Volume 13, Issue 1
Mathematical Modeling and Simulation of Antibubble Dynamics

Numer. Math. Theor. Meth. Appl., 13 (2020), pp. 81-98.

Published online: 2019-12

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• Abstract

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and  outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.

35Q35, 76T10, 81T80

yibaoli@xjtu.edu.cn (Yibao Li)

tinayoyo@kangwon.ac.kr (Darae Jeong)

cfdkim@korea.ac.kr (Junseok Kim)

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@Article{NMTMA-13-81, author = {Yang , JunxiangLi , YibaoJeong , Darae and Kim , Junseok}, title = {Mathematical Modeling and Simulation of Antibubble Dynamics}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {13}, number = {1}, pages = {81--98}, abstract = {

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and  outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2019-0082}, url = {http://global-sci.org/intro/article_detail/nmtma/13431.html} }
TY - JOUR T1 - Mathematical Modeling and Simulation of Antibubble Dynamics AU - Yang , Junxiang AU - Li , Yibao AU - Jeong , Darae AU - Kim , Junseok JO - Numerical Mathematics: Theory, Methods and Applications VL - 1 SP - 81 EP - 98 PY - 2019 DA - 2019/12 SN - 13 DO - http://doi.org/10.4208/nmtma.OA-2019-0082 UR - https://global-sci.org/intro/article_detail/nmtma/13431.html KW - Antibubble, conservative Allen-Cahn equation, Navier-Stokes equation. AB -

In this study, we propose a mathematical model and perform numerical simulations for the antibubble dynamics. An antibubble is a droplet of liquid surrounded by a thin film of a lighter liquid, which is also in a heavier surrounding fluid. The model is based on a phase-field method using a conservative Allen-Cahn equation with a space-time dependent Lagrange multiplier and a modified Navier-Stokes equation. In this model, the inner fluid, middle fluid and  outer fluid locate in specific diffusive layer regions according to specific phase filed (order parameter) values. If we represent the antibubble with conventional binary or ternary phase-field models, then it is difficult to have stable thin film. However, the proposed approach can prevent nonphysical breakup of fluid film during the simulation. Various numerical tests are performed to verify the efficiency of the proposed model.

Junxiang Yang, Yibao Li, Darae Jeong & Junseok Kim. (2019). Mathematical Modeling and Simulation of Antibubble Dynamics. Numerical Mathematics: Theory, Methods and Applications. 13 (1). 81-98. doi:10.4208/nmtma.OA-2019-0082
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