A Study of Droplet Evaporation

Koffi Sagna; Amah D’Almeida

doi:doi:10.11648/j.ajmp.20130202.17

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A Study of Droplet Evaporation

Koffi Sagna, Amah D’Almeida

Published in American Journal of Modern Physics (Volume 2, Issue 2)

Received: 12 December 2012 Accepted: Published: 10 March 2013

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Abstract

We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical d^2 law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.

Published in	American Journal of Modern Physics (Volume 2, Issue 2)
DOI	10.11648/j.ajmp.20130202.17
Page(s)	71-76
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Drop Evaporation; d^2-Law; Quasi- Steady Recession; Mass Flow; Temperature

References

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[2]	Arias-Zugasti M., Garcia-Ybarra P., Castillo J. L., Unsteady Effects in Droplet Vaporisation Lifetimes at Subcritical and Supercritical Conditions, Combust. Sci. and Tech.,153,2000,179–191.
[3]	Arias-Zugasti M., Garcia-Ybarra P., Castillo J. L., Droplet Vaporisation at critical Conditions :Long-time Convec-tive-diffusive profiles along the critical isobar, Physical Re-view E,60, 3, 1999, 2930-2941.
[4]	Préau S., Ouazzani J.,Zappoli B.,Prud’homme R., Supercritical density relaxation as a new approach of droplet vaporization, Phys. Fluids,16 (11),2004,4075–4087.
[5]	Prud’homme R., d’Almeida A., Sphères fluides avec injection, Colloque du GDR MFA, CD Rom CNES,038490-64,2008.
[6]	D’Almeida A., Prud’homme R., Evaporation de gouttes : lois de récession du rayon, 19ème Congrès Français de Mécanique, Marseille, 24-28 août 2009.
[7]	Godsave G. A. E., Studies of the combustion of drops in a fuel spray. The burning of single drops of fuel, in Fourth Symposium on Combustion,The Combustion Institute (ed), 1953,818–830.
[8]	Waldman C., Theory of non-steady state droplet combustion, Proc. Combust. Inst.,15, 429, 1971.
[9]	Sanchez-Tarifa C., Crespo A., Fraga E.,Theoretical model for the combustion of droplets in super-critical conditions and gas pockets, Astronautica Acta,17,685–692, 1972.
[10]	Spalding D. B.,Combustion of fuel particles, Fuel,30, 1951.
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[12]	S. Saengkaew, T. Charinpanikul, C. Laurent, Y. Biscos, G. Lavergne, G. Gouesbet,and G. Grehan, "Processing of indi-vidual rainbow signals", Exp. Fluids, vol. 48,pp. 111-119, 2010.
[13]	S. Saengkaew, D. Bonin, P. Briard, and G. Gréhan, "Réfractométrie d'arc-en-ciel global à faisceau pulsé : Estimation des concentrations et des distancesinter-particulaires", in Congrès Francophone de Techniques Laser (CFTL2010),Vandoeuvre-lès-Nancy (France), 14-17 septembre 2010.

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Koffi Sagna, Amah D’Almeida. (2013). A Study of Droplet Evaporation. American Journal of Modern Physics, 2(2), 71-76. https://doi.org/10.11648/j.ajmp.20130202.17

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Koffi Sagna; Amah D’Almeida. A Study of Droplet Evaporation. Am. J. Mod. Phys. 2013, 2(2), 71-76. doi: 10.11648/j.ajmp.20130202.17

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Koffi Sagna, Amah D’Almeida. A Study of Droplet Evaporation. Am J Mod Phys. 2013;2(2):71-76. doi: 10.11648/j.ajmp.20130202.17

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@article{10.11648/j.ajmp.20130202.17,
  author = {Koffi Sagna and Amah D’Almeida},
  title = {A Study of Droplet Evaporation},
  journal = {American Journal of Modern Physics},
  volume = {2},
  number = {2},
  pages = {71-76},
  doi = {10.11648/j.ajmp.20130202.17},
  url = {https://doi.org/10.11648/j.ajmp.20130202.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130202.17},
  abstract = {We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical d^2 law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.},
 year = {2013}
}

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TY  - JOUR
T1  - A Study of Droplet Evaporation
AU  - Koffi Sagna
AU  - Amah D’Almeida
Y1  - 2013/03/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130202.17
DO  - 10.11648/j.ajmp.20130202.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 71
EP  - 76
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20130202.17
AB  - We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical d^2 law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.
VL  - 2
IS  - 2
ER  -

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Author Information

Koffi Sagna

Laboratory of Solar Energy, Department of Physics, Faculty of Sciences, Université de Lomé, Lomé TOGO
Amah D’Almeida

Laboratory of Solar Energy, Department of Physics, Faculty of Sciences, Université de Lomé, Lomé TOGO; Department of Mathematics, Faculty of Sciences, Université de Lomé, Lomé TOGO

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APA Style

Koffi Sagna, Amah D’Almeida. (2013). A Study of Droplet Evaporation. American Journal of Modern Physics, 2(2), 71-76. https://doi.org/10.11648/j.ajmp.20130202.17

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ACS Style

Koffi Sagna; Amah D’Almeida. A Study of Droplet Evaporation. Am. J. Mod. Phys. 2013, 2(2), 71-76. doi: 10.11648/j.ajmp.20130202.17

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AMA Style

Koffi Sagna, Amah D’Almeida. A Study of Droplet Evaporation. Am J Mod Phys. 2013;2(2):71-76. doi: 10.11648/j.ajmp.20130202.17

Copy | Download

@article{10.11648/j.ajmp.20130202.17,
  author = {Koffi Sagna and Amah D’Almeida},
  title = {A Study of Droplet Evaporation},
  journal = {American Journal of Modern Physics},
  volume = {2},
  number = {2},
  pages = {71-76},
  doi = {10.11648/j.ajmp.20130202.17},
  url = {https://doi.org/10.11648/j.ajmp.20130202.17},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmp.20130202.17},
  abstract = {We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical d^2 law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.},
 year = {2013}
}

Copy | Download

TY  - JOUR
T1  - A Study of Droplet Evaporation
AU  - Koffi Sagna
AU  - Amah D’Almeida
Y1  - 2013/03/10
PY  - 2013
N1  - https://doi.org/10.11648/j.ajmp.20130202.17
DO  - 10.11648/j.ajmp.20130202.17
T2  - American Journal of Modern Physics
JF  - American Journal of Modern Physics
JO  - American Journal of Modern Physics
SP  - 71
EP  - 76
PB  - Science Publishing Group
SN  - 2326-8891
UR  - https://doi.org/10.11648/j.ajmp.20130202.17
AB  - We investigate the problem of the vaporization of a liquid droplet in a hotter environment of the same fluid. The Navier-Stokes equations are solved for a physical model which assumes spherical symmetry and laminar conditions in the quasi steady case. The study is mainly characterized by the fact that the equation of conservation of momentum is effectively taken into account and the velocity of the drop is not always uniform. Recession laws which are different from the classical d^2 law can be derived from the zeroth order approximation solution. Additional assumptions on the thermodynamical properties of the gas phase in subcritical conditions restore the classical law and permit the determination of an analytic expression for the vaporization ratio K. The analysis of the evolution of the temperature, the density and the velocity in the droplet and in the gaseous phase reveals the existence of shock waves which develop from the center of the droplet towards its boundary and an unbalanced energetic layer attached to the interface when the velocity is not uniform in the drop.
VL  - 2
IS  - 2
ER  -

Copy | Download