Evaporation of a thin droplet on a thin substrate with a high thermal resistance

Gavin Dunn, S.K. Wilson, B.R. Duffy, K. Sefiane

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Abstract

A mathematical model for the quasi-steady evaporation of a thin liquid droplet on a thin substrate that incorporates the dependence of the saturation concentration of vapour at the free surface of the droplet on temperature is used to examine an atypical situation in which the substrate has a high thermal resistance relative to the droplet (i.e. it is highly insulating and/or is thick relative to the droplet). In this situation diffusion of heat through the substrate is the rate-limiting evaporative process and at leading order the local mass flux is spatially uniform, the total evaporation rate is proportional to the surface area of the droplet, and the droplet is uniformly cooled. In particular, the qualitative differences between the predictions of the present model in this situation and those of the widely used 'basic' model in which the saturation concentration is independent of temperature are highlighted.
Original languageEnglish
Article number052101
Number of pages7
JournalPhysics of Fluids
Volume21
DOIs
Publication statusPublished - 2009

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thermal resistance
evaporation
saturation
evaporation rate
mathematical models
vapors
heat
temperature
liquids
predictions

Keywords

  • quasisteady evaporation
  • thin droplet
  • mathematical model
  • substrate

Cite this

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Evaporation of a thin droplet on a thin substrate with a high thermal resistance. / Dunn, Gavin; Wilson, S.K.; Duffy, B.R.; Sefiane, K.

In: Physics of Fluids, Vol. 21, 052101, 2009.

Research output: Contribution to journalArticle

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AU - Dunn, Gavin

AU - Wilson, S.K.

AU - Duffy, B.R.

AU - Sefiane, K.

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AB - A mathematical model for the quasi-steady evaporation of a thin liquid droplet on a thin substrate that incorporates the dependence of the saturation concentration of vapour at the free surface of the droplet on temperature is used to examine an atypical situation in which the substrate has a high thermal resistance relative to the droplet (i.e. it is highly insulating and/or is thick relative to the droplet). In this situation diffusion of heat through the substrate is the rate-limiting evaporative process and at leading order the local mass flux is spatially uniform, the total evaporation rate is proportional to the surface area of the droplet, and the droplet is uniformly cooled. In particular, the qualitative differences between the predictions of the present model in this situation and those of the widely used 'basic' model in which the saturation concentration is independent of temperature are highlighted.

KW - quasisteady evaporation

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