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研究生:魏宇昆
研究生(外文):Yeu K. Wei
論文名稱:懸浮液中膠體粒子之擴散泳與多孔介質中溶液之擴散滲透
論文名稱(外文):Diffusiophoresis in Suspensions of Colloidal Particles and Diffusioosmosis of Solutions in Porous Media
指導教授:葛煥彰
指導教授(外文):Huan J. Keh
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:2002
畢業學年度:90
語文別:中文
中文關鍵詞:擴散泳擴散滲透電泳電滲透單元小室模型膠體懸浮液多孔介質
外文關鍵詞:DiffusiophoresisDiffusioosmosisElectrophoresisElectroosmosisUnit cell modelSuspensions of Colloidal ParticlePorous Media
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膠體粒子與孔隙流體系統受到外界所施加的電位、溫度、或溶質濃度梯度的驅動,會產生微小粒子於一連續相中之輸送行為和流體在多孔介質中的流動行為,此二種現象分別稱為”泳動”和”滲透流”現象。 擴散泳是由於膠體粒子受到溶液中溶質濃度梯度的影響而進行的泳動,擴散滲透則是流體在多孔介質中受到溶質濃度梯度的影響而造成的流動。 本文以理論解析,在非電解質和對稱電解質溶質濃度梯度下、對球形和圓柱形粒子、在單顆粒子和多顆粒子均勻懸浮系統中的擴散泳和擴散滲透速度。
對於粒子在非電解質中的擴散泳情況,本文假設溶質分子和粒子表面間的交互作用範圍遠小於粒子的半徑。 然而,由於具強吸附性的擴散溶質在此薄交互作用層內的極化效應則被考慮進來。 對於粒子在對稱電解質中的擴散泳,本文則分別呈現粒子周圍電雙層為薄層和任意厚度的兩種情況。 在薄電雙層的研究中,係假設電雙層厚度遠小於粒子的半徑,但卻考慮擴散離子在此薄電雙層內的極化效應。 在任意厚度電雙層的研究中,則電雙層厚度相對於粒子的半徑可以是任意值,但只有考慮粒子表面為低電荷密度(低表面電位)的情況。
在研究多顆粒子系統之前,第二章先探討單一球形和圓柱形粒子的擴散泳速度。 過去大多數擴散泳相關的研究,僅限於粒子具薄作用層的情況。 在本章中,吾人亦嘗試求解單顆帶電粒子具任意電雙層厚度的擴散泳速度。 所得到的擴散泳速度解析式在粒子表面擴散層很薄並含溶質極化效應的極限下是準確的,但在任意厚度電雙層情況下,所得之解析式只適用至粒子表面電荷密度或表面電位值為二階的近似情況。
在多顆粒子系統的研究中,本文使用單元小室模型考慮粒子之間的交互作用,此法在過去處理相同粒子懸浮液中粒子之沈降運動時,可提供良好的預測結果。 小室模型中,每個粒子在一小室中心,其周圍則由流體充滿小室。 第三章中,本文考慮穩態下均勻懸浮液中相同球形粒子的擴散泳速度。 粒子平均速度和粒子體積分率的函數關係可以解析形式表示出來。 當粒子表面擴散層很薄並含溶質極化效應時,將小室模型的結果與統計力學模型得到之粒子於稀薄懸浮液中的擴散泳速度相比較,發現小室模型和統計力學模型預測的結果能夠相當一致。 對粒子具有任意厚度電雙層時,擴散泳速度解析式只適用至粒子表面電荷密度或表面電位值為二階的近似情況。 將粒子之薄電雙層研究與任意厚度電雙層研究的擴散泳可動度結果進行比較,可以看出當kapa*a 值小於20時,薄作用層研究的結果會有明顯的誤差。
穩態下流體在均勻平行排列圓柱構成的纖維狀多孔介質中的擴散滲透,則在第四章中探討分析。 外加溶質濃度梯度為一常數且相對圓柱軸心可為任意方向。 對數個情況,整體流體的擴散滲透速度和平行排列圓柱多孔介質孔隙度的函數關係,可以解析型式表示出來。 對圓柱具有任意厚度電雙層時,擴散滲透速度解析式只適用至圓柱表面電荷密度或表面電位值為二階的情況。 將圓柱之薄電雙層研究與任意厚度電雙層研究的擴散滲透可動度結果進行比較,亦可以看出當kapa*a值小於20時,薄作用層研究的結果會有明顯的誤差。
Driven by applying an electrical potential, temperature, or solute concentration gradient, the transport behavior of small particles in a continuous medium and the flow behavior of fluids in porous media at low Reynolds numbers are the phenomena known as “phoretic motion” and “osmotic motion”, respectively. Diffusiophoresis is the motion of colloidal particles in an applied interactive solute concentration gradient and diffusioosmosis is the fluid flow induced by the solute gradient in the porous medium. In this work, the diffusiophoretic and diffusioosmotic motions are analytically studied in gradients of both a nonelectrolyte solute and a symmetric electrolyte solute, in particle shapes of both a sphere and a circular cylinder, and in systems of both a single particle and a homogeneous suspension of multiple particles.
