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研究生:陳柏源
研究生(外文):Chen, Po-Yuan
論文名稱:膠體粒子泳動之邊界效應
論文名稱(外文):Boundary effects on Phoretic Motions of Colloidal Spheres:Migration parallel to one or two plane walls
指導教授:葛煥彰
指導教授(外文):Keh, Huan-Jang
學位類別:博士
校院名稱:國立臺灣大學
系所名稱:化學工程學研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2003
畢業學年度:91
語文別:中文
論文頁數:322
中文關鍵詞:泳動擴散泳滲透泳熱毛細泳熱泳
外文關鍵詞:phoresisdiffusiophoresisosmophoresisthermocapillary motionthermophoresis
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摘要
膠體粒子於一連續相中受到外界所施加的電位、溫度、或溶質濃度梯度的驅動,所產生之輸送行為,稱為泳動。本研究考慮單一球形膠體粒子平行於單一無限大平板或二無限大平板之泳動,分別以邊界取點法與反射法計算粒子之泳動速度。
首先,於第二章中,以半解析半數值之方式,計算單一球形膠體粒子於非電解值溶液中,在忽略流體慣性項與溶質對流效應下之擴散泳運動速度。施予平行於平板之定值濃度梯度,為其驅動力。平板之邊界條件,可為溶質不可穿透與溶質呈線性分佈兩種情形。當粒子半徑遠大於粒子與溶質之交互作用層厚度時,平板之邊界效應,其一來自於膠體粒子與平板間產生的濃度梯度交互作用,另一者為流體之黏滯作用。使用邊界取點法計算在不同極化參數與分離參數下之擴散泳速度並與反射法相關結果互相比較驗證。由於粒子之表面特性,粒子與平板的相對距離,與平板上的邊界條件之不同,平板之效應可降低或增加粒子的運動速度。
於第三章中,考慮單一球形胞囊粒子,受到定值濃度梯度驅動,所進行平行於平板之滲透泳運動。平板之邊界條件可為溶質不可穿透與溶質呈線性分佈兩種情形。平板對於滲透泳之邊界效應,其一來自於胞囊粒子與平板間產生的濃度梯度交互作用,另一者為流體之黏滯作用。使用邊界取點法計算胞囊粒子在各種不同狀況下之滲透泳速度,並與反射法結果互相比較,其結果一致。平板施於滲透泳之邊界效應,則由胞囊粒子之特性,其與平板的相對距離,以及溶質於平板上的邊界條件所決定。
於第四章中,以半解析半數值之方式,計算單一球形液滴在忽略流體慣性項與溫度對流效應下之熱毛細泳運動速度。施予平行於平板之定值溫度梯度,為其驅動力,並假設液滴於運動中皆保持球形而不變形。平板之邊界條件可分為絕熱與溫度呈線性分佈兩種情形分別探討。當液滴靠近平板時,平板之邊界效應,其一來自於液滴與平板間產生的溫度梯度交互作用,另一者為流體之黏滯作用。使用邊界取點法計算在不同之流體黏度比、熱導度比與分離參數下之熱毛細泳速度,並與反射法之計算結果互相比較,其結果一致。平板之邊界效應,則由於液滴之特性,液滴與平板的相對距離,與平板之邊界條件之不同,而可降低或增加液滴的運動速度。
在第五章中,考慮單一球形氣膠粒子在忽略流體慣性項與溫度對流效應下之熱泳運動速度。平板之邊界條件亦可分為絕熱與溫度呈線性分佈兩種情形分別探討。當液滴靠近平板時,平板之邊界效應,其一來自於氣膠粒子與平板間產生的溫度梯度交互作用,另一者為流體之黏滯作用。使用邊界取點法可求解在不同之粒子熱導度比、粒子表面性質之相關參數與分離參數下之熱泳速度,並與反射法互相比較驗證。平板之邊界效應,則由於氣膠粒子之表面特性,氣膠粒子與平板間的相對距離,以及平板之邊界條件之不同,而可降低或增加氣膠粒子的運動速度
最後,將此四種泳動綜合比較其特性之相似與相異處,並作表分析,以便於瞭解各種泳動之現象。

