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

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

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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 languageEnglish
Pages (from-to)2075-2096
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number6
DOIs
Publication statusPublished - Apr 2010

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Keywords

  • liquid bridge
  • sessile drop
  • pendant drop
  • asymptotics
  • surface tension
  • curvature
  • matched asymptotic expansions

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