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Physics of Fluids / Volume 24 / Issue 2 / ARTICLES / Interfacial Flows

Phys. Fluids 24, 022102 (2012); http://dx.doi.org/10.1063/1.3681813 (11 pages)

Thermocapillary motion of a slender viscous droplet in a channel

E. Katz1, M. Haj2, A. M. Leshansky1, and A. Nepomnyashchy2

1Department of Chemical Engineering, Technion, Haifa 32000, Israel
2Department of Mathematics, Technion, Haifa 32000, Israel

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(Received 30 June 2011; accepted 10 January 2012; published online 7 February 2012)

We extend the previously developed low-capillary-number asymptotic theory of thermocapillary motion of a long bubble and a moderately viscous droplet in a channel [S. K. Wilson, “The effect of an axial temperature gradient on the steady motion of a large droplet in a tube,” J. Eng. Math. 29, 205 (1995)10.1007/BF00042854; A. Mazouchi and G. M. Homsy, “Thermocapillary migration of long bubbles in cylindrical capillary tubes,” Phys. Fluids 12, 542 (2000)10.1063/1.870260] toward droplets with an arbitrary viscosity. A generalized modified Landau-Levich-Bretherton equation, governing the thickness of the carrier liquid film entrained between the droplet and the channel wall in the transition region between constant thickness film and constant curvature cap, is solved numerically. The resulting droplet velocity is determined applying the mass balance and it is a function of two dimensionless parameters, the modified capillary number, Δσ*, equal to the surface tension variance over a distance of channel half-width scaled with the mean surface tension, and the inner-to-outer liquid viscosity ratio, λ. It is found that the droplet speed decreases with the increase in droplet viscosity, as expected, while this retardation becomes more operative upon the increase in Δσ*.

© 2012 American Institute of Physics

Article Outline

  1. INTRODUCTION
  2. PROBLEM DEFINITION
  3. MATHEMATICAL MODEL AND GOVERNING EQUATIONS
  4. NUMERICAL SOLUTION AND MATCHING
  5. ENTRAINED FILM THICKNESS AND DROPLET SPEED

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KEYWORDS and PACS

Keywords

bubbles, capillarity, channel flow, drops, liquid films

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.3681813

PUBLICATION DATA

ISSN

1070-6631 (print)  
1089-7666 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

For access to fully linked references, you need to log in.
    A. Mazouchi and G. M. Homsy, “Thermocapillary migration of long bubbles in cylindrical capillary tubes,” Phys. Fluids 12, 542 (2000)PHFLE6000012000003000542000001.


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