TY - JOUR

T1 - Theoretical Modeling of Levitated Clusters of Water Droplets Stabilized by Infrared Irradiation

AU - Brewster, M. Q.

N1 - Funding Information:
The first part of this paper (Secs. 1–3 and Figs. 2 and 3) having to do with errors and oversights in Ref. [1] was submitted as a Comment to the Int. J. Heat Mass Transfer in December 2020, but publication of the Comment was declined without addressing or acknowledging these errors and oversights. This work was enabled by support from the H. G. Soo Professorship.
Publisher Copyright:
Copyright © 2022 by ASME.

PY - 2022/4

Y1 - 2022/4

N2 - This paper shows how clusters of radiation-stabilized water droplets levitated in an upward flow of air and water vapor above a heated water surface can be modeled using Spalding’s self-similarity theory of heat and mass transfer and Stefan flow. The model describes equilibrium droplet states, including stability conditions, as well as nonequilibrium (quasi-steady) transient evolution. Equilibrium states are shown to exist when Stefan-flow supersaturation, which has a quadratic-like variation with height above the water surface, and radiation-stabilized equilibrium supersaturation, which is nearly constant with height, are equal. The latter can be predicted by a fundamentally derived function of absorbed radiant flux (linear), droplet radius (linear if opaque), continuum thermal conductivity, and thermodynamic properties. In fact, all of the experimentally observed droplet behavior can be predicted using simple analytical results based on quasi-steady droplet energy and continuum transport. Unsteady droplet energy, Knudsen-layer transport, numerical solutions, and curve-fitting of numerical computations, as used previously in modeling this behavior, are not necessary. An interesting reversal of the usual effect of mass transfer on droplet drag in low-Re flow when levitated droplets are irradiated asymmetrically by significant infrared radiation is also postulated, which relates to the relative importance of normal (pressure) and tangential (shear stress) drag. This theory of radiation-augmented droplet evaporation, condensation, and relative motion in a moving gas has application to conditions in clouds, wherein droplets can experience either net radiative heating or cooling and fluctuating updrafts or downdrafts.

AB - This paper shows how clusters of radiation-stabilized water droplets levitated in an upward flow of air and water vapor above a heated water surface can be modeled using Spalding’s self-similarity theory of heat and mass transfer and Stefan flow. The model describes equilibrium droplet states, including stability conditions, as well as nonequilibrium (quasi-steady) transient evolution. Equilibrium states are shown to exist when Stefan-flow supersaturation, which has a quadratic-like variation with height above the water surface, and radiation-stabilized equilibrium supersaturation, which is nearly constant with height, are equal. The latter can be predicted by a fundamentally derived function of absorbed radiant flux (linear), droplet radius (linear if opaque), continuum thermal conductivity, and thermodynamic properties. In fact, all of the experimentally observed droplet behavior can be predicted using simple analytical results based on quasi-steady droplet energy and continuum transport. Unsteady droplet energy, Knudsen-layer transport, numerical solutions, and curve-fitting of numerical computations, as used previously in modeling this behavior, are not necessary. An interesting reversal of the usual effect of mass transfer on droplet drag in low-Re flow when levitated droplets are irradiated asymmetrically by significant infrared radiation is also postulated, which relates to the relative importance of normal (pressure) and tangential (shear stress) drag. This theory of radiation-augmented droplet evaporation, condensation, and relative motion in a moving gas has application to conditions in clouds, wherein droplets can experience either net radiative heating or cooling and fluctuating updrafts or downdrafts.

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U2 - 10.1115/1.4053415

DO - 10.1115/1.4053415

M3 - Article

AN - SCOPUS:85144602287

SN - 0022-1481

VL - 144

JO - Journal of Heat Transfer

JF - Journal of Heat Transfer

IS - 4

M1 - 043701

ER -