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
