本研究以多相流模式模擬掃流微過濾之濾餅成長情形，探討濾餅的性質與結垢的機制，並進行掃流過濾實驗，取得數據作為比較，並了解掃流微過濾之特性。實驗中使用平均孔徑為0.1 μm的醋酸纖維膜（Mixed cellulose ester）過濾平均粒徑為0.8 μm的聚甲基丙烯酸甲酯（PMMA）粒子。在兩相流動的掃流微過濾中，改變懸浮液濃度與掃流速度，實驗結果顯示，懸浮液濃度越高與掃流速度越慢的條件下濾速越低，平均孔隙度也會逐漸降低。而利用計算流體力學（Computational Fluid Dynamics, CFD）軟體FLUENT6.2的多相流模式模擬濾餅成長是可能的，並可利用受力分析推測結垢機制。最後，根據動態實驗分析結果，得知濾餅的平均孔隙度隨著過濾時間的增加而減小，而濾餅阻力則是隨著過濾時間的增加而增加。

The study simulates cross-flow microfiltration by multiphase flow model. In order to discuss cake property and fouling mechanism, we experiment on cross-flow microfiltration. The data can be compared with simulation results and realize the property of cross-flow microfiltration. A filter membrane, made of mixed cellulose ester, with a mean pore size of 0.1 μm is used to filter 0.8 μm PMMA particles. On two-phase flow while varying suspension concentration and cross-flow velocity, we show that filtration rate is lowered with higher suspension concentration and lower cross-flow velocity, while average porosity is lowered as well. Also, we use Computational Fluid dynamics, CFD, software FLUENT6.2’s multiphase flow model to estimate cake growth and use force analysis to figure out fouling mechanism. Lastly, using results obtained from dynamic experiment, we know that cake average porosity is lower with filtration time, however, cake resistance is higher.

誌謝…………………………………………………………………………I
摘要…………………………………………………………………………II
目錄…………………………………………………………………………IV
	圖目錄…………………………………………………………………VII
	表目錄…………………………………………………………………X

第一章	緒論………………………………………………………………1
1-1	前言………………………………………………………………1
1-2	研究動機與目標…………………………………………………5

第二章	文獻回顧…………………………………………………………7
2-1	掃流過濾及其特性………………………………………………7
2-2	過濾阻塞模式……………………………………………………11
2-3	計算流體力學……………………………………………………15

第三章	理論………………………………………………………………17
3-1	掃流微過濾系統之受力…………………………………………17
3-2	阻力串聯模式……………………………………………………20
3-3	濾餅之空隙度……………………………………………………22
3-4	計算模式…………………………………………………………23
3-4-1	模擬邊界條件……………………………………………26
3-4-2	模擬幾何結構……………………………………………26
3-5	統御方程式……………………………………………………30
3-5-1	連續方程式………………………………………………30
3-5-2	動量方程式………………………………………………31
3-5-3	相之間交互作用力………………………………………32
3-5-4	多孔介質…………………………………………………33
3-6	數值方法………………………………………………………36

第四章	實驗裝置與步驟………………………………………………38
4-1	實驗物料…………………………………………………………38
4-2	實驗裝置…………………………………………………………40
4-3	實驗分析儀器……………………………………………………43
4-4	實驗步驟…………………………………………………………44

第五章  結果與討論………………………………………………………46
5-1  兩相流動中掃流過濾之特性……………………………………46
5-2  多相流模式之掃流過濾模擬……………………………………55
	5-2-1  速度分佈…………………………………………………55
	5-2-2  受力分析…………………………………………………58
	5-2-3  多相流模式模擬與實驗之比較…………………………66
5-3  掃流過濾之動態分析……………………………………………71

第六章  結論………………………………………………………………77

符號說明……………………………………………………………………79

參考文獻……………………………………………………………………84

圖目錄

第一章
	Fig. 1-1  The filtration spectrum………………………………………...2
Fig. 1-2  Schematics of dead-end filtration and cross-flow filtration…...4

