Dynamics of a viscous thread on a non-planar substrate

Mark Bowen, John R. King

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations.

Original languageEnglish
Pages (from-to)39-62
Number of pages24
JournalJournal of Engineering Mathematics
Volume80
Issue number1
DOIs
Publication statusPublished - 2013

Fingerprint

Thread
Substrate
Wedge
Fluids
Substrates
Topography
Drainage
Foams
Reduced Model
Convection-diffusion Equation
Foam
Viscous Fluid
Numerical Computation
Geometry
Liquids
Liquid
Fluid
Model
Convection
Context

Keywords

  • Asymptotics
  • Capillary flow
  • Self-similarity
  • Thin film

ASJC Scopus subject areas

  • Mathematics(all)
  • Engineering(all)

Cite this

Dynamics of a viscous thread on a non-planar substrate. / Bowen, Mark; King, John R.

In: Journal of Engineering Mathematics, Vol. 80, No. 1, 2013, p. 39-62.

Research output: Contribution to journalArticle

@article{7cbe91d76fc7402590b19769dd896e2a,
title = "Dynamics of a viscous thread on a non-planar substrate",
abstract = "We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations.",
keywords = "Asymptotics, Capillary flow, Self-similarity, Thin film",
author = "Mark Bowen and King, {John R.}",
year = "2013",
doi = "10.1007/s10665-012-9571-z",
language = "English",
volume = "80",
pages = "39--62",
journal = "Journal of Engineering Mathematics",
issn = "0022-0833",
publisher = "Springer Netherlands",
number = "1",

}

TY - JOUR

T1 - Dynamics of a viscous thread on a non-planar substrate

AU - Bowen, Mark

AU - King, John R.

PY - 2013

Y1 - 2013

N2 - We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations.

AB - We derive a general reduced model for the flow of a slender thread of viscous fluid on a grooved substrate. Specific choices of the substrate topography allow further analytic progress to be made, and we subsequently focus on a convection-diffusion equation governing the evolution of viscous liquid in a wedge geometry. The model equation that arises also appears in the context of foam drainage, and we take the opportunity to review and compare the results from both applications. After summarising the constant mass results, we introduce a time-dependent fluid influx at one end of the wedge. The analytical results are supported by numerical computations.

KW - Asymptotics

KW - Capillary flow

KW - Self-similarity

KW - Thin film

UR - http://www.scopus.com/inward/record.url?scp=84876824199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84876824199&partnerID=8YFLogxK

U2 - 10.1007/s10665-012-9571-z

DO - 10.1007/s10665-012-9571-z

M3 - Article

AN - SCOPUS:84876824199

VL - 80

SP - 39

EP - 62

JO - Journal of Engineering Mathematics

JF - Journal of Engineering Mathematics

SN - 0022-0833

IS - 1

ER -