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Zeitschrift für Analysis und ihre Anwendungen


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Volume 13, Issue 2, 1994, pp. 209–231
DOI: 10.4171/ZAA/514

Published online: 1994-06-30

Asymptotic Formulas for Small Sessile Drops

Erich Miersemann[1]

(1) Universität Leipzig, Germany

We will prove asymptotic foriiulas for the wetted disk of a drop with small volume resting on a horizontal plane which is in a vertical gravity field. These formulas are general-izations of results of Finn. There is a non-uniformity in the asymptotic behaviour depending on whether the boundary contact angle is near $\pi$ or not. If the contact angle is different from $\pi$ we get a complete asymptotic expansion of the wetted disk in powers of the volume. These results are consequences of the strong non-linearity of the problem.

Keywords: Capillarity, drops, asymptotic expansions

Miersemann Erich: Asymptotic Formulas for Small Sessile Drops. Z. Anal. Anwend. 13 (1994), 209-231. doi: 10.4171/ZAA/514