Diffusion equation for spreading and replenishment in submonolayer lubricant film

Abstract

In magnetic hard disk drives, it is important to evaluate head wear durability in relation to lubricant layer because the head-disk spacing has to be reduced to ~1nm to achieve a high density recording above 1 Tb/in2. This paper presents a new one dimensional diffusion equation to evaluate the replenishment process of a depleted lubricant groove in submonolayer thickness region. Basic equation is derived from a hypothetical concept that the ratio of submonolayer lubricant thickness to monolayer thickness is equal to that of local molecule density to bulk density. Equation of disjoining pressure is also modified from this concept. The local effective viscosity in submonolayer region is assumed to change linearly between solid boundary and monolayer thickness. The derived diffusion equation is nonlinear with respect to lubricant thickness. Calculated examples of spreading and replenishment behaviors are shown in comparison with those of the conventional theory. It was found that the spreading and replenishment speed similar to the experimental data can be obtained by using a realistic viscosity in submonolayer region compared to the conventional theory.

Keywords

• tribology
• nanotribology
• head-disk interface
• submonolayer lubricant flow
• diffusion equation
• lubricant spreading
• lubricant replenishment