Multiscale analysis of liquid lubrication trends from industrial machines to micro-electrical-mechanical systems

An analytic multiscale expression is derived that yields conditions for effective liquid lubrication of oscillating contacts via surface flow over multiple time and length scales. The expression is a logistics function that depends on two quantities, the fraction of lubricant removed at each contact and a scaling parameter given by the logarithm of the ratio of the contact area to the product of the lubricant diffusion coefficient and the cycle time. For industrial machines the expression confirms the need for an oil mist. For magnetic disk drives, the expression predicts that existing lubricants are sufficient for next-generation data storage. For micro-electrical-mechanical systems, the expression predicts that a bound + mobile lubricant composed of tricresyl phosphate on an octadecyltrichlorosilane self-assembled monolayer will be effective only for temperatures greater than ∼200 K and up to ∼MHz oscillation frequencies.