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The Influence of Curvature on the Modelling of Droplet Evaporation at Different Scales

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Droplet Interactions and Spray Processes

Part of the book series: Fluid Mechanics and Its Applications ((FMIA,volume 121))

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Abstract

The evaporation of liquid drops in stagnant gaseous environment is modelled, accounting for the effect of drop curvature and size at the macro- and microscopic scales. At the macro-scale level, the validity of the conjectured dependence of the local fluxes on the drop surface curvature is analysed. Analytical solutions to the gas-phase conservation equations for five drop shapes (sphere, oblate and prolate spheroids and inverse oblate and prolate spheroids), under uniform Dirichlet boundary conditions, are used to calculate the local vapour and heat fluxes. The analysis shows that in general non-dimensional fluxes do not solely depend on local curvature, but possibly the effect of the whole drop shape must be taken into account. At the micro-scale level, the equilibrium vapour pressure at a convex curved surface is higher than that at a flat surface, thus leading to a considerable enhancement of the evaporation rate for nanometre sized droplets. To model the increase in equilibrium vapour pressure, we consider the Kelvin correction. Our analysis shows that the Kelvin correction is strictly required for droplet radii below 20 Å, as typically encountered for modelling the growth of critical clusters in phase transition processes initiated by homogeneous nucleation. At these conditions, it is mandatory to consider also the repartition of molecules in the different phases, in order to prevent a significant overestimation of the equilibrium vapour pressure.

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Authors and Affiliations

  1. Institute of Aerospace Thermodynamics (ITLR), University of Stuttgart, Stuttgart, Germany

    Grazia Lamanna

  2. Department of Engineering and Applied Sciences, University of Bergamo, Bergamo, Italy

    Gianpietro Elvio Cossali & Simona Tonini

Authors
  1. Grazia Lamanna
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  2. Gianpietro Elvio Cossali
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  3. Simona Tonini
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Corresponding author

Correspondence to Grazia Lamanna .

Editor information

Editors and Affiliations

  1. Institute of Aerospace Thermodynamics, University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Grazia Lamanna

  2. Dipartimento di Ingegneria e Scienze Applicate, Università degli Studi di Bergamo, Dalmine, Bergamo, Italy

    Simona Tonini

  3. Dipartimento di Ingegneria e Scienze Applicate, Università degli Studi di Bergamo, Dalmine, Bergamo, Italy

    Gianpietro Elvio Cossali

  4. Institute of Aerospace Thermodynamics, University of Stuttgart, Stuttgart, Baden-Württemberg, Germany

    Bernhard Weigand

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Lamanna, G., Cossali, G.E., Tonini, S. (2020). The Influence of Curvature on the Modelling of Droplet Evaporation at Different Scales. In: Lamanna, G., Tonini, S., Cossali, G., Weigand, B. (eds) Droplet Interactions and Spray Processes. Fluid Mechanics and Its Applications, vol 121. Springer, Cham. https://doi.org/10.1007/978-3-030-33338-6_21

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  • DOI: https://doi.org/10.1007/978-3-030-33338-6_21

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-33337-9

  • Online ISBN: 978-3-030-33338-6

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