Thermocapillary effects on a thin rivulet draining down a heated or cooled surface

D.B. Holland; B.R. Duffy; S.K. Wilson; A C King; Y D Shikhmurzaev

Thermocapillary effects on a thin rivulet draining down a heated or cooled surface

D.B. Holland, B.R. Duffy, S.K. Wilson, A C King (Editor), Y D Shikhmurzaev (Editor)

Mathematics And Statistics

Research output: Contribution to conference › Paper

Abstract

We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid draining down a heated or cooled planar or slowly varying substrate when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular, we find that the variation in surface tension drives a transverse flow that causes fluid particles to spiral down the rivulet in helical vortices. We find that a continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is heated or significantly cooled, but that if it is only slightly cooled then a continuous rivulet is possible only for a sufficiently small volume flux.

Original language	English
Pages	129-136
Number of pages	7
Publication status	Published - 2001
Event	American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics - Washington, USA Duration: 19 Nov 2000 → 21 Nov 2000

Conference

Conference	American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics
City	Washington, USA
Period	19/11/00 → 21/11/00

Keywords

fluid dynamics
numerical analysis
differential equations

Cite this

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title = "Thermocapillary effects on a thin rivulet draining down a heated or cooled surface",

abstract = "We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid draining down a heated or cooled planar or slowly varying substrate when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular, we find that the variation in surface tension drives a transverse flow that causes fluid particles to spiral down the rivulet in helical vortices. We find that a continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is heated or significantly cooled, but that if it is only slightly cooled then a continuous rivulet is possible only for a sufficiently small volume flux.",

keywords = "fluid dynamics, numerical analysis, differential equations",

author = "D.B. Holland and B.R. Duffy and S.K. Wilson and King, {A C} and Shikhmurzaev, {Y D}",

year = "2001",

language = "English",

pages = "129--136",

note = "American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics ; Conference date: 19-11-2000 Through 21-11-2000",

}

TY - CONF

T1 - Thermocapillary effects on a thin rivulet draining down a heated or cooled surface

AU - Holland, D.B.

AU - Duffy, B.R.

AU - Wilson, S.K.

A2 - King, A C

A2 - Shikhmurzaev, Y D

PY - 2001

Y1 - 2001

N2 - We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid draining down a heated or cooled planar or slowly varying substrate when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular, we find that the variation in surface tension drives a transverse flow that causes fluid particles to spiral down the rivulet in helical vortices. We find that a continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is heated or significantly cooled, but that if it is only slightly cooled then a continuous rivulet is possible only for a sufficiently small volume flux.

AB - We use the lubrication approximation to investigate the steady flow of a thin rivulet of viscous fluid draining down a heated or cooled planar or slowly varying substrate when the surface tension of the fluid varies linearly with temperature. Utilizing the (implicit) solution of the governing ordinary differential equation that emerges, we undertake a comprehensive asymptotic and numerical analysis of the flow. In particular, we find that the variation in surface tension drives a transverse flow that causes fluid particles to spiral down the rivulet in helical vortices. We find that a continuous rivulet can run from the top to the bottom of a large horizontal circular cylinder provided that the cylinder is heated or significantly cooled, but that if it is only slightly cooled then a continuous rivulet is possible only for a sufficiently small volume flux.

KW - fluid dynamics

KW - numerical analysis

KW - differential equations

M3 - Paper

SP - 129

EP - 136

T2 - American Physical Society, 53rd Annual Meeting of the Division of Fluid Dynamics

Y2 - 19 November 2000 through 21 November 2000

ER -

Thermocapillary effects on a thin rivulet draining down a heated or cooled surface

Abstract

Conference

Keywords

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Cite this