以晶格波玆曼法結合親/疏水性邊界模擬液氣兩相流之流場

Lattice Boltzmann Simulations of Incompressible Liquid-Gas system on Partial Wetting Surface

施靖祥

指導教授 ： 林昭安

國立清華大學/工學院/動力機械工程學系/碩士(2009年)

https://doi.org/10.6843/NTHU.2009.00130

摘要

In this thesis, a lattice Boltzmann multiphase fluid model capable to deal with large density ratio and with partial wetting surface is introduced. Multiphase fluid behavior can be simulated using the the Navier-Stokes equation coupling with convective Cahn-Hilliard equation [1], where the latter equation is used to capture the interface of multiphase fluid in terms of chemical potential. By adopting the multiphase model and adding an additional
term describing surface energy, a droplet rests on a surface with given contact angle can be computed.

The capability of the present model, which is to compute two phase flows with wettability controllable surface, is validated by simulating a droplet that rests on a surface with given contact angle. The contact angles calculated from the results agree with theory. The effect of gravitational force on droplet shape is also discussed in terms of Bond number. Besides, phenomena caused by different wetting condition of the surface are presented in this thesis, such as droplet on heterogeneous surface and transient response of a droplet with changing wettability.

The present model is applied to simulate liquid lens cases. The simulation result shows good compatibility with the experiment done by Hsieh et al [58], where Bond number is about $0.05$. Further improvement of the lens fabrication technique is suggested with observations in the present work. Optical properties of the lens such as back focal length of the liquid lens can be changed by controlling Bond number to reach wider FOV or longer BFL, which are
important specifications in optics.

關鍵字

晶格波茲曼 ； 兩相流 ； 親水性 ； 疏水性

參考文獻

[1] J.W. Cahn, J.E Hilliard," Free energy of a nonuniform system.-Interfacial energy," J. Chem. Phys. 28(2)(1958)

[2] U. Frisch, B. Hasslacher, and Y. Pomeau, ``Lattice-gas automata for the Navier-Stokes equation," Phys. Rev. Lett. 56, 1505, (1986).

[3] S. Wolfram, ``Cellular automaton fluids 1: Basic theory," J. Stat. Phys. 45, 471, (1986).

[4] F. J. Higuera, S. Sussi, and R. Benzi, ``3-dimensional flows in complex geometries with the lattice Boltzmann method," Europhys. Lett. 9, 345, (1989).

[5] F. J. Higuera, and J. Jemenez, ``Boltzmann approach to lattice gas simulations," Europhys. Lett. 9, 663, (1989).