Katsuhiko Shinjo

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

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,

Van der Waals-Navier Stokes Equation for Boiling Phenomena —Bubble Formation by Heating—

N\geqslant2

CANTILEVER TYPE PROBE, SCANNING TUNNELING MICROSCOPE AND INFORMATION PROCESSING DEVICE EQUIPPED WITH SAID PROBE

) 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.

Micro-displacement type information detection probe device and scanning tunneling microscope, atomic force microscope, information processing device by use thereof

By making use of a simulation scheme incorporating the Navier–Stokes equation and the van der Waals equation, we study the combined dynamics of fluid motion and phase separation in a bubble generation process. The thermodynamic force for phase separation is taken into account by the entropy density of the van der Waals fluid, which is a function of local density and local energy. With this force and the surface tension, explicit forms of equations of motion are given for the density, momentum, and energy. In this scheme, we are able to treat gas and liquid states in a unified way and study a spontaneous bubble generation process by heating. In this paper, we demonstrate the processes of bubble generation in a pinpoint-heated one-dimensional system of water, and study their characteristics. For example, before the bubble generation, a step-like pressure domain wall propagates from the the position where the liquid is heated. After further heating, thermodynamic instability takes place and a gas region is g...