根據修正型阻力串聯模式，考慮濃度極化現象沿著薄膜管增加並透膜壓差、體積流率隨之下降，一組估算管式薄膜超過濾器局部和平均濾速之關係式可透過質量與動量平衡求得。在各種進料濃度、透膜壓差及體積流率等操作條件變化下，以Dextran T500水溶液在陶瓷薄膜管中的超過濾實驗為例，由10個濾液出口局部濾速的實驗數據證實了估算式的正確性，並進而討論濃度極化遞增造成濾速沿薄膜管的衰退。
    接下來，我們在薄膜管中插入一鋼棒，於其上繞環，觀察改變繞環密度並沿管軸改變繞環間距對濾速的影響，並進行理論分析。結果顯示適當地調整繞環間距，藉以消除濃度極化的影響，並維持有效的透膜壓差，將可大大改善超過濾的操作效率。

The correlation equations for predicting local and average permeate fluxes in tubular-membrane ultrafilters was derived from mass and momentum balances by the modified resistance-in-series model with the consideration of concentration polarization along the membrane tube. Ultrafiltration of Dextran T500 aqueous solution in a tubular microporous ceramic module has been carried out under various operation conditions, in which experimental data of ten local permeate fluxes along the tube were obtained to confirm the correlation predictions. The increment of concentration polarization, as well as the decline of permeate flux, along the tube was also discussed. The theoretical predictions and experimental study were also carried out for ultrafiltration in a tubular module inserted concentrically with a steel rod wrapped by rings with various ring distances also the flow channel. Considerable improvement in performance was obtained by properly adjusting the ring distance, so that the undesirable concentration polarization resistance is suppressed while still preserving the effective transmembrane pressure.

目錄

圖索引 V
表索引 IX
附錄索引 X
第一章 緒論 1
1 − 1 薄膜及薄膜分離 1
1 − 2 超過濾的應用 7
1 − 2.1 半導體工業 7
1 − 2.2 生技工業 7
1 − 2.3 表面處理工業 8
1 − 2.4 食品工業 8
1 − 3 驅動力之種類及薄膜分離能力之劃分 9
1 − 4 濃度極化現象及結垢 13
1 − 4.1 濃度極化現象 13
1 − 4.2 結垢 14
1 − 5 影響濾速之因素 16
1 − 5.1 薄膜材質的影響	16
1 − 5.2 pH值與離子強度的影響 16
1 − 5.3 進料濃度的影響	18
1 − 5.4 溫度的影響 18
1 − 5.5 壓力的影響 19
1 − 5.6 流速與擾流的影響 20
1 − 6 研究目的 22
第二章 文獻回顧 23
2 − 1 濾速分析模式 23
2 − 1.1 阻力串聯模式 24
2 − 1.2 滲透壓模式 27
2 − 1.3 膠化層模式 29
2 − 2 濾速提升的方法 33
2 − 2.1 薄膜材質 33
2 − 2.2 過濾模組中擾流誘導物的設置 34
2 − 2.3 前處理 38
2 − 2.4 逆洗程序與脈衝流動 38
第三章 理論分析 40
3 − 1 沿薄膜管濾速的遞減與濃度極化效應的遞增 40
3 − 1.1 修正型阻力串聯模式 42
3 − 1.2 質量平衡 43
3 − 1.3 動量平衡 43
3 − 1.4 平均濾速 44
3 − 2 插棒繞環薄膜管模組 46
3 − 2.1 質量平衡 48
3 − 2.2 動量平衡 48
3 − 2.3 透膜壓差之衰退 49
3 − 2.4 平均濾速 50
第四章 結果與討論 51
4 − 1  沿薄膜管濾速的遞減與濃度極化效應的遞增 51
4 − 1.1  實驗裝置與條件 51
4 − 1.2  Rm和Rf之實驗關係式 54
4 − 1.3   和 之實驗關係式 61
4 − 1.4  濾速關係式與實驗結果的比較 68
4 − 1.5  濃度極化層阻力沿著流動方向的遞增 77
4 − 2  插棒繞環薄膜管模組 80
4 − 2.1  實驗裝置與條件 80
4 − 2.2  Rm、Rf以及 之實驗關係式	84
4 − 2.3  摩擦因子f之實驗關係式 96
4 − 2.4  繞環分段數N對濾速的影響 107
4 − 2.5  繞環間距公差a對濾速的影響 116
第五章 結論 129
符號說明 130
參考文獻 135
附錄 144

