

doi:10.1021/acs.langmuir.8b02861

Einstein's Viscosity Equation for Nanolubricated Friction

Langmuir. 2018 Oct 30;34(43):12968-12973. doi: 10.1021/acs.langmuir.8b02861. Epub 2018 Oct 18.

Authors

Alexander Breki¹, Michael Nosonovsky²

Affiliations

¹ Department of Machine Design , Peter the Great St. Petersburg Polytechnic University , 29 Polytechnicheskaya Street , St. Petersburg 195251 , Russia.
² Mechanical Engineering , University of Wisconsin-Milwaukee , 3200 N. Cramer Street , Milwaukee , Wisconsin 53211 , United States.

PMID: 30296098
DOI: 10.1021/acs.langmuir.8b02861

Abstract

The generalized Einstein equation for the viscosity of a dispersion/suspension, μ = (1 + α_fϕ)μ₀, where μ₀ is the liquid viscosity, ϕ is the solid volume fraction, and α_f 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.