第二章
	Fig. 2-1  Schematic drawing of the fouling mechanisms……………...12

第三章
Fig. 3-1  Force exerted on a depositing particle in cross-flow microfiltration………………………………………………...18
Fig. 3-2  Control volume force analysis on the membrane surface..…..19
Fig. 3-3  The resistance of microfiltration……………………………..21
Fig. 3-4  The procedural steps of numerical simulation……………….25
Fig. 3-5  Conditional geometry of cross-flow filtration.………………27
Fig. 3-6  Structural and Meshed geometry of cross-flow filtration……29

第四章
Fig. 4-1  The SEM picture of PMMA powder（49,650X）………….38
Fig. 4-2(a)  The top view SEM picture of the mixed cellulose ester membrane（50,000X）.……………………………………..39
Fig. 4-2(b)  The side view SEM picture of the mixed cellulose ester membrane（50,000X）……………………………………...40
Fig. 4-3  The schematic diagram of cross-flow filtration system……..41
Fig. 4-4(a)  The picture of cross-flow filtration system……………….42
Fig. 4-4(b)  The picture of cross-flow filtration units…………………42

第五章
Fig. 5-1  Decay of filtration rates during cross-flow microfiltration at v=0.1 m/s under different feed concentration………………...47
Fig. 5-2  Decay of filtration rates during cross-flow microfiltration at v=0.2 m/s under different feed concentration………………...48
Fig. 5-3  Decay of filtration rates during cross-flow microfiltration at C0=0.2wt% under different cross-flow velocity……………...50
Fig. 5-4  Decay of filtration rates during cross-flow microfiltration at C0=0.3wt% under different cross-flow velocity……………...51
Fig. 5-5  The relation between steady flux and feed concentration under different cross-flow velocity………………………………….53
Fig. 5-6  The relation between average porosity and feed concentration under different cross-flow velocity…………………………...54
Fig. 5-7  Vectors of velocity above membrane surface 0.5 mm
（v = 0.2 m/s, C0 = 0.2 wt%, ΔP = 25 kPa, t = 7200 s）……..56
Fig. 5-8  Contour of water velocity at different level
（v = 0.2 m/s, C0 = 0.2 wt%, ΔP = 25 kPa, t = 7200 s）……..57

Fig. 5-9  The relation between force and distance of flow direction during cross-flow microfiltration（v = 0.1 m/s, C0 = 0.2 wt%, 
ΔP =25 kPa）…………………………………………………59
Fig. 5-10  The relation between force and distance of flow direction during cross-flow microfiltration（v = 0.2 m/s, C0 = 0.2 wt%, 
ΔP = 25 kPa）…………………………………………………61
Fig. 5-11  The relation between force and distance of flow direction during cross-flow microfiltration（v = 0.3 m/s, C0 = 0.2 wt%, 
ΔP = 25 kPa）…………………………………………………62
Fig. 5-12  The relation between force and distance of flow direction on membrane surface under different cross-flow velocity……… 63
Fig. 5-13  Images of filtration cake at different cross-flow velocity
（C0 = 0.2 wt%, ΔP = 25 kPa）………………………………..64
Fig. 5-14  The relation between force and distance of flow direction on membrane surface under different cross-flow velocity by single-phase flow……………………………………………..65
Fig. 5-15  The relation between surface integral of solid volume fraction and height under different feed concentration………………...67
Fig. 5-16  Comparison of simulation and experiment cake thickness under different feed concentration……………………………68
Fig. 5-17  Comparison of simulation and experiment cake weight under different feed concentration…………………………………..69
Fig. 5-18  Comparison of simulation and experiment average porosity under different feed concentration……………………………70
Fig. 5-19  The time evolution of cake weight per unit area and cake thickness during cross-flow microfiltration…………………72
Fig. 5-20  The time evolution of average porosity and cake resistance during cross-flow microfiltration……………………………74
Fig. 5-21  Images of filtration cake at different time
（ΔP = 25 kPa, v = 0.2 m/s, C0 = 0.2 wt%）………………….75
Fig. 5-22  The SEM pictures of filtration cake at different time
（ΔP = 25 kPa, v = 0.2 m/s, C0 = 0.2 wt%）（10,000X）…….76

表目錄

Table 2-1  The characteristics of fouling mechanisms………………..14
Table 4-1  The operating conditions…………………………………..43

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