晶格波茲曼法在電滲流的模擬及分析

Electroosmosis Simulation by Lattice Boltzmann Method and its Analysis

楊世銓(Shr-Chuan Yang)

指導教授 ： 許文翰

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2018年)

https://doi.org/10.6342/NTU201801204

摘要

本論文使用modified equation分析以及傅立葉穩定性分析方法探討晶格波茲曼法(Lattice Boltzmann method)在二維對流-擴散方程式，
以求解Poisson-Nernst-Planck方程組，
此系統包含了描述高斯定律的Poisson方程式、描述離子濃度分布之Nernst-Planck方程以及由庫倫力所驅動的不可壓縮Navier-Stokes方程組。
論文之內容主要是使用晶格波茲曼Poisson-Nernst-Planck (PNP)方程組來描述電滲流行為，以了解電位對離子分布的影響，以及庫倫靜電力造成的流場變化，並推導解析解驗證，以及使用Helmholtz-Smoluchowski公式比較。

關鍵字

晶格波茲曼法 ； Poisson-Nernst-Planck方程組 ； Navier-Stokes方程組 ； 電滲流

並列摘要

In this thesis, the Poisson-Nernst-Planck (electro-diffusion) model will be adopted to simulate the diffuse double layer, including equilibrium between Coulomb's force and diffusion of ion. And the governing equations are solved by an efficient numerical method, the Lattice Boltzmann method (LBM). This article proves the consistency of the Lattice Boltzmann Method based on the modified equation. Otherwise, the stability condition with different relaxation times by the Fourier (Von Neumann) stability analysis is implemented in D2Q5 lattice. Finally, the simulation of the electro-diffusion phenomenon exhibits how the electric-potential influences the distribution of ions, and the impact of Coulomb force on the flow pattern is presented. The numerical result is validated by the analytic solution and Helmholtz-Smoluchowski formula.

並列關鍵字

Lattice Boltzmann method ； Poisson-Nernst-Planck ； Navier-Stokes equation ； Electrokinetics ； Electro-osmotic flow ； Helmholtz-Smoluchowski

參考文獻

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