Phase-field modeling and computer simulation of the coffee-ring effect

Junxiang Yang; Hyundong Kim; Chaeyoung Lee; Sangkwon Kim; Jian Wang; Sungha Yoon; Jintae Park; Junseok Kim

doi:10.1007/s00162-020-00544-w

Phase-field modeling and computer simulation of the coffee-ring effect

Junxiang Yang, Hyundong Kim, Chaeyoung Lee, Sangkwon Kim, Jian Wang, Sungha Yoon, Jintae Park, Junseok Kim

Department of Mathematics

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

4 Citations (Scopus)

Abstract

In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.

Original language	English
Pages (from-to)	679-692
Number of pages	14
Journal	Theoretical and Computational Fluid Dynamics
Volume	34
Issue number	5-6
DOIs	https://doi.org/10.1007/s00162-020-00544-w
Publication status	Published - 2020 Dec 1

Keywords

Allen–Cahn equation
Brownian dynamics
Coffee-ring effect
Monte Carlo simulation
Pinning boundary condition

ASJC Scopus subject areas

Computational Mechanics
Condensed Matter Physics
Engineering(all)
Fluid Flow and Transfer Processes

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10.1007/s00162-020-00544-w

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title = "Phase-field modeling and computer simulation of the coffee-ring effect",

abstract = "In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.",

keywords = "Allen–Cahn equation, Brownian dynamics, Coffee-ring effect, Monte Carlo simulation, Pinning boundary condition",

author = "Junxiang Yang and Hyundong Kim and Chaeyoung Lee and Sangkwon Kim and Jian Wang and Sungha Yoon and Jintae Park and Junseok Kim",

note = "Funding Information: The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have significantly improved the quality of this paper. J. Yang is supported by China Scholarship Council (201908260060). 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). Publisher Copyright: {\textcopyright} 2020, Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s00162-020-00544-w",

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AU - Yang, Junxiang

AU - Kim, Hyundong

AU - Lee, Chaeyoung

AU - Kim, Sangkwon

AU - Wang, Jian

AU - Yoon, Sungha

AU - Park, Jintae

AU - Kim, Junseok

N1 - Funding Information: The authors greatly appreciate the reviewers for their constructive comments and suggestions, which have significantly improved the quality of this paper. J. Yang is supported by China Scholarship Council (201908260060). 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). Publisher Copyright: © 2020, Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2020/12/1

Y1 - 2020/12/1

N2 - In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.

AB - In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.

KW - Allen–Cahn equation

KW - Brownian dynamics

KW - Coffee-ring effect

KW - Monte Carlo simulation

KW - Pinning boundary condition

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IS - 5-6

ER -

Phase-field modeling and computer simulation of the coffee-ring effect

Abstract

Keywords

ASJC Scopus subject areas

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