本研究以懸臂式離心過濾純化雙成分懸浮液中之蛋白質，探討操作條件對分離效率之影響。懸浮液係以酵母菌及牛血清蛋白懸浮於不同pH值的緩衝溶液中配置而成，以離心轉速500-4000rpm進行離心過濾。本研究以數值方法模擬懸浮液中酵母菌在不同離心轉速時的移動速度，藉以估計過濾過程中酵母菌的沈積速度，計算不同離心轉速(離心效應)下之濾餅質量及過濾速度，並藉由濾餅之黏彈性模式估計過濾比阻以及孔隙度在過濾過程之變化，並與實驗數據比較。
結果顯示：濾餅都在過濾初期(300s)即已成長完全；隨著離心轉速越高，濾餅的形成也越快，濾餅平均過濾比阻亦會大幅提昇。將這些因素納入模擬程序中，可以精確模擬出不同pH值及離心轉速下的濾餅生成速率及過濾速度，並配合黏彈模式可估計出與實驗值相符合的平均過濾比阻及孔隙度。藉由量測蛋白質的通過率來關聯操作條件與蛋白質分離效率之間的關係，並據以追求達到最高分離效率的最適操作條件。本研究經比較離心過濾與掃流過濾間的分離效率，結果顯示唯有在高轉速離心過濾時，分離效果才會高於掃流過濾。

Centrifugal filtration is used to purify protein from binary suspension prepared by yeast cells and BSA under rotational speeds ranged from 500 to 4000rpm and various pH values. The cake growths under various conditions are simulated by analyzing the migration velocity of particles in the filter chamber, while the average specific filtration resistance and average porosity of cake are estimated based on a Voigt-in-series model.
The results show that the cake growth rate increases with the increase of rotational speed. Since the cake is compressed continuously during a centrifugal filtration, this effect should be taken into consideration in order to simulate the cake properties, the cake mass and the filtration rate accurately. The predicted results of average specific filtration resistance and average porosity of cake agree fairly well with the available experimental data. In addition, the protein separation efficiency can be predicted once the BSA permeation through the cake and filter septum is analyzed. The separation efficiency is higher under a higher rotational speed due to higher filtration rate. Compare the received filtration volume in centrifugal filtration with that in cross-flow microfiltration, the efficiency of centrifugal filtration is higher only under higher rotating speeds.

誌謝……Ⅰ
摘要……Ⅱ
目錄……Ⅳ
圖目錄……Ⅶ
表目錄……ⅩⅡ
第一章 緒 論……1
第二章 文 獻 回 顧……6
2-1 重力及離心沈降之研究……6
2-2 干擾沈降模式(The hindered settling model)……10
2-3 離心過濾之研究……15
2-4 懸浮液性質對過濾之影響……20
2-5 離心裝置之改進……24
第三章 理 論……26
3-1 離心過濾理論……26
3-2 離心過濾中粒子運動之模擬……29
3-2.1 懸浮液中粒子之受力解析……29
3-2.2 干擾沈降模式(Hindered settling model)……34
3-2.3 可變形粒子濾餠結構之黏彈性模式……35
3-2.4 濾餅局部過濾比阻……38
3-2.5 離心過濾機構之模擬程序……38
第四章 實驗裝置與步驟……43
4 - 1 實驗裝置……43
4-2 實驗物料……46
4-3 分析儀器……46
4-4 實驗步驟……47
4-4.1 緩衝溶液的配置……47
4-4.2 離心過濾步驟……48
4-4 BSA 濃度之測量方法……49
第五章 實驗結果與討論……50
5-1 懸浮粒子的特性……50
5-1.1 酵母菌(Yeast)及牛血清蛋白(BSA)的基本性質……50
5-1.2 酵母菌的恆壓過濾……53
5-2 離心轉速對過濾之影響……56
5-2.1 離心濾速之探討……56
5-2.2 離心過濾之濾餅性質……59
5-3 不同pH 值對離心過濾之影響……64
5-4 離心過濾的分離效率……68
5-5 離心過濾和掃流過濾之比較……71
5-6 離心過濾機構之模擬……75
5-6.1 自恆壓過濾獲取濾餅之性質……75
5-6.2 離心過濾濾餅性質之模擬……79
5-6.3 離心過濾濾餅成長之模擬……82
第六章 結論……90
符 號 說 明……93
參 考 文 獻……97
附 錄……104

圖目錄
Fig.1-1 Schematics of cross-flow filtration and dead-end filtration……2
Fig.1-2 The classification of centrifuge……2
Fig. 2-1 Interfaces in sedimentation. Sambuichi(1987)……8
Fig. 2-2 The theory of sedimentation. (a)Kynch theory. (b)modification of
the Kynch theory by Tiller.……10
Fig.2-3 Schematic diagram in a centrifugal basket……16
Fig.3-1 Schematic diagram of a one-dimensional centrifugal filtration……28
Fig.3-2 Interaction energy of Van der Waals force and electrical double
layer repulsive force under different distance……31
Fig.3-3 Analogy of filter cake structure with Voigt in series model……37
Fig.3-4 Schematic diagram of the particles migration……40
Fig.3-5 A flowchart for the simulation of centrifugal filtration……42
Fig.4-1 Schematic diagram of centrifugal filtration……44
Fig.4-2 Profile of filter chamber in centrifugal……45
Fig.4-3 The calibration curve of BSA concentration of 0~0.2
wt% at various pH values……49
Fig.5-1 The zeta potential of Yeast, Yeast/BSA and BSA particle under
various pH values……51
Fig.5-2 The size distribution of Yeast/BSA under various pH values……52
