Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 2075-2096 |
| Number of pages | 22 |
| Journal | SIAM Journal on Applied Mathematics |
| Volume | 70 |
| Issue number | 6 |
| DOIs | |
| Publication status | Published - Apr 2010 |
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Keywords
- liquid bridge
- sessile drop
- pendant drop
- asymptotics
- surface tension
- curvature
- matched asymptotic expansions
Cite this
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