Film dynamics and lubricant depletion by droplets moving on lubricated surfaces*

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 must be solved. Despite recent progress, a quantitative mechanistic understanding of depletion is still lacking. In this work, we showed that the lubricant film thicknesses beneath, behind, and wrapping around a moving droplet change dynamically with the droplet's speed -- analogous to the classical Landau-Levich-Derjaguin problem. The interconnected lubricant dynamics result 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.