NDLI: Surface Tension of Multi-phase Flow with Multiple Junctions Governed by the Variational Principle

Content Provider	Springer Nature Link
Author	Shinjo, Katsuhiko Matsutani, Shigeki Naka, Kota
Copyright Year	2011
Abstract	We explore a computational model of an incompressible fluid with a multi-phase field in three-dimensional Euclidean space. By investigating an incompressible fluid with a two-phase field geometrically, we reformulate the expression of the surface tension for the two-phase field found by Lafaurie et al. (J Comput Phys 113:134–147, 1994) as a variational problem related to an infinite dimensional Lie group, the volume-preserving diffeomorphism. The variational principle to the action integral with the surface energy reproduces their Euler equation of the two-phase field with the surface tension. Since the surface energy of multiple interfaces even with singularities is not difficult to be evaluated in general and the variational formulation works for every action integral, the new formulation enables us to extend their expression to that of a multi-phase (N-phase, $N\geqslant2$ ) flow and to obtain a novel Euler equation with the surface tension of the multi-phase field. The obtained Euler equation governs the equation for motion of the multi-phase field with different surface tension coefficients without any difficulties for the singularities at multiple junctions. In other words, we unify the theory of multi-phase fields which express low dimensional interface geometry and the theory of the incompressible fluid dynamics on the infinite dimensional geometry as a variational problem. We apply the equation to the contact angle problems at triple junctions. We computed the fluid dynamics for a two-phase field with a wall numerically and show the numerical computational results that for given surface tension coefficients, the contact angles are generated by the surface tension as results of balances of the kinematic energy and the surface energy.
Ending Page	278
Page Count	42
Starting Page	237
File Format	PDF
ISSN	13850172
e-ISSN	15729656
Journal	Mathematical Physics, Analysis and Geometry
Issue Number	3
Volume Number	14
Language	English
Publisher	Springer Netherlands
Publisher Date	2011-07-30
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Volume-preserving diffeomorphism Multi-phase flow Theoretical, Mathematical and Computational Physics Geometry Three or more component flows Analysis Hamiltonian systems on groups of diffeomorphisms and on manifolds of mappings and metrics Capillarity (surface tension) Surface tension Group Theory and Generalizations Multiple junction Applications of Mathematics Applications to minimal surfaces (problems in two independent variables)
Content Type	Text
Resource Type	Article
Subject	Mathematical Physics Geometry and Topology

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