Unsteady motion of a long bubble or droplet in a self-rewetting system

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Abstract

Motivated by the potential use of self-rewetting fluids (i.e. fluids that exhibit a non-monotonic variation of surface tension with temperature) in various heat transfer applications, in the present work we formulate and analyse a theoretical model for the unsteady motion of a long bubble or droplet in a self-rewetting system in a non-uniformly heated tube due to a combination of Marangoni effects due to the variation of surface tension with temperature, gravitational effects due to the density difference between the two fluids, and an imposed background flow along the tube. We find that the evolution of the shape (but not of the position) of the bubble or droplet is driven entirely by Marangoni effects, and depends on the initial value of its radius in relation to a critical value. In the case in which Marangoni effects are absent the bubble or droplet always moves with constant velocity without changing shape. In the case in which only Marangoni effects are present the bubble or droplet either always moves away from or always moves towards the position of minimum surface tension; in the latter case it ultimately fills the entire cross-section of the tube at a final stationary position which is closer to the position of minimum surface tension than its original position. In the cases in which either only Marangoni effects and gravitational effects or only Marangoni effects and background-flow effects are present the competition between the two effects can lead to a non-monotonic evolution of the position of the centre of mass of the bubble or droplet. The behaviour of a self-rewetting system described in the present work is qualitatively different from that for ordinary fluids, in which case the bubble or droplet always moves with constant velocity without changing shape.
LanguageEnglish
Article number123603
JournalPhysical Review Fluids
Volume3
Issue number12
DOIs
Publication statusPublished - 17 Dec 2018

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Marangoni Effect
Bubbles (in fluids)
Droplet
Bubble
Surface Tension
Surface tension
Motion
Gravitational effects
Fluid
Tube
Fluids
Barycentre
Theoretical Model
Critical value
Heat Transfer
Cross section
Radius
Entire
Heat transfer
Temperature

Keywords

  • self-rewetting fluids
  • heat-transfer applications
  • unsteady motion
  • Marangoni effects

Cite this

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title = "Unsteady motion of a long bubble or droplet in a self-rewetting system",
abstract = "Motivated by the potential use of self-rewetting fluids (i.e. fluids that exhibit a non-monotonic variation of surface tension with temperature) in various heat transfer applications, in the present work we formulate and analyse a theoretical model for the unsteady motion of a long bubble or droplet in a self-rewetting system in a non-uniformly heated tube due to a combination of Marangoni effects due to the variation of surface tension with temperature, gravitational effects due to the density difference between the two fluids, and an imposed background flow along the tube. We find that the evolution of the shape (but not of the position) of the bubble or droplet is driven entirely by Marangoni effects, and depends on the initial value of its radius in relation to a critical value. In the case in which Marangoni effects are absent the bubble or droplet always moves with constant velocity without changing shape. In the case in which only Marangoni effects are present the bubble or droplet either always moves away from or always moves towards the position of minimum surface tension; in the latter case it ultimately fills the entire cross-section of the tube at a final stationary position which is closer to the position of minimum surface tension than its original position. In the cases in which either only Marangoni effects and gravitational effects or only Marangoni effects and background-flow effects are present the competition between the two effects can lead to a non-monotonic evolution of the position of the centre of mass of the bubble or droplet. The behaviour of a self-rewetting system described in the present work is qualitatively different from that for ordinary fluids, in which case the bubble or droplet always moves with constant velocity without changing shape.",
keywords = "self-rewetting fluids, heat-transfer applications, unsteady motion, Marangoni effects",
author = "Duffy, {B. R.} and Wilson, {S. K.} and Conn, {J. J. A.} and K. Sefiane",
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AU - Wilson, S. K.

AU - Conn, J. J. A.

AU - Sefiane, K.

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N2 - Motivated by the potential use of self-rewetting fluids (i.e. fluids that exhibit a non-monotonic variation of surface tension with temperature) in various heat transfer applications, in the present work we formulate and analyse a theoretical model for the unsteady motion of a long bubble or droplet in a self-rewetting system in a non-uniformly heated tube due to a combination of Marangoni effects due to the variation of surface tension with temperature, gravitational effects due to the density difference between the two fluids, and an imposed background flow along the tube. We find that the evolution of the shape (but not of the position) of the bubble or droplet is driven entirely by Marangoni effects, and depends on the initial value of its radius in relation to a critical value. In the case in which Marangoni effects are absent the bubble or droplet always moves with constant velocity without changing shape. In the case in which only Marangoni effects are present the bubble or droplet either always moves away from or always moves towards the position of minimum surface tension; in the latter case it ultimately fills the entire cross-section of the tube at a final stationary position which is closer to the position of minimum surface tension than its original position. In the cases in which either only Marangoni effects and gravitational effects or only Marangoni effects and background-flow effects are present the competition between the two effects can lead to a non-monotonic evolution of the position of the centre of mass of the bubble or droplet. The behaviour of a self-rewetting system described in the present work is qualitatively different from that for ordinary fluids, in which case the bubble or droplet always moves with constant velocity without changing shape.

AB - Motivated by the potential use of self-rewetting fluids (i.e. fluids that exhibit a non-monotonic variation of surface tension with temperature) in various heat transfer applications, in the present work we formulate and analyse a theoretical model for the unsteady motion of a long bubble or droplet in a self-rewetting system in a non-uniformly heated tube due to a combination of Marangoni effects due to the variation of surface tension with temperature, gravitational effects due to the density difference between the two fluids, and an imposed background flow along the tube. We find that the evolution of the shape (but not of the position) of the bubble or droplet is driven entirely by Marangoni effects, and depends on the initial value of its radius in relation to a critical value. In the case in which Marangoni effects are absent the bubble or droplet always moves with constant velocity without changing shape. In the case in which only Marangoni effects are present the bubble or droplet either always moves away from or always moves towards the position of minimum surface tension; in the latter case it ultimately fills the entire cross-section of the tube at a final stationary position which is closer to the position of minimum surface tension than its original position. In the cases in which either only Marangoni effects and gravitational effects or only Marangoni effects and background-flow effects are present the competition between the two effects can lead to a non-monotonic evolution of the position of the centre of mass of the bubble or droplet. The behaviour of a self-rewetting system described in the present work is qualitatively different from that for ordinary fluids, in which case the bubble or droplet always moves with constant velocity without changing shape.

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KW - heat-transfer applications

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