A mathematical model of the evaporation of a thin sessile liquid droplet: comparison between experiment and theory

G.J. Dunn, S.K. Wilson, B.R. Duffy, S. David, K. Sefiane

Research output: Contribution to journalArticle

85 Citations (Scopus)

Abstract

A mathematical model for the quasi-steady diffusion-limited evaporation of a thin axisymmetric sessile droplet of liquid with a pinned contact line is formulated and solved. The model generalises the theoretical model proposed by Deegan et al. [Contact line deposits in an evaporating drop, Phys. Rev. E, 62 (2000) 756-765] to include the effect of evaporative cooling on the saturation concentration of vapour at the free surface of the droplet, and the dependence of the coefficient of diffusion of vapour in the atmosphere on the atmospheric pressure. The predictions of the model are in good qualitative, and in some cases also quantitative, agreement with recent experimental results. In particular, they capture the experimentally observed dependence of the total evaporation rate on the thermal conductivities of the liquid and the substrate, and on the atmospheric pressure.
LanguageEnglish
Pages50-55
Number of pages6
JournalColloids and Surfaces A: Physicochemical and Engineering Aspects
Volume323
Issue number1-3
DOIs
Publication statusPublished - 30 Jun 2008

Fingerprint

mathematical models
Evaporation
evaporation
Mathematical models
Contacts (fluid mechanics)
Atmospheric pressure
atmospheric pressure
Liquids
liquids
Vapors
vapors
evaporative cooling
evaporation rate
Experiments
Thermal conductivity
thermal conductivity
Deposits
deposits
Cooling
saturation

Keywords

  • evaporation
  • liquid droplet
  • evaporative cooling
  • atmosphericpressure

Cite this

@article{5c3056343a234c3196650f3d4f8e42b2,
title = "A mathematical model of the evaporation of a thin sessile liquid droplet: comparison between experiment and theory",
abstract = "A mathematical model for the quasi-steady diffusion-limited evaporation of a thin axisymmetric sessile droplet of liquid with a pinned contact line is formulated and solved. The model generalises the theoretical model proposed by Deegan et al. [Contact line deposits in an evaporating drop, Phys. Rev. E, 62 (2000) 756-765] to include the effect of evaporative cooling on the saturation concentration of vapour at the free surface of the droplet, and the dependence of the coefficient of diffusion of vapour in the atmosphere on the atmospheric pressure. The predictions of the model are in good qualitative, and in some cases also quantitative, agreement with recent experimental results. In particular, they capture the experimentally observed dependence of the total evaporation rate on the thermal conductivities of the liquid and the substrate, and on the atmospheric pressure.",
keywords = "evaporation, liquid droplet, evaporative cooling, atmosphericpressure",
author = "G.J. Dunn and S.K. Wilson and B.R. Duffy and S. David and K. Sefiane",
year = "2008",
month = "6",
day = "30",
doi = "10.1016/j.colsurfa.2007.09.031",
language = "English",
volume = "323",
pages = "50--55",
journal = "Colloids and Surfaces A: Physicochemical and Engineering Aspects",
issn = "0927-7757",
number = "1-3",

}

TY - JOUR

T1 - A mathematical model of the evaporation of a thin sessile liquid droplet

T2 - Colloids and Surfaces A: Physicochemical and Engineering Aspects

AU - Dunn, G.J.

AU - Wilson, S.K.

AU - Duffy, B.R.

AU - David, S.

AU - Sefiane, K.

PY - 2008/6/30

Y1 - 2008/6/30

N2 - A mathematical model for the quasi-steady diffusion-limited evaporation of a thin axisymmetric sessile droplet of liquid with a pinned contact line is formulated and solved. The model generalises the theoretical model proposed by Deegan et al. [Contact line deposits in an evaporating drop, Phys. Rev. E, 62 (2000) 756-765] to include the effect of evaporative cooling on the saturation concentration of vapour at the free surface of the droplet, and the dependence of the coefficient of diffusion of vapour in the atmosphere on the atmospheric pressure. The predictions of the model are in good qualitative, and in some cases also quantitative, agreement with recent experimental results. In particular, they capture the experimentally observed dependence of the total evaporation rate on the thermal conductivities of the liquid and the substrate, and on the atmospheric pressure.

AB - A mathematical model for the quasi-steady diffusion-limited evaporation of a thin axisymmetric sessile droplet of liquid with a pinned contact line is formulated and solved. The model generalises the theoretical model proposed by Deegan et al. [Contact line deposits in an evaporating drop, Phys. Rev. E, 62 (2000) 756-765] to include the effect of evaporative cooling on the saturation concentration of vapour at the free surface of the droplet, and the dependence of the coefficient of diffusion of vapour in the atmosphere on the atmospheric pressure. The predictions of the model are in good qualitative, and in some cases also quantitative, agreement with recent experimental results. In particular, they capture the experimentally observed dependence of the total evaporation rate on the thermal conductivities of the liquid and the substrate, and on the atmospheric pressure.

KW - evaporation

KW - liquid droplet

KW - evaporative cooling

KW - atmosphericpressure

U2 - 10.1016/j.colsurfa.2007.09.031

DO - 10.1016/j.colsurfa.2007.09.031

M3 - Article

VL - 323

SP - 50

EP - 55

JO - Colloids and Surfaces A: Physicochemical and Engineering Aspects

JF - Colloids and Surfaces A: Physicochemical and Engineering Aspects

SN - 0927-7757

IS - 1-3

ER -