本研究設計不同迴轉盤並解析在動態微過濾中之流體力學與濾餅形成。微過濾應用中薄膜結垢被視為主要缺點，為了提高過濾性能和降低功耗，在動態過濾中使用迴轉盤所產生之剪切力可減少薄膜結垢。
    本研究的第一部分是評估局部過濾通量和濾餅之不均勻性。為了瞭解轉速對過濾性能和通量行為之影響，可藉由過濾實驗中分析濾餅形成機制、局部濾餅特性和粒徑分佈。此實驗部分是使用平均孔徑為0.1 μm之醋酸纖維酯膜過濾粒徑分佈為1.5 μm至25 μm之聚甲基丙烯酸甲酯（PMMA）球型微粒，並且使用計算流體動學（CFD）模擬薄膜表面上的速度和剪切力分佈，藉由力平衡方程式結合實驗局部濾餅性質可分析濾餅形成機制。局部過濾通量、臨界粒徑和操作條件之間的關係可推導出非線性方程式。此研究方法可以估計局部濾餅量和過濾通量，找出最佳操作條件，作為設計高效迴轉盤結構或過濾模組支之基礎。
    本研究的第二部分是在動態微過濾中選擇最佳操作條件與迴轉盤幾何結構以去除海水中之膠體結垢物。此研究使用計算流體力學模擬各種類型的迴轉盤在動態過濾器中的流體流動。藉由剪切力模擬值可建立濾餅質量和過濾通量之經驗方程式，並且基於過濾性能和功耗之間的關係設計出最佳迴轉盤幾何結構。由結果指出，除去海水中微粒可操作於低轉速度且具有兩個圓形通孔葉片的迴轉盤有高過濾通量和相對低的功率消耗。
    本研究的第三部分為在動態過濾系統中設計九種迴轉盤並評估微藻濃縮和薄膜結構之過濾性能。藉由過去研究所得知的微藻濾餅性質，並選擇適當的模型以估計濾餅質量和過濾通量。從平均薄膜表面剪切力估算可建立濾餅質量和過濾通量的關係經驗式，並且以高過濾通量和低功耗之間的觀點來判定迴轉盤之最佳設計，本研究可提供未來設計迴轉盤動態過濾器和最佳化操作的指引。

This thesis investigated the hydrodynamics and cake formation with different rotating-disk designs in dynamic microfiltration. Membrane fouling is recognized as a major drawback for the application of microfiltration. In order to enhance high filtration performance and low power consumption, the reduction of membrane fouling, which is caused by the shear stress at the membrane, is created by a rotating-disk in dynamic filtration.
    A local flux behavior and cake properties was evaluated to represent the nonuniformity of cake formation. In order to understand the effect of rotating speed on filtration performance and flux behavior, mechanism of cake formation, local cake properties, and particle size distribution were investigated in the filtration experiment. The mixed cellulose ester membrane with mean pore size of 0.1 μm was used for filtering Polymethyl methacrylate (PMMA) spherical fine particles with the particle size distribution ranged from 1.5 μm to 25 μm. The distributions of velocity and shear stress on the membrane surface were simulated using computational fluid dynamics (CFD). Combined with experimental data concerning local cake properties, the mechanism of cake formation based on a force balance model was analyzed. The relationship between local filtration flux, critical particle size, and operation conditions can be expressed as a nonlinear equation. This method estimates the local cake mass and filtration rate for optimizing operating conditions and designing high-efficiency disk structures or filter modules.
    The selection of optimum operating conditions and the design of disk structures for removing colloidal foulants from artificial seawater was applied in rotating-disk dynamic microfiltration. The fluid flows in dynamic filer with various types of rotating disks were simulated using computational fluid dynamics. The cake mass and filtration flux were estimated from the shear stress and calculated using empirical equations. The optimal design of rotating-disk was determined from comparing the filtration performances and power consumptions. The results indicated that a rotating-disk with two vanes of circular orifice under low disk rotation speed shows the optimal design and operating condition in removing the particles from seawater with high filtration flux and relatively low power consumption.
    Nine types of rotating-disk were designed and installed above the filter membrane in a filter chamber to study the filtration performances of microalgae concentration and membrane fouling. The cake property of microalgae was obtained from our previous study, and proper models were chosen to elucidate the cake mass and filtration flux. Once the mean shear stress on the membrane surface was known, the cake mass and filtration flux were estimated based on empirical equations. The optimal design of the rotating-disk was then determined from the viewpoints of high filtration flux and low power consumption. This study provides a guide for the design and optimized operation of rotating-disk dynamic filter.