For the case of diffusiophoresis in a nonelectrolyte solution, the range of the interaction between the solute molecules and the particle surface is assumed small relative to the radius of the particle. However, the effect of polarization of the mobile solute in the thin diffuse layer at the particle surface caused by the strong adsorption of the solute is taken into account. For the case of diffusiophoresis in a symmetric electrolyte, analyses for both thin and arbitrary electric double layers surrounding the particle are presented. In the thin-double-layer analysis, the thickness of the double layer is assumed to be small relative to the radius of the particle, but the polarization effect of the diffuse ions in the double layer is incorporated. In the arbitrary-double-layer analysis, the double layer may have an arbitrary thickness relative to the radius of the particle, and only the particle surface with a small surface charge density (or zeta potential) is considered.
Before studying multiple-particle systems, the steady diffusiophoretic motions of an isolated sphere and circular cylinder are investigated in Chapter 2. In the past, most of the relevant studies were concerning with the particle with a thin diffuse layer. In this chapter, we attempt an analysis of the diffusiophoretic motion of a charged particle for arbitrary double-layer thickness. The analytical expression for the diffusiophoretic velocity is exact in the limit of thin but polarized diffuse layer, and is correct to the second order of the surface charge density or zeta potential of the particle in the general case.
In the analysis for the multiple-particle systems, the effects of interaction among individual particles are taken into explicit account by employing a unit cell model which is known to provide good predictions for the sedimentation of monodisperse suspensions of particles. Each particle is envisaged to be surrounded by a concentric shell of suspending fluid. In Chapter 3, the diffusiophoretic motion of a homogeneous suspension of identical spherical particles is considered at the steady state. Analytical expressions for the mean particle velocity are obtained in closed form as functions of the volume fraction of the particles. For particles with thin but polarized diffuse layers, comparisons between the ensemble-averaged diffusiophoretic velocity of a test particle in the dilute suspension and the cell-model results are made, and it is found that the prediction from a cell model can agree well with the ensemble-averaged results. For particles with an arbitrary double-layer thickness, the expressions for the diffusiophoretic velocity are obtained in closed form correct to the second order of their surface charge density or zeta potential. A comparison between the results of the diffusiophoretic mobility obtained in the thin-layer analysis and in the arbitrary-layer analysis for the cell model is made. The diffusiophoretic results predicted by the thin-double-layer analysis can be in significant errors when the value of kapa*a is less than about 20.
The steady diffusioosmotic flow of a fluid solution in the fibrous porous medium constructed by a homogeneous array of parallel circular cylinders is analytically investigated in Chapter 4. The imposed solute concentration gradient is constant and can be oriented arbitrarily with respect to the axes of the cylinders. Analytical expressions for the diffusioosmotic velocity of the bulk fluid as functions of the porosity of the ordered array of cylinders are obtained for various cases. For cylinders with an arbitrary double-layer thickness, the expressions for the diffusioosmotic velocity are obtained in closed form correct to the second order of their surface charge density or zeta potential. A comparison of the results of the diffusioosmotic mobility obtained in the thin-layer analysis and in the arbitrary-layer analysis for the cell model is made. Again, the diffusioosmosis results predicted by the thin-double-layer analysis can be in significant errors when the value of kapa*a is less than about 20.
第一章 緒 論 1
1-1 擴散泳 1
1-2 擴散滲透 6
1-3 泳動粒子間的交互作用效應與小室模型 8
第二章 單一粒子之擴散泳 11
2-1 單一球形粒子之擴散泳 11
2-1-1 非電解質溶液中球形粒子之擴散泳 11
2-1-2 電解質中具薄電雙層球形粒子之擴散泳 15
2-1-3 電解質中低帶電量球形粒子之擴散泳 18
2-1-3-1 基本電動力方程式 18
2-1-3-2 粒子擴散泳速度之求解 20
2-1-3-3 結果與討論 24
2-2 單一圓柱形粒子之擴散泳 31
2-2-1 非電解質溶液中圓柱形粒子之擴散泳 31
2-2-2 電解質中具薄電雙層圓柱形粒子之擴散泳 34
2-2-3 電解質中低帶電量圓柱形粒子之擴散泳 36
2-2-3-1 基本電動力方程式 37
2-2-3-2 粒子擴散泳速度之求解 38
2-2-3-3 結果與討論 39
第三章 懸浮液中球形膠體粒子之擴散泳 47
3-1 非電解質懸浮液中粒子之擴散泳 47
3-1-1 數學分析 47
3-1-2 結果與討論 51
3-2 電解質懸浮液中具薄電雙層粒子之擴散泳 61
3-2-1 數學分析 61
3-2-2 結果與討論 65
3-2-3 粒子之電泳 79
3-3 電解質懸浮液中低帶電量粒子之擴散泳 85
3-3-1 數學分析 85
3-3-2 結果與討論 91
第四章 溶液於纖維狀多孔介質中之擴散滲透 107
4-1 非電解質溶液於多孔介質中之擴散滲透 107
4-1-1 數學分析 107
4-1-2 結果與討論 112
4-2 電解質溶液於具薄電雙層多孔介質中之擴散滲透 120
4-2-1 數學分析 120
4-2-2 結果與討論 124
4-2-3 多孔介質中之電滲透 136
4-3 電解質溶液於低帶電量多孔介質中之擴散滲透 143
4-3-1 數學分析 143
4-3-1-1 垂直圓柱軸向之擴散滲透 143
4-3-1-2 平行圓柱軸向之擴散滲透 149
4-3-2 結果與討論 150
4-3-2-1 垂直圓柱軸向之擴散滲透 150
4-3-2-2 平行圓柱軸向之擴散滲透 165
第五章 結 論 175
符 號 說 明 180
參 考 文 獻 185
附錄A 第三章中部分函數之定義 190
附錄B 第四章中部分函數之定義 193
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