Film dynamics and lubricant depletion by droplets moving on lubricated surfaces

TL;DR

This paper provides a mechanistic understanding of lubricant depletion caused by droplets on lubricated surfaces, revealing how droplet speed influences lubricant loss and informing the design of longer-lasting surfaces.

Contribution

It introduces a quantitative model linking droplet dynamics to lubricant depletion, including an analytic expression for maximum depletion and insights into the effects of droplet speed.

Findings

Lubricant film thickness varies dynamically with droplet speed.

Wetting ridge growth is the main source of lubricant depletion.

Faster droplets deplete less lubricant despite higher forces.

Abstract

Lubricated surfaces have shown promise in numerous applications where impinging foreign droplets must be removed easily; however, before they can be widely adopted, the problem of lubricant depletion, which eventually leads to decreased performance, must be solved. Despite recent progress, a quantitative mechanistic explanation for lubricant depletion is still lacking. Here, we first explained the shape of a droplet on a lubricated surface by balancing the Laplace pressures across interfaces. We then showed that the lubricant film thicknesses beneath, behind, and wrapping around a moving droplet change dynamically with droplet's speed---analogous to the classical Landau-Levich-Derjaguin problem. The interconnected lubricant dynamics results in the growth of the wetting ridge around the droplet, which is the dominant source of lubricant depletion. We then developed an analytic expression for the maximum amount of lubricant that can be depleted by a single droplet. Counter-intuitively, faster moving droplets subjected to higher driving forces deplete less lubricant than their slower moving counterparts. The insights developed in this work will inform future work and the design of longer-lasting lubricated surfaces.