TY - JOUR
T1 - Mathematical modeling and simulation of antibubble dynamics
AU - Yang, Junxiang
AU - Li, Yibao
AU - Jeong, Darae
AU - Kim, Junseok
N1 - Funding Information:
Science Foundation (No. 2018M640968). 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).
Funding Information:
Acknowledgements The author (D. Jeong) was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP) (NRF-2017R1E1A1A03070953). The author (Y. B. Li) is supported by National Natural Science Foundation of China (Nos. 11601416, 11631012) and by the China Postdoctoral
Publisher Copyright:
© 2020 Global-Science Press.
PY - 2020/2
Y1 - 2020/2
N2 - 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.
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.
KW - Antibubble
KW - Conservative Allen-Cahn equation
KW - Navier-Stokes equation
UR - http://www.scopus.com/inward/record.url?scp=85085987927&partnerID=8YFLogxK
U2 - 10.4208/NMTMA.OA-2019-0082
DO - 10.4208/NMTMA.OA-2019-0082
M3 - Article
AN - SCOPUS:85085987927
SN - 1004-8979
VL - 13
SP - 81
EP - 98
JO - Numerical Mathematics
JF - Numerical Mathematics
IS - 1
ER -