圖索引
圖 1 − 1 掃流超過濾系統之示意圖...........................................................................6
圖 1 − 2 各分離程序處理粒徑能力之配置圖.........................................................11
圖 1 − 3 操作參數對濾速之關係圖.........................................................................17
圖 2 – 1 影響薄膜過濾之各種阻力示意圖..............................................................26
圖2 – 2 滲透壓模式與膠化層模式之示意圖...........................................................32
圖2 – 3 Kenics static mixer之示意圖.....................................................................36
圖2 – 4 模組中擾流誘導物設置之示意圖...............................................................36
圖2 – 5 Mavrov實驗中模組之示意圖...................................................................37
圖2 – 6 傳統操作與逆洗操作之示意圖...................................................................37
圖3 − 1 超過濾薄膜管示意圖..................................................................................41
圖3 − 2 插棒繞環薄膜管模組示意圖......................................................................47
圖4 − 1 分段薄膜管實驗裝置圖..............................................................................53
圖4 – 2 純水濾速圖...................................................................................................56
圖 4 – 3 在低流速、低濃度時，)(ξβ對ξ作線性回歸求iβ與α.....................66
圖 4 – 4 在高流速、高濃度時，)(ξβ對ξ作圖求iβ與α.................................67
圖 4 – 5 Ci = 0.1 wt%時，平均濾速J理論值與實驗值之比較..........................69
圖 4 – 6 Ci = 0.5 wt%時，平均濾速J理論值與實驗值之比較..........................70
圖 4 – 7 Ci = 1.0 wt%時，平均濾速J理論值與實驗值之比較..........................71
圖 4 – 8 Ci = 0.1 wt%、ui = 0.059 m/s時，局部濾速)(ξJ理論值與實驗值之比較...................................................................................................................73
V
圖 4 – 9 Ci = 0.5 wt%、ui = 0.059 m/s時，局部濾速)(ξJ理論值與實驗值之比較...................................................................................................................74
圖4 – 10 Ci = 1.0 wt%、ui = 0.059 m/s時，局部濾速)(ξJ理論值與實驗值之比較...................................................................................................................75
圖4 – 11 Ci = 1.0 wt%、ui = 0.147 m/s時，局部濾速)(ξJ理論值與實驗值之比較...................................................................................................................76
圖 4 – 12 Ci = 0.1 wt% 、= 80 kPa時，濃度極化層阻力的變化................78 iPΔ
圖 4 – 13 Ci = 1.0 wt% 、= 80 kPa時，濃度極化層阻力的變化................79 iPΔ
圖 4 − 14 實驗裝置圖.............................................................................................81
圖 4 – 15 、a = 0時， wt%1.0=iCφ與N的關係圖......................................88
圖 4 – 16 、a = 0時， wt%5.0=iCφ與N的關係圖......................................89
圖 4 – 17 時， wt%1.0=iCφ與da的關係圖...............................................90
圖 4 – 18 時， wt%5.0=iCφ與da的關係圖................................................91
圖 4 – 19 、a = 0時，與N的關係圖...................................92 wt%1.0=iCfR
圖 4 – 20 、a = 0時，與N的關係圖....................................93 wt%5.0=iCfR
圖 4 – 21 時，與 wt%1.0=iCfRda的關係圖.............................................94
圖 4 – 22 時，與 wt%5.0=iCfRda的關係圖.............................................95
圖 4 – 23 f與Re的關係圖................................................................................104
圖 4 – 24 a = 0時，f與N的關係圖.................................................................105
圖 4 – 25 N = 10時，f與da的關係圖..........................................................106
VI
圖 4 – 26 sm1067.136−×=iQ時，繞環對平均濾速J的影響...................108
圖 4 – 27 sm102.5036−×=iQ時，繞環對平均濾速J的影響...................109
圖 4 – 28 sm1033.336−×=iQ時，繞環對平均濾速J的影響....................110
圖 4 – 29 sm1017.436−×=iQ時，繞環對平均濾速J的影響...................111
圖 4 – 30 高壓高流速時，J隨著N變化的趨勢..............................................112
圖 4 – 31 高壓低流速時，J隨著N變化的趨勢..............................................113
圖 4 – 32 低壓高流速時，J隨著N變化的趨勢..............................................114
圖 4 – 33 低壓低流速時，J隨著N變化的趨勢..............................................115
圖 4 – 34 sm1067.136−×=iQ、kPa 30=ΔiP時，J隨著da變化的趨勢.................................................................................................................117
