Heating and evaporation of a mono-component spheroidal droplet with non-uniform surface temperature

Dmitry Antonov; Simona Tonini; Gianpietro Cossali; Pavel Stryzhak; Sergei Sazhin

doi:10.1016/j.apm.2023.10.019

Heating and evaporation of a mono-component spheroidal droplet with non-uniform surface temperature

Dmitry Antonov, Simona Tonini, Gianpietro Cossali, Pavel Stryzhak, Sergei Sazhin

School of Arch, Tech and Eng

Research output: Contribution to journal › Article › peer-review

Abstract

A new mathematical model for spheroidal droplet heating and evaporation is proposed. This model takes into account the effect of liquid finite thermal conductivity and is based on the previously obtained analytical solution for the vapour mass fraction at the droplet surface and a new correlation for the convective heat transfer coefficient incorporated into the numerical code. The heat transfer equation in the liquid phase is solved numerically using the finite-element heat transfer module of COMSOL Multiphysics. It is shown that the lifetime of spheroidal (prolate and oblate) droplets is shorter than that of spherical droplets of the same volume. The difference in the lifetimes of spheroidal and spherical droplets, predicted by the new model, is shown to increase with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. As in the case of stationary spherical droplets, the d 2 -law is shown to be valid for spheroidal droplets after the completion of the heat-up period. The predictions of this model agree with experimental observations. The duration of the heat-up period is shown to decrease with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. The maximal surface temperatures are predicted near the regions where the surface curvature is maximal. The aspect ratios are shown to be weak functions of time, in agreement with experimental observations.

Original language	English
Pages (from-to)	687-703
Number of pages	17
Journal	Applied Mathematical Modelling
Volume	125
Issue number	Part B
DOIs	https://doi.org/10.1016/j.apm.2023.10.019
Publication status	Published - 13 Oct 2023

Bibliographical note

Funding Information:
The authors are grateful to the Ministry of Science and Higher Education of the Russian Federation (Grant 075-15-2021-575 ) and the Tomsk Polytechnic University (TPU) development program, Priority 2030 ( Priority-2030-NIP/EB-038-375-2023 ) for their financial support. Grant 075-15-2021-575 supported the contributions by D Antonov (who contributed mainly to the development of the numerical code, formal analysis, and performance of the experiments) and S Sazhin (who coordinated the work on the paper, and contributed to formal analysis, and writing and editing the paper). Grant Priority 2030 supported the contributions by S Tonini and G Cossali (who were mainly responsible for the development of the model and its implementation in the numerical code used in the analysis) and P Strizhak (who contributed mainly to the development of the experimental program and comparison of the experimental results with predictions of the model). The research presented in this paper was initiated during work on a project supported by the Royal Society (United Kingdom) (Grant IEC 192007 ).

Publisher Copyright:
© 2023 The Author(s)

Keywords

Spheroidal droplet
Heating
Evaporation
Mathematical model
COMSOL multiphysics
Couples solution

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Cite this

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title = "Heating and evaporation of a mono-component spheroidal droplet with non-uniform surface temperature",

abstract = "A new mathematical model for spheroidal droplet heating and evaporation is proposed. This model takes into account the effect of liquid finite thermal conductivity and is based on the previously obtained analytical solution for the vapour mass fraction at the droplet surface and a new correlation for the convective heat transfer coefficient incorporated into the numerical code. The heat transfer equation in the liquid phase is solved numerically using the finite-element heat transfer module of COMSOL Multiphysics. It is shown that the lifetime of spheroidal (prolate and oblate) droplets is shorter than that of spherical droplets of the same volume. The difference in the lifetimes of spheroidal and spherical droplets, predicted by the new model, is shown to increase with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. As in the case of stationary spherical droplets, the d 2 -law is shown to be valid for spheroidal droplets after the completion of the heat-up period. The predictions of this model agree with experimental observations. The duration of the heat-up period is shown to decrease with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. The maximal surface temperatures are predicted near the regions where the surface curvature is maximal. The aspect ratios are shown to be weak functions of time, in agreement with experimental observations.",

