Asymptotic Formulas for Small Sessile Drops

Abstract

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.