| Summary: | A key question in the interaction of droplets with lubricated and liquid-infused surfaces
is what determines the apparent contact angle of droplets. Previous work has determined
this using measured values of the geometry of the ‘skirt’ — the meniscus-like deformation
that forms around the base of the deposited droplet. Here, we consider theoretically the
equilibrium of a droplet on a smooth, impermeable lubricant-coated surface, and argue
that the small effect of gravity within the skirt and the size of the substrate are important
for determining the final equilibrium. However, we also show that the evolution of the
skirt towards this ultimate equilibrium is extremely slow (on the order of days for typical
experimental parameter values). We therefore suggest that previous experiments on smooth
lubricated surfaces may have observed only slowly-evolving transients, rather than ‘true’
equilibria, potentially explaining why a wide range of skirt sizes have been reported.
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