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

Cregan, V. and O'Brien, S.B.C. and McKee, Sean (2010) The shape of a small liquid drop on a cone and plate rheometer. SIAM Journal on Applied Mathematics, 70 (6). pp. 2075-2096. ISSN 0036-1399

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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.