@article {1142248, title = {Film Dynamics and Lubricant Depletion by Droplets Moving on Lubricated Surfaces}, journal = {PHYSICAL REVIEW}, volume = {8}, year = {2018}, 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 explain the shape of a droplet
on a lubricated surface by balancing the Laplace pressures across interfaces. We then show that the
lubricant film thicknesses beneath, behind, and wrapping around a moving droplet change dynamically

with the droplet{\textquoteright}s speed{\textemdash}analogous to the classical Landau-Levich-Derjaguin problem. The intercon-
nected lubricant dynamics results in the growth of the wetting ridge around the droplet, which is the

dominant source of lubricant depletion. We then develop an analytic expression for the maximum amount
of lubricant that can be depleted by a single droplet. Counterintuitively, 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.

}, author = {Michael J. Kreder and Dan Daniel and Adam Tetreault and Zhenle Cao and Baptiste Lemaire and Jaakko V.I. Timonen and Aizenberg, Joanna} }