Diffusion Equation for Spreading and Replenishment in Submonolayer Lubricant Film

In the field of head–disk interface technology, evaluating the effects of lubrication of a submonolayer lubricant film is becoming increasingly important as the thickness of the mobile lubricant film is reduced to <0.3 nm. Although the spreading and replenishment speed of a submonolayer lubricant can be evaluated by conventional diffusion theory if a large effective viscosity value is selected, it is commonly considered inappropriate to use the conventional diffusion equation based on continuum mechanics for a submonolayer liquid film. This paper presents a new diffusion equation that formulates the averaged flow of a submonolayer liquid film with a reduced density compared to the bulk density. The Hamaker constant for disjoining pressure in the submonolayer liquid film is also modified to be proportional to the film thickness. The difference between the viscosity in the submonolayer film and the bulk viscosity is also taken into account. From the derived diffusion equation for a submonolayer film, the spreading of a lubricant boundary and replenishment process of a depleted lubricant surface are studied in comparison with the results obtained using the conventional diffusion equation. The replenishment process of submonolayer lubricant profiles in a depleted groove for the Z-tetraol lubricant with a 0.24-nm-thick mobile layer can be calculated from submonolayer diffusion theory by using a low viscosity value consistent with that measured by a blow-off experiment.