Oscillatory and steady shear viscosity: The Cox-Merz rule, superposition, and application to EHL friction

The new quantitative approach to elastohydrodynamic lubrication requires a description of the steady shear dependent viscosity for calculations of film thickness and friction. This property can be obtained from measurements in pressurized thin-film Couette viscometers. However, frequency dependent viscosity can be obtained from a torsionally vibrating quartz crystal viscometer at high pressure or a relatively simple ambient pressure measurement with a shear impedance spectrometer. Here it is shown for squalane and for a cyclic hydrocarbon and for a diester that both the steady shear dependent viscosity and the frequency dependent viscosity obey time-temperature-pressure superposition with the simplest shifting rule over the range of conditions investigated. Flow curves shift along a constant steady stress path or a constant complex modulus path. The Cox-Merz rule has been confirmed only for squalane and then only near the transition. The EHL friction for squalane at low pressure may be predicted with fair accuracy from the frequency dependent viscosity measured at ambient pressure. It appears that the Cox-Merz rule only applies to low-molecular-weight liquids when the molecule is composed of a long chain.