Numerical Rheological Modeling of Thin Lubricating Oil Films Considering Polymolecular Adsorption and ZDP

Abstract

A computational approach is proposed for evaluating the rheological and frictional behaviour of highly confined lubricant films, with particular attention to molecular adsorption and the formation of strongly structured interfacial regions. The viscosity variation between the opposing surfaces is represented using an adsorption-based formulation derived from the Polanyi potential concept. Near each solid boundary, the model introduces a quasi-solid lubricant region whose properties gradually approach those of the bulk oil with increasing distance from the surface. The integral response of the film is characterized by a harmonically averaged viscosity, calculated numerically by the trapezoidal method using 200 discretization intervals in Microsoft Excel. The shear-dependent rheology of the bulk lubricant is described by the C–Y relationship. Experimental friction data for I-20A base oil and formulations containing 1.25 and 2.5 wt% zinc dialkyldithiophosphate (ZDP) were used to determine the interfacial model parameters. Increasing the ZDP concentration produced substantial changes in the properties of the adsorbed lubricant region. The estimated surface viscosity increased from 0.14 to 1.68 Pa·s, while the characteristic attenuation length increased from 2.1 to 4.6 nm and the optimal thickness of the quasi-solid interfacial layer increased from 0.8 to 1.9 nm. Agreement between the simulations and experimental measurements was satisfactory, with mean relative deviations of 6.9–10.2%. The calculated minimum of the friction coefficient occurred at approximately 5 MPa for the base oil and shifted to about 8 MPa after ZDP addition. This shift suggests that the additive extends the range of operating conditions under which fluid-film lubrication can be maintained.