Fig.5-3 Filtration curves of dt/dv v.s. v under various filtration pressure
with pH7.0……53
Fig.5-4 Filtration curves of dt/dv v.s. v under various filtration pressure
with pH3.0……55
Fig.5-4.1 An enlarge plot of the first and second stages in Fig.5-4……55
Fig.5-5 Filtrate weight during centrifugal filtration under various
rotational speeds with pH7.0……57
Fig.5-6 The pressure drop during centrifugal filtration under various
rotational speeds with pH7.0……58
Fig.5-7 Filtration rates during centrifugal filtration under various
rotational speeds with pH7.0……58
Fig.5-8 The time courses of cake mass during centrifugal filtration under
various rotational speeds with pH7.0……60
Fig.5-9 Average porosity of cakes during centrifugal filtration under
various rotational speeds with pH7.0……62
Fig.5-10 The average specific cake resistance during centrifugal filtration
under various rotational speeds with pH7.0……62
Fig.5-11 The filtration rates versus the pressure drop during centrifugal
filtration under various rotational speeds with pH7.0……63
Fig.5-12 Filtrate weight during centrifugal filtration under various
rotational speeds with pH5.0……65
Fig.5-13 Filtrate weight during centrifugal filtration under various
rotational speeds with pH3.0……65
Fig.5-14 Filtration rates during centrifugal filtration under various pH
values with 500rpm……66
Fig.5-15 Filtration rates during centrifugal filtration under various pH
values with 4000rpm……67
Fig.5-16 The average specific cake resistance during centrifugal filtration
under various pH values with 4000rpm……68
Fig.5-17 The filtrate weight of BSA versus the filtrate volumes under
various rotational speeds and pH values……70
Fig.5-18 The separation efficiency under various rotational speeds and
pH values……70
Fig.5-19 The period of batchwise centrifugal filtration……71
Fig.5-20 A comparison of the filtration time and separation efficiency
between cross-flow (∆P=50kPa) and centrifugal system with
pH7.0……73
Fig.5-21 Average porosity of cakes during constant pressure filtration
under various pressures with pH7.0……76
Fig.5-22 A plot of ln(εex-εex,f) v.s. t under various pressures with
pH7.0……78
Fig.5-23 A plot of εex,f、εex,0 and τex v.s. t under various pressures with
pH7.0……78
Fig.5-24 A comparison of the time dependence of average specific cake
resistance measured with the predicated values……79
Fig.5-25 A comparison of the average porosity of cakes with time
between the predicated values and experimental data……81
Fig.5-26 A comparison of the average specific cake resistance with time
between the predicated values and experimental data……81
Fig.5-27 The sedimentation velocity of Yeast during gravity
sedimentation under various concentrations and pH values……83
Fig.5-28 The size distribution of Yeast on the supernatant-suspension
interface during sedimentation under various pH values……84
Fig.5-29 Variations of particle concentration profiles during centrifugal
filtration with 500rpm and pH7.0……85
Fig.5-30 Variations of particle concentration profiles during centrifugal
filtration with 4000rpm and pH7……85
Fig.5-31 Comparison of particle concentration profiles during centrifugal
filtration under various rotating speeds with pH7.0……87
Fig.5-32 The cake mass of simulated values and experimental data……87
Fig.5-33 A comparison of filtration rates between the predicated values
and experimental data under various rotational speeds……89
Fig.5-34 A comparison of the pressure drop between the predicated
values and experimental data under various rotational speeds……89
Fig.A-1 The SEM picture of yeast (10,000X)……105
Fig.A-2 Particle size distribution of Yeast under various pH
values……105
