Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation

Hyun Geun Lee; Junxiang Yang; Sangkwon Kim; Junseok Kim

doi:10.1016/j.amc.2020.125591

Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation

Hyun Geun Lee, Junxiang Yang, Sangkwon Kim, Junseok Kim

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

15 Citations (Scopus)

Abstract

In this paper, we propose a mathematical model, its numerical scheme, and some computational experiments for droplet evaporation. In order to model the evaporation, a classical Cahn–Hilliard equation with an interfacial evaporation mass flux term is proposed. An unconditionally gradient stable scheme is used to discretize the governing equation, and the multigrid method is applied to solve the resulting system. The proposed model is first validated via a proper interfacial parameter ϵ, and then, the effect of evaporation rate and effect of contact angle on volume and surface area changes are investigated. The numerical results indicate that the dynamics of evaporation are dependent on the contact angle on a solid substrate.

Original language	English
Article number	125591
Journal	Applied Mathematics and Computation
Volume	390
DOIs	https://doi.org/10.1016/j.amc.2020.125591
Publication status	Published - 2021 Feb 1

Bibliographical note

Funding Information:
The first author (H.G. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1C1C1011112 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors thank the reviewers for their constructive and helpful comments on the revision of this article.

Publisher Copyright:
© 2020 Elsevier Inc.

Keywords

Contact angle
Droplet evaporation
Modified Cahn–Hilliard equation

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/j.amc.2020.125591

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title = "Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation",

abstract = "In this paper, we propose a mathematical model, its numerical scheme, and some computational experiments for droplet evaporation. In order to model the evaporation, a classical Cahn–Hilliard equation with an interfacial evaporation mass flux term is proposed. An unconditionally gradient stable scheme is used to discretize the governing equation, and the multigrid method is applied to solve the resulting system. The proposed model is first validated via a proper interfacial parameter ϵ, and then, the effect of evaporation rate and effect of contact angle on volume and surface area changes are investigated. The numerical results indicate that the dynamics of evaporation are dependent on the contact angle on a solid substrate.",

keywords = "Contact angle, Droplet evaporation, Modified Cahn–Hilliard equation",

author = "Lee, {Hyun Geun} and Junxiang Yang and Sangkwon Kim and Junseok Kim",

note = "Funding Information: The first author (H.G. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1C1C1011112 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors thank the reviewers for their constructive and helpful comments on the revision of this article. Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

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doi = "10.1016/j.amc.2020.125591",

language = "English",

volume = "390",

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TY - JOUR

T1 - Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation

AU - Lee, Hyun Geun

AU - Yang, Junxiang

AU - Kim, Sangkwon

AU - Kim, Junseok

N1 - Funding Information: The first author (H.G. Lee) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1C1C1011112 ). The corresponding author (J.S. Kim) was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education ( NRF-2019R1A2C1003053 ). The authors thank the reviewers for their constructive and helpful comments on the revision of this article. Publisher Copyright: © 2020 Elsevier Inc.

PY - 2021/2/1

Y1 - 2021/2/1

N2 - In this paper, we propose a mathematical model, its numerical scheme, and some computational experiments for droplet evaporation. In order to model the evaporation, a classical Cahn–Hilliard equation with an interfacial evaporation mass flux term is proposed. An unconditionally gradient stable scheme is used to discretize the governing equation, and the multigrid method is applied to solve the resulting system. The proposed model is first validated via a proper interfacial parameter ϵ, and then, the effect of evaporation rate and effect of contact angle on volume and surface area changes are investigated. The numerical results indicate that the dynamics of evaporation are dependent on the contact angle on a solid substrate.

AB - In this paper, we propose a mathematical model, its numerical scheme, and some computational experiments for droplet evaporation. In order to model the evaporation, a classical Cahn–Hilliard equation with an interfacial evaporation mass flux term is proposed. An unconditionally gradient stable scheme is used to discretize the governing equation, and the multigrid method is applied to solve the resulting system. The proposed model is first validated via a proper interfacial parameter ϵ, and then, the effect of evaporation rate and effect of contact angle on volume and surface area changes are investigated. The numerical results indicate that the dynamics of evaporation are dependent on the contact angle on a solid substrate.

KW - Contact angle

KW - Droplet evaporation

KW - Modified Cahn–Hilliard equation

UR - http://www.scopus.com/inward/record.url?scp=85089732802&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2020.125591

DO - 10.1016/j.amc.2020.125591

M3 - Article

AN - SCOPUS:85089732802

SN - 0096-3003

VL - 390

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

M1 - 125591

ER -

Modeling and simulation of droplet evaporation using a modified Cahn–Hilliard equation

Abstract

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Keywords

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