The shape of a small liquid drop on a cone and plate rheometer

V. Cregan; S.B.C. O'Brien; Sean McKee

doi:10.1137/090765201

The shape of a small liquid drop on a cone and plate rheometer

V. Cregan, S.B.C. O'Brien, Sean McKee

Mathematics And Statistics

Research output: Contribution to journal › Article

1 Citation (Scopus)

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.

Language	English
Pages	2075-2096
Number of pages	22
Journal	SIAM Journal on Applied Mathematics
Volume	70
Issue number	6
DOIs	10.1137/090765201
Publication status	Published - Apr 2010

Fingerprint

Rheometers

Cones

Cone

Liquid

Liquids

Matched Asymptotic Expansions

Asymptotic Solution

Length Scale

Substrate

Scaling

Substrates

Configuration

Approximation

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

Cregan, V. ; O'Brien, S.B.C. ; McKee, Sean. / The shape of a small liquid drop on a cone and plate rheometer. In: SIAM Journal on Applied Mathematics. 2010 ; Vol. 70, No. 6. pp. 2075-2096.

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Cregan, V, O'Brien, SBC & McKee, S 2010, 'The shape of a small liquid drop on a cone and plate rheometer' SIAM Journal on Applied Mathematics, vol. 70, no. 6, pp. 2075-2096. https://doi.org/10.1137/090765201

The shape of a small liquid drop on a cone and plate rheometer. / Cregan, V.; O'Brien, S.B.C.; McKee, Sean.

In: SIAM Journal on Applied Mathematics, Vol. 70, No. 6, 04.2010, p. 2075-2096.

Research output: Contribution to journal › Article

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