Abstract
Driven by applying an electrical potential, temperature, or solute concentration gradient, the transport of colloidal particles in a continuous medium is known as the “phoretic motion”. In this work, a boundary collocation method and a reflection method are utilized to calculate the various phoretic velocities of small spherical particles migrating parallel to one or two plane walls.
First, in chapter 2, the quasisteady diffusiophoretic motion of a spherical particle in a fluid solution of a nonionic solute located between two infinite parallel plane walls is studied in the absence of fluid inertia and solute convection. The imposed solute concentration gradient is constant and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle radius and to the particle-wall gap widths, but the polarization effect of the diffuse solute in the thin interfacial layer caused by the strong adsorption of the solute is incorporated. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. Numerical results for the diffusiophoretic velocity of the particle relative to that under identical conditions in an unbounded fluid solution are presented for various values of the relaxation parameter of the particle as well as the relative separation distances between the particle and the two plates. For the special case of diffusiophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending on the surface properties of the particle, the relative particle-wall separation distances, and the solutal boundary condition at the walls.
A theoretical study is presented in chapter 3 for the quasisteady osmophoretic motion of a spherical vesicle in a solution located between two infinite parallel plane walls in the limit of negligible Reynolds and Peclet numbers. The applied solute concentration gradient is uniform and parallel to the two plane walls, which may be either impermeable to the solute molecules or prescribed with the far-field concentration distribution. The presence of the neighboring walls causes two basic effects on the vesicle velocity: first, the local concentrations on both sides of the vesicle surface are altered by the walls, thereby speeding up or slowing down the vesicle; secondly, the walls enhance the viscous interaction effect on the moving vesicle. Numerical results for the osmophoretic velocity of the vesicle relative to that under identical conditions in an unbounded solution are presented for various values of the relevant properties of the vesicle as well as the relative separation distances between the vesicle and the two plates. For the special case of osmophoretic motions of a spherical vesicle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the vesicle velocity, depending upon the relevant properties of the vesicle, the relative vesicle-wall separation distances, and the solutal boundary condition at the walls.
In chapter 4, the steady thermocapillary migration of a fluid droplet located between two infinite parallel plane walls is examined in the absence of fluid inertia and thermal convection. The imposed temperature gradient is constant and parallel to the two plates, and the droplet is assumed to retain a spherical shape. The plane walls may be either insulated or prescribed with the far-field temperature distribution. The presence of the neighboring walls causes two basic effects on the droplet velocity: first, the local temperature gradient on the droplet surface is enhanced or reduced by the walls, thereby speeding up or slowing down the droplet; secondly, the walls increase viscous retardation of the moving droplet. Numerical results for the thermocapillary migration velocity of the droplet relative to that under identical conditions in an unbounded medium are presented for various values of the relative viscosity and thermal conductivity of the droplet as well as the relative separation distances between the droplet and the two plates. For the special cases of thermocapillary motions of a spherical droplet parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the droplet velocity, depending upon the relative transport properties of the droplet, the relative droplet-wall separation distances, and the thermal boundary condition at the walls.
In chapter 5, the quasisteady thermophoretic motion of a spherical particle in a gaseous medium located in an arbitrary position between two infinite parallel plane walls is studied in the absence of fluid inertia and thermal convection. The Knudsen number is assumed to be small so that the fluid flow is described by a continuum model with a temperature jump, a thermal slip, and a frictional slip at the particle surface. The imposed temperature gradient is constant and parallel to the two plane walls, which may be either insulated or prescribed with the far-field temperature distribution. The presence of the neighboring walls causes two basic effects on the particle velocity: first, the local temperature gradient on the particle surface is enhanced or reduced by the walls, thereby speeding up or slowing down the particle; secondly, the walls increase viscous retardation of the moving particle. Numerical results for the thermophoretic velocity of the particle relative to that under identical conditions in an unbounded gaseous medium are presented for various values of the relative thermal conductivity and surface properties of the particle as well as the relative separation distances between the particle and the two plates. For the special case of thermophoretic motions of a spherical particle parallel to a single plate and on the central plane of a slit, the collocation results agree well with the approximate analytical solutions obtained by using a method of reflections. The presence of the lateral walls can reduce or enhance the particle velocity, depending upon the relative thermal conductivity and surface properties of the particle, the relative particle-wall separation distances, and the thermal boundary condition at the walls.
Finally, the four phoretic motions considered in chapters 2-5 are simply compared.

目 錄
第一章 緒 論 …………..…………………………..…….…1
1-1 前言……………………………………………………….1
1-2 擴散泳動……….…………..………………………….3
1-3 滲透泳動………………..………..………………….7
1-4 熱毛細泳動 ……………..………………………..…………11
1-5 熱泳動…………………………..…………………………14
第二章 球形膠體粒子平行平板之擴散泳動…………………19
2-1 理論分析 ………………………..……………….…………19
2-1.1 溶質濃度分佈……………………………………………21
2-1.2 流體速度分佈……………..………………………………25
2-1.3 粒子擴散泳速度之衍導………….……………………30
2-1.4 數值計算方法………………..……………………31
2-2 結果與討論…………………..……….………………….32
2-2.1 粒子平行單一平板之擴散泳動…………………………32
2-2.2 粒子平行兩平板之擴散泳動……………………………40
第三章 球形胞囊粒子平行平板之滲透泳動……………..47
3-1 理論分析…………………………………………….…..47
3-1.1 溶質濃度分佈……………………………………………...49
3-1.2 流體速度分佈……………………………………………...53
3-1.3 粒子滲透泳速度之衍導…………………….……………..56
3-2 結果與討論 ………………………..………………………57
3-2.1 粒子平行單一平板之滲透泳動…………………………...57
3-2.2 粒子平行兩平板之滲透泳動……………………………...66
第四章 球形液滴平行平板之熱毛細泳動……………………75
4-1 理論分析 ………..………………….………………….75
4-1.1 溫度分佈…………………………………………………...77
4-1.2 流體速度分佈……………………………………………...80
4-1.3 液滴熱毛細泳速度之衍導……………………..………….84
4-2 結果與討論 …………………………..………………...…85
4-2.1 液滴平行單一平板之熱毛細泳動………………………...85
4-2.2 液滴平行兩平板之熱毛細泳動…………………………...95
第五章 球形氣膠粒子平行平板之熱泳動…………………103
5-1 理論分析………………..………………………………103
5-1.1 溫度分佈………………………………………………….105
5-1.2 流體速度分佈……………………………….……………108
5-1.3 粒子熱泳速度之衍導…………………………………….110
5-2 結果與討論 …………………………..…………..……….112
5-2.1 粒子平行單一平板之熱泳動…………………………….112
5-2.2 粒子平行兩平板之熱泳動……………………………….125
第六章 綜合討論與結論…………………………………….135
6-1 綜合討論……………………………………………..……135
6-2 結論…………………………………………………..…..141
符 號 說 明 ………………...…………………...………………143
參 考 文 獻………………...…...…………………….……………147
附錄A 球形液滴平行平板之緩慢運動……………………155
附錄B 表面滑移球形粒子平行平板之緩慢運動…….….…177
附錄C 球形粒子平行平板各種泳動之反射法解析解…...205
附錄D 一些繁複函數之定義 ………….…………….……241
附錄E 相關計算機程式.............................249
作者簡介............................................321

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