Apparent contact angle of drops on liquid infused surfaces: geometric interpretation

Abstract

We theoretically investigate the apparent contact angle of droplets on liquid infused surfaces as a function of the relative size of the wetting ridge and the deposited droplet. We provide...

Droplets on Lubricated Surfaces: The slow dynamics of skirt formation

“…However, there appears to be no clear consensus on what the size of this skirt region is. For example, Semprebon et al presented theoretical arguments for the apparent contact angle assuming given (constant) curvatures of the interfaces in the skirt region [19,20]. Their results were consistent with some experiments, in which the radius of curvature of the skirt was constant and, further, small compared with the droplet size [5,7,21,22].…”

“…3b with fig. 4 of Semprebon et al [20]). However, we emphasize that our result goes beyond that of Semprebon et al [20] by determining the height of the contact line and the curvature/pressure of the skirt in terms of the key control parameters within the system, namely X ∞ and α.…”

“…3b as a function of system size, X ∞ /X c , for different film thicknesses. Previously, Semprebon et al [19,20] obtained a relationship between the contact line height, H c , and the radius of curvature of the meniscus, κ ∝ P ∞ , under the assumption that the skirt remains small compared to the droplet. Such geometrical arguments are entirely compatible with our approach since the film pressure is determined as part of the solution; indeed, plotting H c /α = h c /x c as a function of α/(−P ∞ ) produces a collapse of our numerical data onto a master curve that is very similar to that provided by Semprebon et al [20] (compare the inset of fig.…”

“…The equilibrium of the pulling of the contact line has been considered by a variety of authors; perhaps most notably, Semprebon et al [19,20] considered the equilibrium of the Neumann triangle at the contact line under the assumption that external contact lines form on the planar substrate. At the same time, the early stages of this formation have been studied in a related problem by Hack et al [13].…”

“…However, in other experiments, Schellenberger et al [15] observed menisci that did not have constant curvature and were of a size comparable to the capillary length. Even without this discrepancy, current models appear unable to predict either the height of the contact line in the equilibrium state or the effective contact angle; for example, the theory of Semprebon et al [20] takes the ratio of pressures within the droplet and layer as a control parameter, but does not determine from first principles what this ratio should be.…”