Contents
致謝 -----I
中文提要 -----V
Abstract -----VII
Contents -----IX
Index of figures -----XIV
Index of tables -----XIX
Chapter 1: Introduction -----1
1.1 Research Background -----1
1.2 Research Aims -----3
1.3 Structure of the thesis -----3
Chapter 2: Literature Review -----5
2.1 Filtration of fine particles -----5
2.1.1 Membrane fouling -----5
2.1.1.1 Blocking models -----5
2.1.1.2 Cake filtration models -----9
2.1.2 Membrane morphology -----10
2.1.3 Particle deposition -----11
2.1.4 Hydrodynamic method -----12
2.2 Filtration of soft particles -----15
2.2.1 Effect of particle deformation -----16
2.2.2 Effect of cake compression -----20
2.2.3 Effect of particle interactions -----23
2.3 Dynamic filtration systems -----25
2.3.1 Rotating-disk dynamic filtration systems -----26
2.3.2 Computational fluid dynamics -----28
2.3.3 Calculation of shear stress on rotating disk and membrane -----28
2.3.4 Expression of filtration characteristics -----30
2.3.5 Energy considerations -----31
2.3.6 Microfiltration application of rotating-disk systems -----34	
Chapter 3: Analysis on the nonuniformity of cake formation in rotating-disk dynamic microfiltration -----38
3.1 Introduction -----39
3.2 Materials and experiments -----40
3.2.1 Materials and membrane -----40
3.2.2 Rotating-disk dynamic filtration and analyses -----42
3.2.3 Basic filtration equations and cake properties -----44
3.2.4 Local cake properties and filtration performance -----46
3.2.5 Force analysis on depositing particles -----47
3.2.5.1 Tangential drag force -----48
3.2.5.2 Normal drag force -----48
3.2.5.3 Net gravitational force -----49
3.2.5.4 Inertial lift force -----49
3.2.5.5 Net interparticle force -----49
3.2.6 The derivation process of local filtration flux -----50
3.3 Numerical simulation methods -----51
3.4 Results and discussion -----53
3.4.1 Simulated velocity and shear stress distributions -----53
3.4.2 Experimental filtration and cake structure -----55
3.4.3 Local cake properties -----59
3.4.4 Local filtration flux -----64
3.5 Summary -----67
Chapter 4: Structure design of rotating-disk dynamic microfiltration in improving filtration performances for fine particle removal -----68
4.1 Introduction -----69
4.2 Analyzed systems and numerical methods -----72
4.2.1 Analyzed systems -----72
4.2.2 Materials -----74
4.2.3 Numerical methods -----75
4.3 Theory -----76
4.3.1 Filtration equation and cake properties -----76
4.3.2 Power consumption -----77
4.4 Results and discussion -----78
4.4.1 Effect of disk rotation speed and feed flow rate -----78
4.4.2 Effect of disk structure -----84
4.4.3 The specific filtration flux -----87
4.5 Summary -----90
Chapter 5: Disk structure on the performance of a rotating-disk dynamic filter – A case study on microalgae microfiltration -----92
5.1 Introduction -----93
5.2 Analyzed Systems and Numerical methods -----95
5.2.1 Analyzed systems -----95
5.2.2 Materials -----98
5.2.3 Numerical methods -----99
5.3 Results and discussion -----101
5.3.1 Effect of disk rotation speed and feed flow rate -----101
5.3.2 Effect of geometric rotating-disk filter -----109
5.4 Summary -----119
Chapter 6: Conclusion -----120
6.1 General -----120
6.2 Analysis on the nonuniformity of cake formation -----121
6.3 Design of rotating-disk structure for fine particle removal -----122
6.4 Design of rotating-disk dynamic filter for microalgae microfiltration -----123
Chapter 7: Future Work -----124
Appendix -----126
A.1 Velocity profiles of parallel-disk system -----126
A.2 Power required of parallel-disk system -----128
A.3 Energy considerations of cross-flow system -----129
A.4 Energy considerations of rotating-disk system -----131
Abbreviations and Nomenclature -----134
References -----138
List of Publications -----154

Index of figures
Figure 1.1  Application range of various membrane processes.-----1
Figure 2.1  Four kinds of blocking phenomena in the membrane.-----7
Figure 2.2  The membrane blockages of (a) MF-Millipore (b) Durapore and (c) Isopore membranes at the initial stage of filtration. (Hwang et al., 2002)-----8
Figure 2.3  Two typical examples for explaining how the blocking index varies during microfiltration. (Hwang et al., 2007)-----9