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author = "Dmitry Antonov and Simona Tonini and Gianpietro Cossali and Pavel Stryzhak and Sergei Sazhin",

note = "Funding Information: The authors are grateful to the Ministry of Science and Higher Education of the Russian Federation (Grant 075-15-2021-575 ) and the Tomsk Polytechnic University (TPU) development program, Priority 2030 ( Priority-2030-NIP/EB-038-375-2023 ) for their financial support. Grant 075-15-2021-575 supported the contributions by D Antonov (who contributed mainly to the development of the numerical code, formal analysis, and performance of the experiments) and S Sazhin (who coordinated the work on the paper, and contributed to formal analysis, and writing and editing the paper). Grant Priority 2030 supported the contributions by S Tonini and G Cossali (who were mainly responsible for the development of the model and its implementation in the numerical code used in the analysis) and P Strizhak (who contributed mainly to the development of the experimental program and comparison of the experimental results with predictions of the model). The research presented in this paper was initiated during work on a project supported by the Royal Society (United Kingdom) (Grant IEC 192007 ). Publisher Copyright: {\textcopyright} 2023 The Author(s)",

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AU - Tonini, Simona

AU - Cossali, Gianpietro

AU - Stryzhak, Pavel

AU - Sazhin, Sergei

N1 - Funding Information: The authors are grateful to the Ministry of Science and Higher Education of the Russian Federation (Grant 075-15-2021-575 ) and the Tomsk Polytechnic University (TPU) development program, Priority 2030 ( Priority-2030-NIP/EB-038-375-2023 ) for their financial support. Grant 075-15-2021-575 supported the contributions by D Antonov (who contributed mainly to the development of the numerical code, formal analysis, and performance of the experiments) and S Sazhin (who coordinated the work on the paper, and contributed to formal analysis, and writing and editing the paper). Grant Priority 2030 supported the contributions by S Tonini and G Cossali (who were mainly responsible for the development of the model and its implementation in the numerical code used in the analysis) and P Strizhak (who contributed mainly to the development of the experimental program and comparison of the experimental results with predictions of the model). The research presented in this paper was initiated during work on a project supported by the Royal Society (United Kingdom) (Grant IEC 192007 ). Publisher Copyright: © 2023 The Author(s)

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N2 - A new mathematical model for spheroidal droplet heating and evaporation is proposed. This model takes into account the effect of liquid finite thermal conductivity and is based on the previously obtained analytical solution for the vapour mass fraction at the droplet surface and a new correlation for the convective heat transfer coefficient incorporated into the numerical code. The heat transfer equation in the liquid phase is solved numerically using the finite-element heat transfer module of COMSOL Multiphysics. It is shown that the lifetime of spheroidal (prolate and oblate) droplets is shorter than that of spherical droplets of the same volume. The difference in the lifetimes of spheroidal and spherical droplets, predicted by the new model, is shown to increase with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. As in the case of stationary spherical droplets, the d 2 -law is shown to be valid for spheroidal droplets after the completion of the heat-up period. The predictions of this model agree with experimental observations. The duration of the heat-up period is shown to decrease with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. The maximal surface temperatures are predicted near the regions where the surface curvature is maximal. The aspect ratios are shown to be weak functions of time, in agreement with experimental observations.

AB - A new mathematical model for spheroidal droplet heating and evaporation is proposed. This model takes into account the effect of liquid finite thermal conductivity and is based on the previously obtained analytical solution for the vapour mass fraction at the droplet surface and a new correlation for the convective heat transfer coefficient incorporated into the numerical code. The heat transfer equation in the liquid phase is solved numerically using the finite-element heat transfer module of COMSOL Multiphysics. It is shown that the lifetime of spheroidal (prolate and oblate) droplets is shorter than that of spherical droplets of the same volume. The difference in the lifetimes of spheroidal and spherical droplets, predicted by the new model, is shown to increase with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. As in the case of stationary spherical droplets, the d 2 -law is shown to be valid for spheroidal droplets after the completion of the heat-up period. The predictions of this model agree with experimental observations. The duration of the heat-up period is shown to decrease with increasing aspect ratios for prolate droplets and decreasing aspect ratios for oblate droplets. The maximal surface temperatures are predicted near the regions where the surface curvature is maximal. The aspect ratios are shown to be weak functions of time, in agreement with experimental observations.

KW - Spheroidal droplet

KW - Heating

KW - Evaporation

KW - Mathematical model

KW - COMSOL multiphysics

KW - Couples solution

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DO - 10.1016/j.apm.2023.10.019

M3 - Article

SN - 0307-904X

VL - 125

SP - 687

EP - 703

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

IS - Part B

ER -

Heating and evaporation of a mono-component spheroidal droplet with non-uniform surface temperature

Abstract

Bibliographical note

Keywords

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