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Thermocapillary transport of energy during water evaporation

Fei Duan1, V. K. Badam2, F. Durst2, and C. A. Ward1,*

  • 1Thermodynamics and Kinetics Laboratory, Department of Mechanical and Industrial Engineering, 5 King’s College Road, Toronto, Ontario, Canada M5S 3G8
  • 2Institute of Fluid Mechanics, Friedrich-Alexander-University, Erlangen-Nürnberg Germany, Cauerstrasser 4, D-91058 Erlangen, Germany

  • *Corresponding author. FAX: 416-978-7322. Electronic address: ward@mie.utoronto.ca
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Phys. Rev. E 72, 056303 – Published 2 November, 2005

DOI: https://doi.org/10.1103/PhysRevE.72.056303

Abstract

When evaporation occurs at a spherical water-vapor interface maintained at the circular mouth of a small funnel, studies of the energy transport have indicated that thermal conduction alone does not provide enough energy to evaporate the liquid at the observed rate. If the Gibbs model of the interface is adopted and the “surface-thermal capacity” is assigned a value of 30.6±0.8kJ∕(m2K), then for evaporation experiments with the interfacial temperature in the range −10°C⩽TLV⩽3.5°C and Marangoni number (Ma) in the range 100<Ma<22,000, it was found that if energy transport by both thermocapillary convection and thermal conduction were taken into account, conservation of energy was fully satisfied. The question addressed herein is whether the assigned value of the surface-thermal capacity is an ad hoc empirical parameter or a property of the water-vapor interface that can be used in other circumstances. Accordingly, a series of experiments has been conducted in which water evaporated at cylindrical interfaces that were, on average, 4.4 times larger in area than that of the spherical interfaces used to measure the surface-thermal capacity initially. It is shown that using the value of the surface-thermal capacity determined at a spherical interface, the energy transported by thermocapillary convection and thermal conduction at a cylindrical interface is sufficient to evaporate the liquid at the observed rate. Knowing the value of the surface-thermal capacity also allows the local evaporation flux to be calculated from the measured temperature profiles in the liquid and vapor phases. The calculated local evaporation flux can then be used with statistical rate theory to calculate the vapor-phase pressure along the interface. The predicted mean vapor-phase pressure is in close agreement with that measured, and the predicted pressure gradient is consistent with that expected when thermocapillary convection is present.

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See Also

Surface excess properties from energy transport measurements during water evaporation

Fei Duan and C. A. Ward
Phys. Rev. E 72, 056302 (2005)

Surface-thermal capacity of D2O from measurements made during steady-state evaporation

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Phys. Rev. E 72, 056304 (2005)

Article Text

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Phys. Rev. E 72, 056303– Published 2 November, 2005
  • Received 21 August 2004

© 2005 American Physical Society

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