F i g . A - 3 T h e t o p v i e w o f t h e f i l t r a t e p a p e r b y
SEM(5,000X)……106
Fig.B-1 Filtrate weight during centrifugal filtration under various
rotational speeds with pH5.0……107
Fig.C-1 The drying curve for the filtration cake of yeast/BSA……......110
Fig.D-1 The calculation compressibility coefficient n under various pH
values……111
Fig.D-2 The calculation compressibility coefficient β under various pH
values……112
Fig.D-3 A comparison of the average porosity of cakes with time between
the predicated values and experimental data under pH5.0……112
Fig.D-4 A comparison of the time dependence of average specific cake
resistance measured with the predicated values under pH5.0……113
Fig.D-5 A comparison of the average porosity of cakes with time between
the predicated values and experimental data under pH3.0……113
Fig.D-6 A comparison of the time dependence of average specific cake
resistance measured with the predicated values under pH3.0……114
Fig.F-1 A comparison of the average porosity of cakes with time between
the predicated values and experimental data under pH5.0……116
Fig.F-2 A comparison of the average specific cake resistance with time
between the predicated values and experimental data under
pH5.0……117
Fig.F-3 A comparison of the average porosity of cakes with time between
the predicated values and experimental data under pH3.0……117
Fig.F-4 A comparison of the average specific cake resistance with time
between the predicated values and experimental under data
pH3.0……118

表目錄
Tab.2-1 The modified Stokes’ law. (for dilute suspension in the creeping
flow region)……12
Table.4-1 The relationship of rotational speeds, angular speeds,
centrifugal effects, and maximum pressures……44
Table.5-1 The coefficients of Tiller’s empirical equations……56
Table.5-2 The time of centrifugal period under various rotational speed
and pH values……72
Table.E-1 The filtration time various wall shear stresses and pH values
under cross-flow filtration……115
Table.E-2 The separation efficiency various wall shear stresses and pH
values under cross-flow filtration……115

Al-Naafa, M. A. ,and M. Sami Selim, “Sedimentation of Monodisperse amd Bidisperse Hard-Sphere Colloidal Suspensions,” AIChE J. ,Vol.38(10), 1618-1630 (1992)
Barr, J.D and, L. R.White, “Centrifugal Drum Filtration : Ⅰ. Com- pression Rheology Model of Cake Formation,” AIChE J., vol.52(2), 545-556 (2006a)
Barr, J.D and, L. R.White, “Centrifugal Drum Filtration : Ⅱ. Com- pression Rheology Model of Cake Formation,” AIChE J., vol.52(2), 557-564 (2006b)
Batchelor, G. K., and C. S. Wen, “Sedimentation in a dilute polydisperse system of interacting sphere Part2. Numerical results,” J. Fluid Mech., vol.124, 495-528 (1982)
Bird, R. B., W. E. Stewart, E. N. Lightfoot, “Transport Phenomena,” 2rd John Wiley, Chap.2 (2002) 
Burger, R., S. Evje, K. Hvistendahl Karlsen and, K. A. Lie, “Numerical Method for the Simulation of the Settling of Flocculated suspension,” Chem. Eng. J., vol.80, 91-104 (2000)
Coulson, J. M., J. M. Richardson et al, “Chemical Engineering,” Vol.2, 3rd, Maxwell House, Chap.5 (1979)

Chu, C. P. and, D. J. Lee, “Centrifugation of Polyelectrolyte Flocculated Clay Slurry,” Separation Science and Technology, vol.37(3), 591-605 (2002)
Davies, R. and B. H. Kaye, ”Experimental Investigation into the Settling Behavior of Suspensions,” Powder Technol., Vol.5,61-68 (1971)
Davis, R. H. and A. Acrivos, ”Sedimentation of Noncolloidal particles at Low Reynolds Numbers,” Ann. Rev. Fluid Mech., Vol.17, 91 (1985)
Davis, R. H. and, K. H. Birdsell, ”Hindered settling of Semidilute Monodisperse and Polydisperse Suspension,” AIChE J., Vol.34(1), 123-129 (1988).
