用格子Boltzmann方法研究微管内二元流体的混合问题
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摘要
微管内二元流体的混合问题是微流动领域中最基础的问题之一。由于微尺度条件下,二元流体的流动趋向于层流,扩散式主要的,而通过扩散发生的混合将花费相当长的时间。总的说来,微流动混合问题的应用跨越了当今各个专业领域,例如化学分析和传统普遍存在的混合工作(如反应,气体吸收,乳化,起泡和调配等)的样品制备。因此,研究微流动混合问题具有非常重要的意义。
微混合器的内部结构非常复杂而描述流体运动的控制方程具有高度的非线性,所以很难通过理论方法精确研究。而且,由于微混合器内部的流体混合效果差别很小,难于用观测,且微流动的数据读取很难,使得用实验方法研究微流动混合问题面临很多困难。随着计算机技术的发展,计算流体力学方法的产生使直接解决复杂流体问题成为可能。
近年来,格子Boltzmann方法(LBM)已经发展成为模拟流体流动和流体物理建模领域中一个有前景的数值方法。该方法在模拟多组分多相流体和复杂边界的流体等方面尤其成功。与其他传统的计算方法比起来,格子Boltzmann方法具有编码简单、边界条件容易实现、完全并行性等优点。本文将采用格子Boltzmann方法来研究微管内二元流体的混合问题：
1.LBM的基本理论：
a.介绍了LBM的发展历史和研究现状。(第1章)
b.严格推导和验证了LBM方法。(第2章)
c.讨论了格子Boltzmann方法应用中的几种典型的边界条件：反弹边界、反射边界、外推格式和周期边界,二维的压力和速度边界。(第3章)
d.重点介绍了Luo和Girimaji提出的二元流混合模型。(第2章)
2.微流体混合问题：
a.介绍了微流动混合问题的研究背景。(第1、4章)
b,介绍了关于微流动混合的基本问题,包括混合原则,混合方法,混合效果的鉴定。(第4章)
c.提出了一种通过混合边界来促进混合的被动式混合器,并利用它研究了流体粘性对于混合效果的影响.。并发现混合边界的设计和流体的粘性对混合效果有一定的影响。(第4章)
d.提出一种障碍式被动混合器。(第4章)
e.设计了一种简单易行的通过加时间脉冲压力的主动式微混合器,并讨论了必要的条件。并得出结论：通过控制T型微混合器内入口流体的速度可以达到混沌的混合效果。(第4章)
Mixing of binary fluids in a micro mixer is one of the most basic and revealing cases in the general subject of micro fluidics. Due to the micro scale, the binary fluids flow is typically laminar, the diffusion is dominant, and it would take quite long time to get well mixed.Generally, application fields of Mixing in a micro mixer encompass both modern, specialised issues such as sample preparation for chemical analysis and traditional, widespread usable mixing tasks such as reaction, gas absorption, emulsification, foaming, and blending. Therefore Mixing of binary fluids in a micro mixer is of great significance.
As the internal structure of the micro mixer is very complex and the governing equations are highly nonlinear, some of the flow properties are extremely difficulty to determine accurately with theoretical method. Moreover, it is difficult to read the tiny difference in micro mixing effect in the laborary with the observation method. With the development of computer technology, computational fluid dynamics (CFD) methods have gradually made it possible to directly solve many complex fluid dynamic problems.
In recent years, the lattice Boltzmann method (LBM) has developed into promising numerical scheme for simulating fluid flows and modeling physics in fluids. The scheme is particularly successful in fluid flow applications involving simulations of multiphase and multicomponent flows and complex boundaries and so on. Compared with the traditional CFD methods, LBM has many unique advantages, such as simple codes, easy implementation of boundary conditions, and fully parallelism. In this dissertation, lattice Boltzmann method is used to study mixing of binary fluids in a micro mixer.
The main jobs can be summarized on two dimensions:
1. The basic theoretics of LBM:
a. Introducing the history and present research situation of the lattice Boltzmann method. (in Chapter 1)
b. rigorous derivation and proving process for LBM is given at length. (in Chapter 2)
c. several kind of typical boundary condition in the lattice Boltzmann method are discussed such as bounce back boundary, specular reflection boundary, extrapolation method, periodic boundary, pressure and velocity boundary. (in Chapter 3)
d. the lattice Boltzmann model for binary mixtures proposed by Luo and Girimaji is produced particularly.