圖 4 – 35 sm1067.136−×=iQ、kPa 80=ΔiP時，J隨著da變化的趨勢.................................................................................................................118
圖 4 – 36 sm1067.136−×=iQ、kPa 140=ΔiP時，J隨著da變化的趨勢.................................................................................................................119
圖 4 – 37 sm1050.236−×=iQ、kPa 30=ΔiP時，J隨著da變化的趨勢.................................................................................................................120
圖 4 – 38 sm1050.236−×=iQ、kPa 80=ΔiP時，J隨著da變化的趨勢.................................................................................................................121
圖 4 – 39 sm1050.236−×=iQ、kPa 140=ΔiP時，J隨著da變化的趨勢
VII
.................................................................................................................122
圖 4 – 40 sm103.3336−×=iQ、kPa 30=ΔiP時，J隨著da變化的趨勢.................................................................................................................123
圖 4 – 41 sm103.3336−×=iQ、kPa 80=ΔiP時，J隨著da變化的趨勢.................................................................................................................124
圖 4 – 42 sm103.3336−×=iQ、kPa 140=ΔiP時，J隨著da變化的趨勢.................................................................................................................125
圖 4 – 43 sm104.1736−×=iQ、kPa 30=ΔiP時，J隨著da變化的趨勢.................................................................................................................126
圖 4 – 44 sm104.1736−×=iQ、kPa 80=ΔiP時，J隨著da變化的趨勢.................................................................................................................127
圖 4 – 45 sm104.1736−×=iQ、kPa 140=ΔiP時，J隨著da變化的趨勢.................................................................................................................128
VIII
表索引
表 1 − 1 依各驅動力劃分之薄膜程序.....................................................................10
表 1 − 2 以壓力差驅動之薄膜分離程序性質的比較.............................................12
表4 – 1 純水濾速的實驗值....................................................................................55
表4 – 2 Dextran T500水溶液的平均濾速實驗值.................................................58
表4 – 3 不同操作條件下之與fRφ值..................................................................59
表4 – 4 當Ci = 0.1 wt%、Qi = 1.67×10-6 m3/s時，局部濾速以及濃度極化層阻力之實驗值...................................................................................................62
表4 – 5 當Ci = 0.5 wt%、Qi = 1.67×10-6 m3/s時，局部濾速以及濃度極化層阻力之實驗值...................................................................................................63
表4 – 6 當Ci = 1.0 wt%、Qi = 1.67×10-6 m3/s時，局部濾速以及濃度極化層阻力之實驗值...................................................................................................64
表4 – 7 當Ci = 1.0 wt%、Qi = 4.17×10-6 m3/s時，局部濾速以及濃度極化層阻力之實驗值...................................................................................................65
表4 – 8 不同操作條件下之iβ與α值.................................................................68
表 4 – 9 不同操作條件下之φ值.............................................................................85
表 4 – 10 不同操作條件下之值.........................................................................86 fR
表 4 – 11 Dextran T500水溶液之濾速實驗值......................................................97
表 4 – 12 插棒薄膜管模組在各種條件下的平均摩擦因子f...........................102
IX
附錄索引
附錄 (A – 1) Dextran T500水溶液的平均濾速理論值.......................................144
附錄 (A – 2) 時，Dextran T500水溶液的局部濾速理論值.....145 kPa 30=ΔiP
附錄 (A – 3) 時，Dextran T500水溶液的局部濾速理論值....146 kPa 014=ΔiP
附錄 (A – 4) = 80 kPa時，濃度極化層阻力的變化情形............................147 iPΔ
附錄 (B – 1) φ與的理論值............................................................................148 fR
附錄 (B – 2) 平均摩擦因子f的理論值.............................................................150
附錄 (B – 3) Dextran T500水溶液之濾速理論值...............................................151
附錄 (B – 4) 不同N值之下，Dextran T500水溶液之濾速理論值..................156
X

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