臺灣博碩士論文加值系統

本論文主要目的在探討膠體粒子在靜態溶液中之吸附凝集作用，研究可分為兩部份。第一部份：結合了凡得瓦爾吸引力、電荷排斥力、流體動力學交互作用力，並可同時考慮強重力/弱布朗運動及強布朗運動/弱重力的情況下，推導出兩球形膠體粒子間的臨界吸附軌跡方程式，再利用數值分析中的Runge-Kutta解法，以電腦模擬方法畫出膠體粒子的臨界吸附軌跡曲線，依照公式即可得到凝集效率。其中，凡得瓦爾吸引力與電荷排斥力結合成粒子間的交互作用力，以DLVO理論討論，流體動力學交互作用力的影響則以阻滯參數來表示，重力則採用圓球座標、低雷諾數系統下，兩膠體粒子的線性移動方程式來計算，布朗運動的描述用Langevin方程式解之，並以無因次重力參數Gr建立重力與布朗運動間的相互關係。第二部份：使用隨機推測學法，研究多顆膠體粒子分散的溶液系統，探討在不同穩定狀況下，膠體最終平衡位置及凝集構形。
由研究結果發現，第一部份：當兩膠體粒子間一致性越高時λ2γ≒1，重力作用越小時，凝集時間會增長，使得凝集效率會產生陡升的趨勢，此時無因次重力數Gr會呈陡降趨勢，若Gr<0.1而不考慮布朗運動時，就會高估凝集效率(α)，而考慮布朗運動則會修正凝集效率。第二部份：當膠體不考慮重力時，膠凝後的凝集結構則由膠體所處於的穩定區域位置所決定。當膠體之間作用力包含重力時，沉降後的沉降層數則與穩定區域沒有絕對的關係，需視膠體粒子的單位距離總能障大小(fR/R)與重力(fG)之間的關係而定。

The main purpose of this thesis is to investigate the flocculation behavior of colloidal particles with different sizes and densities in quiescent media. The thesis was divided into two parts as follows：1. to calculate the capture efficiency of colloidal particles under condition of strong gravity/weak Brownian effect and strong Brownian/weak gravity effect. In thesis simulation, with consideration of interparticle force, hydrodynamic interaction, gravitational force and Brownian diffusion force (i.e. described by the Langevin equation), the limiting trajectory between two flocculating particles was determined by solving the force balanced equation using the Runge-Kutta method. 2. to simulate the flocculation behavior by using the Monte Carlo method, at which the flocculation state in a poly-dispersed system was investigated.
From the above analyses, we found this：1. when the sizes and densities of two interacting particles are close to each other (i.e. λ2γ≒1), because of the steep decreases of gravity factor, both the time required for flocculation and the capture efficiency with increase with the decrease of gravitational force. The capture efficiency will be over-estimated at Gr<0.1 when the Brownian diffusion force on behavior of particles is not considered. 2. the find flocculation structure of particles will be determined by their stability region in the stability phase diagram when the gravitational force are not considered. On the contrary, when the gravitational force are considered, the final flocculation state of particles is independent of their stability region, but dependent on the relationship between the potential energy barrier per unit of separation distance (fR/R) and gravitational force (fG).

目錄

頁次
誌謝...........................................................I
中文摘要......................................................II
英文摘要.....................................................III
目錄..........................................................IV
圖目錄.......................................................VII
符號說明...................................................... XI

第一章 緒論...................................................1

第二章 文獻回顧...............................................3
2-1 簡介......................................................3
2-2 DLVO理論..................................................4
2-2-1 凡得瓦爾吸引力........................................5
2-2-2 靜電排斥力............................................6
2-2-3 電雙層理論............................................6
2-2-4 溶劑分子結構力........................................7
2-3 流體動力學交互作用力......................................8
2-4 重力.....................................................10
2-5 布朗運動.................................................12
2-6 模擬方法.................................................13
2-6-1 蒙地卡羅法...........................................14

第三章 程式建立..............................................15
3-1 程式模型.................................................15
3-2 相對速度.................................................19
3-3 膠體粒子間交互作用項.....................................20
3-3-1 凡得瓦爾吸引位能vA...................................20
3-3-2 電雙層排斥位能vR.....................................21
3-3-3 DLVO理論特性........................................24
3-4 流體動力交互作用項.......................................28
3-4-1 對稱平移運動.........................................28
3-4-2 不對稱平移運動.......................................30
3-5 重力項...................................................33
3-6 布朗運動項...............................................34
3-6-1 Langevin方程式......................................34
3-6-2 重力與布朗運動交互影響...............................36
3-7 軌跡方程式...............................................38
3-8 凝集效率.................................................41
3-9 蒙地卡羅法...............................................43
3-9-1 交互作用項...........................................45
3-9-2 重力.................................................47
3-9-3 結果判定.............................................48

第四章 結果討論..............................................49
4-1 粒徑比與阻滯度對能障的影響...............................50
4-2 密度比與無因次重力數的影響...............................56
4-3 不具布朗運動時的凝集效率曲線.............................59
4-3-1 高電解質濃度時的凝集效率曲線.........................59
4-3-2 具DLVO交互作用之凝集效率曲線........................59
4-3-3 相對密度比對凝集效率曲線的影響.......................66
4-3-4 不同重力場下電解質濃度對凝集效率的影響...............67
4-4 具布朗運動時的凝集效率曲線...............................77
4-4-1 布朗運動對臨界捕捉軌跡的影響.........................81
4-4-2 布朗運動對臨界電解質濃度的影響.......................81
4-5 顆膠體粒子分散系統.......................................88
4-5-1 電解質濃度對懸浮凝集結構的影響.......................88
4-5-2 電解質濃度對沉降凝集結構的影響.......................93

第五章 結論與建議............................................95
5-1 結論.....................................................95
5-2 建議.....................................................96

參考文獻......................................................97
附錄A
附錄B
簡歷

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