2. The problem of mixing in micro mixer:
a. Introducing the present research situation of the problem of mixing in micro mixer.(in Chapter 1,4)
b. Introducing mixing principles, means to induce mixing, determination of mixing efficiency.(in Chapter 4)
c. Proposed a new passive micro mixer to affect mixing by changing the hydrophobic and hydrophilic properties of the substrate surface, and numerically studied the effect of viscosity and viscosity difference and boundary patterned slip on mixing in the micro mixer using lattice Boltzmann method (LBM). It has been found that it is feasible to optimize the micro mixer design by combining the viscosity effect and boundary patterned ratio altogether. (in Chapter 4)
d. Proposed another passive micro mixer with obstacle disturbance. (in Chapter 4)
e. Proposed a novel, simple and convenient active micro mixer using time pulsing, and the essential factors for the mixing are discussed. It has been found that the chaos in T type micro mixer can be induced easily through controling the fluids velocity in inlets. (in Chapter 4)
微混合器的内部结构非常复杂而描述流体运动的控制方程具有高度的非线性,所以很难通过理论方法精确研究。而且,由于微混合器内部的流体混合效果差别很小,难于用观测,且微流动的数据读取很难,使得用实验方法研究微流动混合问题面临很多困难。随着计算机技术的发展,计算流体力学方法的产生使直接解决复杂流体问题成为可能。
近年来,格子Boltzmann方法(LBM)已经发展成为模拟流体流动和流体物理建模领域中一个有前景的数值方法。该方法在模拟多组分多相流体和复杂边界的流体等方面尤其成功。与其他传统的计算方法比起来,格子Boltzmann方法具有编码简单、边界条件容易实现、完全并行性等优点。本文将采用格子Boltzmann方法来研究微管内二元流体的混合问题：
1.LBM的基本理论：
a.介绍了LBM的发展历史和研究现状。(第1章)
b.严格推导和验证了LBM方法。(第2章)
c.讨论了格子Boltzmann方法应用中的几种典型的边界条件：反弹边界、反射边界、外推格式和周期边界,二维的压力和速度边界。(第3章)
d.重点介绍了Luo和Girimaji提出的二元流混合模型。(第2章)
2.微流体混合问题：
a.介绍了微流动混合问题的研究背景。(第1、4章)
b,介绍了关于微流动混合的基本问题,包括混合原则,混合方法,混合效果的鉴定。(第4章)
c.提出了一种通过混合边界来促进混合的被动式混合器,并利用它研究了流体粘性对于混合效果的影响.。并发现混合边界的设计和流体的粘性对混合效果有一定的影响。(第4章)
d.提出一种障碍式被动混合器。(第4章)
e.设计了一种简单易行的通过加时间脉冲压力的主动式微混合器,并讨论了必要的条件。并得出结论：通过控制T型微混合器内入口流体的速度可以达到混沌的混合效果。(第4章)
Mixing of binary fluids in a micro mixer is one of the most basic and revealing cases in the general subject of micro fluidics. Due to the micro scale, the binary fluids flow is typically laminar, the diffusion is dominant, and it would take quite long time to get well mixed.Generally, application fields of Mixing in a micro mixer encompass both modern, specialised issues such as sample preparation for chemical analysis and traditional, widespread usable mixing tasks such as reaction, gas absorption, emulsification, foaming, and blending. Therefore Mixing of binary fluids in a micro mixer is of great significance.
As the internal structure of the micro mixer is very complex and the governing equations are highly nonlinear, some of the flow properties are extremely difficulty to determine accurately with theoretical method. Moreover, it is difficult to read the tiny difference in micro mixing effect in the laborary with the observation method. With the development of computer technology, computational fluid dynamics (CFD) methods have gradually made it possible to directly solve many complex fluid dynamic problems.
In recent years, the lattice Boltzmann method (LBM) has developed into promising numerical scheme for simulating fluid flows and modeling physics in fluids. The scheme is particularly successful in fluid flow applications involving simulations of multiphase and multicomponent flows and complex boundaries and so on. Compared with the traditional CFD methods, LBM has many unique advantages, such as simple codes, easy implementation of boundary conditions, and fully parallelism. In this dissertation, lattice Boltzmann method is used to study mixing of binary fluids in a micro mixer.
The main jobs can be summarized on two dimensions:
1. The basic theoretics of LBM:
a. Introducing the history and present research situation of the lattice Boltzmann method. (in Chapter 1)
b. rigorous derivation and proving process for LBM is given at length. (in Chapter 2)
c. several kind of typical boundary condition in the lattice Boltzmann method are discussed such as bounce back boundary, specular reflection boundary, extrapolation method, periodic boundary, pressure and velocity boundary. (in Chapter 3)
d. the lattice Boltzmann model for binary mixtures proposed by Luo and Girimaji is produced particularly.
2. The problem of mixing in micro mixer:
a. Introducing the present research situation of the problem of mixing in micro mixer.(in Chapter 1,4)
b. Introducing mixing principles, means to induce mixing, determination of mixing efficiency.(in Chapter 4)
c. Proposed a new passive micro mixer to affect mixing by changing the hydrophobic and hydrophilic properties of the substrate surface, and numerically studied the effect of viscosity and viscosity difference and boundary patterned slip on mixing in the micro mixer using lattice Boltzmann method (LBM). It has been found that it is feasible to optimize the micro mixer design by combining the viscosity effect and boundary patterned ratio altogether. (in Chapter 4)
d. Proposed another passive micro mixer with obstacle disturbance. (in Chapter 4)
e. Proposed a novel, simple and convenient active micro mixer using time pulsing, and the essential factors for the mixing are discussed. It has been found that the chaos in T type micro mixer can be induced easily through controling the fluids velocity in inlets. (in Chapter 4)
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