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

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

Research output: Contribution to journalArticle

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.
LanguageEnglish
Pages2075-2096
Number of pages22
JournalSIAM Journal on Applied Mathematics
Volume70
Issue number6
DOIs
Publication statusPublished - 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, 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.
@article{cb19da1cfa4945e9977a98d1138657a6,
title = "The shape of a small liquid drop on a cone and plate rheometer",
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.",
keywords = "liquid bridge, sessile drop, pendant drop, asymptotics, surface tension, curvature, matched asymptotic expansions",
author = "V. Cregan and S.B.C. O'Brien and Sean McKee",
year = "2010",
month = "4",
doi = "10.1137/090765201",
language = "English",
volume = "70",
pages = "2075--2096",
journal = "SIAM Journal on Applied Mathematics",
issn = "0036-1399",
number = "6",

}

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 journalArticle

TY - JOUR

T1 - The shape of a small liquid drop on a cone and plate rheometer

AU - Cregan, V.

AU - O'Brien, S.B.C.

AU - McKee, Sean

PY - 2010/4

Y1 - 2010/4

N2 - 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.

AB - 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.

KW - liquid bridge

KW - sessile drop

KW - pendant drop

KW - asymptotics

KW - surface tension

KW - curvature

KW - matched asymptotic expansions

UR - http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=SMJMAP000070000006002075000001&idtype=cvips&gifs=yes

U2 - 10.1137/090765201

DO - 10.1137/090765201

M3 - Article

VL - 70

SP - 2075

EP - 2096

JO - SIAM Journal on Applied Mathematics

T2 - SIAM Journal on Applied Mathematics

JF - SIAM Journal on Applied Mathematics

SN - 0036-1399

IS - 6

ER -