Djilali, N., J. G. Pharoach and, G. W. Vickers, “Fluid Meachanics and Mass Transport in Centrifugal Membrane Separation,” J. Membr. Sci., vol.176, 277-289 (2000)
Fyles, T. M., A. Bergen, D. S. Lycon, G. W. Vickers and, P. Wild, “Flux Enhancement in Reverse Osmosis Using Centrifugal Membrane Separation,” J. Membr. Sci., vol.176, 257-266 (2000a)
Fyles, T. M. and, D. S. Lycon, “Fouling Reduction Using Centrifugal Membrane Separation,” J. Membr. Sci., vol.176, 267-276 (2000b)
Grace, H. P., “Resistance and Compressibility of Filter Cake,” Chem. Eng. Prog., Vol.49(6), 303-317 (1953)
Happel, J. and, H. Brenner, “Low Reynolds Number Hydrodynamics,” Chap.6-8, Prentice-Hall (1965)
Harris, C. C., P. Somasundaran, and R. R. Jensen, “Sedimentation of Compressible Materials : Analysis of Batch Sedimentation Curve,” Powder Technology, 11, 75-84 (1975)
Hwang, K. J., Y. C. Chiou and, W. M. Lu, “Studies on Mechanism of Centrifugal Filtration,” Proceedings of Symposium on Transport Phenomena and Applications., Dept. Chem. Eng., National Taiwan University, Taipei, 387-392 (1994)
Hwang, K. J., “Effect of Particle Size on the Performance of Batchwise Centrifugal Filtration,” Water Science and Technology, vol.44(10), 185-189 (2001)
Hwang, K. J., W. T. Chu and, W. M. Lu, “A Method to Determine the Cake Properties in Centrifugal Dewatering,” Separation Science and Technology, vol.36(12), 2693-2706 (2001)
Hwang, K. J. and, C. L. Hsueh, “Dynamic Analysis of Cake Properties in Microfiltration of Soft Colloid,” J. Membr. Sci., vol.214, 259-273 (2003)
Hwang, K. J., Y. C. Shie and, Y. S. Lin, “Cake formation and Flux Decline in Centrifugal Filter Basket,” J. Chin. Inst. Chem. Engrs., vol.36(5), 1-9 (2005)
Hwang, K. J., S. Y. Lyu and, F. F. Chen, “The Preparation and Filtration Characteristics of Dextran-MnO2 Gel Particles,” Powder Technol., vol.161, 41-47 (2006)

Kuberkar, V. T. and, R. H. Davis, “Effects of Added Yeast on Protein Transmission and Flux in Cross-Flow Membrane Microfiltration,” Biotechnol. Prog., vol.15 ,472-479 (1999).
Kuberkar, V. T. and, R. H. Davis, “Microfiltration of Protein-Cell Mixtures with Crossflushing or Backflushing,” J. Membr. Sci. , vol.183, 1-14 (2001).
Kynch, G. J.; “Trans. Faraday Soc,” Vol.46, 166 (1952)
Landman, K. A. and, L. R. White, “Determination of the Hindered Settling Factor for Flocculated Suspension,” AIChE J., Vol.38(2), 184-192 (1992).
