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 - <p style="text-align: justify;">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&nbsp; 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.</p>