Figure 2.4  Force analysis on a depositing particle in the (a) cross-flow and (b) submerged microfiltration system. (Hwang et al., 2006, 2010)-----12
Figure 2.5  The four stages of cake compression during a filtration. (Hwang et al., 2009)-----16
Figure 2.6  A comparison of cake structures formed by rigid and soft particles (a) PMMA rigid particles, (b) pseudomonas cells.-----17
Figure 2.7  Distributions of local cake porosity in cake at different filtration times. (Hwang et al., 2001b)-----18
Figure 2.8  The relationships between specific cake filtration resistance and P at different times. (Hwang et al., 2009)-----23
Figure 2.9  Specific energy consumed per m3 of permeate as a function of rotation speeds for various disks. (Brou et al., 2003)-----32
Figure 2.10  Power of rotating disk motor and feed pump at different TMP and rotating speed. (Luo et al., 2010)-----33
Figure 3.1  PMMA particle size distribution.-----41
Figure 3.2  Cross-sectional view of the chamber of a rotating-disk dynamic filter.-----42
Figure 3.3  Schematic view of the membrane.-----43
Figure 3.4  Schematic diagram of the dynamic microfiltration system.-----43
Figure 3.5  Forces on depositing particles in dynamic microfiltration.-----47
Figure 3.6  Simulated velocity distributions on x- and y- planes of rotating-disk dynamic filter at three disk rotating speeds.-----54
Figure 3.7  Simulated velocity distributions on the x-planes and velocity vectors near the rotating disk of a rotating-disk dynamic filter at three disk rotation speeds.-----54
Figure 3.8  Time courses of filtration flux during dynamic microfiltration at three TMPs, 20, 60 and 100 kPa, and Q = 3 × 10-6 m3/s and w = 500 rpm.-----55
Figure 3.9  Effects of disk rotating speed on the pseudo-steady filtration flux at TMPs from 20 to 100 kPa.-----57
Figure 3.10  Simulated shear stress distributions and cake formations at 1 hour of operation at three disk rotation speeds.-----57
Figure 3.11  The variation of the simulated compressive pressure and cake thickness distribution for different radial position with various disk rotating speeds.-----60
Figure 3.12  Local cake mass at different radial positions; TMP = 100 kPa for w = 100–500 rpm.-----61
Figure 3.13  Local specific cake filtration resistances at different radial positions; TMP = 100 kPa for w = 100–500 rpm.-----62
Figure 3.14  Particle size distributions in original PMMA suspension and the cake at various disk rotation speeds at TMP = 20 kPa.-----63
Figure 3.15  Comparison of calculated results and experimental data for average specific cake filtration resistances and cake mass at various disk rotation speeds at TMP = 20 kPa.-----64
Figure 3.16  Local filtration flux effects on critical particle size under various operating conditions.-----65
Figure 3.17  Local filtration flux at different r/r0 with various disk rotation speeds at TMP = 20 kPa.-----66
Figure 4.1  Schematic diagram of a cylindrical filter chamber with Type 1 rotating-disk.-----73
Figure 4.2  Schematic diagram of various types of rotating-disk dynamic filters.-----74
Figure 4.3  Comparison of mean shear rate between previous literature and this study under various disk rotation speeds.-----78
Figure 4.4  Effects of Q on mean shear stress at three disk rotation speeds, 100, 300 and 500 rpm with Type 1 rotating-disk.-----79
Figure 4.5  Simulated velocity distributions on xz-planes for type 1 rotating-disk under Q = 5×10-6 m3/s and disk rotation speeds from 500 to 3000 rpm.------80
Figure 4.6  The local shear stress on membrane surface at y = 0 of Type 1 rotating-disk at disk rotation speeds from 500 to 3000 rpm.-----81
Figure 4.7  Simulated shear stress distributions on membrane surface of Type 1 rotating-disk at different disk rotation speeds, (a)w= 500 rpm, (b)w= 1000 rpm, (c)w= 2000 rpm and (d)w= 3000 rpm.-----82
Figure 4.8  Effects of mean shear stress on the mean cake mass and pseudo-steady filtration flux of Type 1 rotating-disk at Q = 5×10-6 m3/s and P = 20 kPa.-----83