Lu, W. M. and, K. J. Hwang, “Mechanism of Cake Formation in Constant Pressure Filtration,” Sep. Technol., 3, 122-132 (1993)
Lu, W. M., K. L. Tung, C. H. Pan and, K. J. Hwang, “The Effect of Particle Sedimentation on Gravity Filtration,” Separation Science and Technology, vol.33(12), 1723-1746 (1998)
Lu, W. M., K. L. Tung, S. M. Hung, J. S. Shiau and, K. J. Hwang, “Constant pressure filtration of mono-dispersed deformable particle slurry,” Sep. Sci. Technol., vol.36, 2351–2379(2001)
Lustenberger, C., T. Friedmann and, E. J. Windhab, “Filtration Experiments with Compressible Filter Cakes in Centrifugal Fields with Superimposed Static Pressure,” Int. J. Miner. Process, vol.73, 261-267 (2004)
Maloney, J. O., “Centrifugation,” Ind. Eng. Chem., vol.38, 24 (1946)
Mandersloot, W. G. B., K.J. Scott, and C. P. Geyer, “Sedimentation in the Hindered Settling Regime,” In Advanced in Solid-Liquid Separation (H. S. Muralidhara,Ed.), Battelle Press, Columbus, OH, Chap.3 (1986)
Masliyah, J. H., “Hindered Settling in a Multi-Species Particles System,” Chem. Eng. Sci., vol.34, 1166-1168 (1979)
Miri, R., R. Dizene and, R. Joulie, “Influence of Adsorbent on a Dynamic Protein Membrane in Cross Flow Filtration,” Desalination, vol.168, 329-339 (2004)
Mota, M., J. A. Teixeira and, A. Yelshin, “Influence of Cell-shape on the Cake Resistance in Dead-end and Cross-flow Filtration,” Separat. Purif. Technol., vol.27, 137-144(2002)
Richardson, J. F., and W. N. Zaki, “Sedimentation and Fluidization.Ⅰ,” Trans. Inst. Chem. Eng., vol.32, 35 (1954)
Roberts, E. J.; “Min. Eng. And Min Trans,” Vol.18, 869 (1926)
Sambuichi, M., H. Nakakura, K. Osasa, and F. M. Tiller, “Theory of Batchwise Centrifugal Filtration,” AIChE J., Vol.33 (1), 109-120 (1987)
Shiirato, M., T. Murase and, H. Mori, “Centrifugal Dehydration of a Packed Particulate Bed,” Int. Chem. Eng., vol.23(2), 298-306 (1983)
Tiller, F. M., editor “Theory and Practice of Solid-Liquid Separation,” Univ. of Houston, Tx., U.S.A. (1975)

Tiller, F. M., “Revision of Kynch Sedimentation Theory,” AIChE J., Vol.27 (5), 823-828 (1981)
Tiller, F. M., C. S. Yeh, and N. B. Hsyung, “Unifying the Theory of Thickening, Filtration, and Centrifugation,” Water. Sci. Technol., Vol.28, 1 (1993)
Tiller, F. M., N. B. Hsyung, and D. Z. Cong, “Role of porosity in Filtration：ⅩⅡ.Filtration with Sedimentation,” AIChE J., Vol.41 (5), 1153-1164 (1995)
Tsang, K. R. and P. A.Vesilind , “Moisture Distribution in Sludge,” Wat. Sci. Technol. , 22 , 135-142 (1990).
Valleroy, V. V., and J. O. Maloney, “Comparison of the Specific Resistance of Cake Formed in Filters and Centrifuges,” AIChE J., Vol.6, 346 (1960)
Van Wie, B. J., D. M. Leatzow, B. N. Weyrauch and, T. O. Tiffany, “Design Optimization Characterization of a Small-scale Centrifugal Cell Separator,” Analytica Chimica Acta, vol.435, 299-307 (2001)
Wakeman, R. J., “Residual Saturation and Dewatering of Fine Coal and Filter Cake,” Powder Techno., vol.40, 53-63 (1984)
Wakeman, R. J. and, A. Vince, “Engineering Model for the Kinetics of Drainage from Centrifuge Cake,” Chem. Eng. Res. Des., vol.64, 104-108 (1986)
Wakeman, R. J., “Modeling Slurry Dewatering and Cake Growth in Filtering Centrifuges,” Filtr. Sep., vol.31, 75-81 (1994)
Wickramasinghe, S. R., Y. Wu and, B. Han, “Enhanced Microfiltration of Yeast by Flocculation,” Desalination, vol.147, 25-30 (2002)
Work, L. T., and A. S. Kohler; “Ind. Eng. Chem,” Vol.32, 1329 (1940)
Zydney, A. L. and, C. C. Ho, “Transmembrane Pressure Profiles During Constant Flux Microfiltration of Bovine Serum Albumin,” J. Membr. Sci., vol.209, 363-377 (2002)
Zydney, A. L., L. Palacio, C. C. Ho, P. Pradanos and, A. Hernandez, “Fouling with Protein mixtures in Microfiltration: BSA-lysozyme and BSA-pepsin,” J. Membr. Sci., vol.222, 44-51 (2003)
呂維明 編, ”固液過濾技術,” 高立圖書, chap.3, chap.4, chap.9 (2004)
邱盈錡, 黃國楨, ”離心過濾機構之研究,” 碩士學位論文, 淡江大學化工系(1994)
黃信杰, 黃國楨, ”操作條件對酵母菌/牛血清蛋白雙成份懸浮液之掃流微過濾性能之影響,” 碩士學位論文, 淡江大學化材系(2005)