Quantitative Viscosity Mapping Using Fluorescence Lifetime Measurements

Abstract

Lubricant viscosity is a key driver in both the tribological performance and energy efficiency of a lubricated contact. Elastohydrodynamic (EHD) lubrication produces very high pressures and shear rates, conditions hard to replicate using conventional rheometry. In situ rheological measurements within a typical contact are therefore important to investigate how a fluid behaves under such conditions. Molecular rotors provide such an opportunity to extract the local viscosity of a fluid under EHD lubrication. The validity of such an application is shown by comparing local viscosity measurements obtained using molecular rotors and fluorescence lifetime measurements, in a model EHD lubricant, with reference measurements using conventional rheometry techniques. The appropriateness of standard methods used in tribology for high-pressure rheometry (combining friction and film thickness measurements) has been verified when the flow of EHD lubricant is homogeneous and linear. A simple procedure for calibrating the fluorescence lifetime of molecular rotors at elevated pressure for viscosity measurements is proposed.

Keywords: Elastohydrodynamic lubrication; Fluorescence lifetime; High-pressure rheology; In situ; Molecular rotor; Viscosity.

Fig. 1

a Pressure–ThT lifetime relationship in IGEPAL from the high-pressure cell. b Pressure–viscosity relationship for IGEPAL. c Resulting calibration curve showing the relationship between ThT lifetime and the viscosity of IGEPAL

Fig. 2

Maps obtained in contact at 380 MPa peak pressure under pure rolling, $h_c$ ≈ 170 nm. a ThT fluorescence lifetime and b IGEPAL viscosity distributions within the contact. Note that the conversion between ThT fluorescence lifetime and IGEPAL viscosity is based on Fig. 1. Arrows show flow direction

Fig. 3

Cross section of local IGEPAL ${\mathit{\tau }}_{\text{ThT}}$ profile for a 380 MPa peak pressure contact (in pure rolling, $h_c$ ≈ 170 nm) both parallel and orthogonal to the flow direction. Arrow indicates the direction of flow. Inset shows the increase in ${\mathit{\tau }}_{\text{ThT}}$ at the inlet compared to the side edges of the contact

Fig. 4

$U_{\text{e}}$ = 110 mm/s, 30% SRR, 370 MPa peak pressure, glass–steel SLIM (spacer layer imaging) image with optical interferometry. Central film thickness is approximately 170 nm, and the minimum film thickness is approximately 110 nm. The inset shows the film thickness profile in the flow direction (indicated by the arrow)

Fig. 5

Local IGEPAL viscosity obtained across all SRR tested, showing the spread of data. Rheological fits at 26 (ambient temperature) and 33 °C (estimated average lubricant temperature at the inlet) shown for reference. Deviations from the rheological fit at 33 °C are likely due to variations in experimental temperatures

Fig. 6

Local pressure versus viscosity for IGEPAL CO520 under pure rolling at a peak pressure of 380 MPa, h ≈ 170 nm. The inset shows this on a log-linear plot. Average viscosity from a lifetime threshold and based on the contact area are also displayed as a triangle and an asterisk, respectively. The maximum viscosity obtained at the maximum pressure is the square. The dash line is viscosity estimates based on contact temperature = 33.6 °C. The red line is the exponential fit through the experimental data points. This temperature is estimated by measuring the IGEPAL viscosity outside of the EHD contact (Color figure online)

Fig. 7

Comparison of viscosity estimates from combined friction and film thickness measurements (5 and 50% SRR average pressure of 185–276 MPa) at 26 °C, high-pressure rheological estimations at a range of temperatures between 21 and 33 °C and Fluorescence lifetime measurements under pure rolling conditions (4 tests undertaken on the same day)

Fig. 8

Shear stress map for a 342 MPa peak pressure contact at 30% SRR (1.771 × 10⁵ s⁻¹), h ≈ 165 nm. Arrow shows the flow direction

Fig. 9

Flow chart on how to calibrate the fluorescence lifetime–viscosity relationship of a molecular rotor in a lubricant without a pressure cell