Figure 4.9  Simulated fluid velocity distribution of a cross-sectional view in the xz-plane for (a) Type 1, (b) Type 2 and (c) Type 3 rotating-disk and shear stress distribution on membrane surface for (d) Type 1, (e) Type 2 and (f) Type 3 rotating-disk at w = 3000 rpm.-----86
Figure 4.10  The cake resistances and pseudo-steady filtration fluxes for different types of rotating-disk dynamic filters at three disk rotation speeds, 1000, 2000 and 3000 rpm.-----87
Figure 4.11  The specific filtration fluxes for different types of rotating-disk dynamic filters at three disk rotation speeds, 1000, 2000 and 3000 rpm.-----89
Figure 5.1  The filter chamber of a rotating-disk dynamic filter used in this study.-----95
Figure 5.2  Schematic diagrams of different types of rotating-disks.-----97
Figure 5.3  Schematic diagrams of different types of rotating-disks with orifices. -----98
Figure 5.4  The microphotograph of Chlorella sp. (900x). (Lin, 2013)-----99
Figure 5.5  The mesh of rotating-disk dynamic filter.-----100
Figure 5.6  Comparisons of the mean shear rate between previous literature and this study under various rotating speeds.-----101
Figure 5.7  Fluid velocity on xz-plane at y = 0 for Type A1 rotating-disk at feed flow rates from 0 to 60 L/h.-----102
Figure 5.8  Distributions of shear rate on the membrane surface for Type A1 rotating-disk at feed flow rates from 0 to 60 L/h.-----103
Figure 5.9  Effects of feed flow rate on the mean shear rate at four rotating speeds of Type A1 rotating disk.-----104
Figure 5.10  Shear rate distributions on membrane surface at y = 0 for Type A1 rotating-disk at disk rotating speeds from 1000 to 3000 rpm.-----105
Figure 5.11  Effects of mean shear stress on the pseudo-steady filtration flux and mean cake mass for Type A1 rotating disk filter at Q = 30.8 L/h and P = 100 kPa.-----106
Figure 5.12  Effects of disk rotating speed on the power consumption and pseudo-steady filtration flux for Type A1 rotating disk filter at Q = 30.8 L/h and P = 100 kPa.-----108
Figure 5.13  Shear stress distributions at the membrane surface for different types of rotating-disks under w= 3000 rpm.-----111
Figure 5.14  The mean shear stress on the membrane surface for different types of rotating-disk filters with orifice disk at three disk rotating speeds, 150 500 and 3000 rpm.-----112
Figure 5.15  The power consumptions and pseudo-steady filtration fluxes for different types of rotating-disk filters at Q = 30.8 L/h and P = 100 kPa.-----113
Figure 5.16  Comparisons of the flux increase rate among different types of rotating-disk filters at three disk rotating speeds, 150 500 and 3000 rpm (on the basis of Type A1).-----114
Figure 5.17  Comparisons of the flux increase rate among different types of rotating-disk filters with orifice disk at three disk rotating speeds, 150 500 and 3000 rpm (on the basis of Type A1).-----115
Figure 5.18  Comparisons of the relative specific energy among different types of rotating-disk filters at three disk rotating speeds, 150 500 and 3000 rpm (on the basis of Type A1).-----117
Figure 5.19  Comparisons of the relative specific energy among different types of rotating-disk filters with orifice disk at three disk rotating speeds, 150 500 and 3000 rpm (on the basis of Type A1).-----118
Figure A.1  Schematic of parallel-disk system for cylindrical coordinates.-----126
Figure A.2  Schematic of two-parallel-plate cross-flow system for rectangular cartesian coordinates.-----129
Figure A.3  Schematic of parallel-disk system for cylindrical coordinates.-----131
Figure A.4  Effects of cross-flow velocity and disk rotation speed on the specific energy in cross-flow and rotating-disk dynamic filtration under P = 20 kPa.-----132

Index of tables
Table 4.1  Seawater quality characterization for pretreatment. (Voutchkov, 2010)-----70
Table 4.2  Constituents in artificial seawater.-----75
Table A.1  Effects of cross-flow velocity on the pseudo-steady filtration flux* (Hwang et al., 2016), power consumption and specific energy in cross-flow microfiltration.-----130
Table A.2  Effects of disk rotation speed on the pseudo-steady filtration flux* (Hwang et al., 2016), power consumption and specific energy in rotating-disk microfiltration. -----132

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