We construct asymptotic solutions for the shape of a small liquid sessile drop in a cone and plate rheometer. The approximation is based on small Bond number or, equivalently, on a characteristic length scale which is much smaller than the capillary length. The drop has a complicated asymptotic structure, consisting of five separate scalings, which is resolved using the method of matched asymptotic expansions. We find that the presence of a substrate above (and below) the drop gives rise to qualitatively new drop configurations.
- liquid bridge
- sessile drop
- pendant drop
- surface tension
- matched asymptotic expansions
Cregan, V., O'Brien, S. B. C., & McKee, S. (2010). The shape of a small liquid drop on a cone and plate rheometer. SIAM Journal on Applied Mathematics, 70(6), 2075-2096. https://doi.org/10.1137/090765201