臺灣博碩士論文加值系統

一般而言，細微孔隙內流體流動的驅動力包括：孔隙兩端動態壓差(對流)，孔隙二端溶液中不可穿透溶質之濃度差(滲透)，以及鄰近帶電孔壁之電雙層和切線方向外加電場所產生之交互作用(電滲透)。另有一種尚未受到廣泛研究的液態溶液在毛細管中流動的驅動力，涉及沿孔壁方向可穿透溶質之濃度梯度和孔壁間的作用力，由這種機制所產生的流動稱為擴散滲透。
本文將對電解質溶液在受到外加切線方向溶質濃度梯度之作用下，分別對沿一帶電平板、一表面帶電平板形孔隙、一表面帶電圓管型孔隙及一帶電孔壁表面吸附帶電高分子層的平板型孔隙內之穩態擴散滲透流動進行理論探討。其中帶電孔壁可為任意大小的固定表面電位或固定表面電荷密度，鄰近帶電孔壁的電雙層厚度可為任意值，且電位分布可藉由求解波森-波玆曼方程式而得到。在各種不同情況下，由外加電解質濃度梯度所產生的軸向巨觀電場和流體流速在徑向的分布，可利用求解修正後的納維-斯托克斯方程式，配合沒有淨電流經由電解質離子同向流擴散、電遷移及擴散滲透對流產生而求得。
研究結果顯示，電雙層中軸向誘導電場之徑向分布和電雙層外主體電場間差異的效應以及流體擴散滲透速度造成的鬆弛效應，在一般的情況下對流體速度的影響相當顯著，甚至在電雙層很薄的情況下亦然。

In general, driving forces for the fluid transport through micropores include dynamic pressure differences between the two ends of a capillary pore (convection), concentration differences of an impermeable solute between the two bulk solutions outside the pores (osmosis), and tangential electric fields that interact with the electric double layer adjacent to a charged pore wall (electroosmosis). Another driving force for the flow of liquid solutions in a capillary pore, which has commanded less attention, involves concentration gradients of a permeable solute along the capillary that interacts with the pore wall. The fluid motion associated with this mechanism is termed diffusioosmosis.
The steady diffusioosmotic flows of an electrolyte solution along a charged plane wall, in a capillary slit, in a capillary tube, and in a slit with its walls coated with polyelectrolyte layers generated by an imposed tangential concentration gradient are theoretically examined in this study. The charged walls may have either a constant surface potential or a constant surface charge density of an arbitrary quantity. The electric double layers adjacent to the charged walls may have an arbitrary thickness and their electrostatic potential distributions are governed by the Poisson-Boltzmann equation. Solving a modified Navier-Stokes equation with the constraint of no net electric current arising from the cocurrent diffusion, electric migration, and diffusioosmotic convection of the electrolyte ions, the macroscopic electric field and the fluid velocity in the tangential direction induced by the imposed electrolyte concentration gradient are obtained as functions of the lateral position for various cases.
The results indicate that the effect of the deviation of the local induced tangential electric field inside the double layer from its bulk-phase quantity and the relaxation effect on the diffusioosmotic velocity of the fluid are significant in most practical situations, even for the case of very thin double layer.

Chapter 1 Introduction................................................................................................ 1
1.1 Diffusiophoresis.................................................................................................... 1
1.2 Diffusioosmosis..................................................................................................... 3

Chapter 2 Diffusioosmosis along a Charged Plane Wall………………………... 7
2.1 Electrostatic Potential Distribution....................................................................... 9
2.1.1 General analysis........................................................................................... 10
2.1.2 Case of low surface potential....................................................................... 11
2.2 Induced Tangential Electric Field........................................................................ 11
2.2.1 General analysis........................................................................................... 12
2.2.2 Bulk-phase quantity..................................................................................... 13
2.3 Fluid Velocity Distribution................................................................................. 14
2.3.1 General analysis........................................................................................... 15
2.3.2 Result of previous work............................................................................... 16
2.4 Diffusioosmosis without Relaxation Effect........................................................ 16
2.4.1 Induced electric field and net electrolyte diffusivity................................... 17
2.4.2 Fluid velocity……………………………………………………….…….. 19
2.5 Results and Discussion…………………...…………………………………… 22
2.5.1 Induced electric field…………………………………………………........ 22
2.5.2 Diffusioosmotic velocity…………………………………………………. 26
2.5.3 Diffusioosmosis without relaxation effect………………………………... 36

Chapter 3 Diffusioosmosis in a Capillary Slit......................................................... 47
3.1 Electrostatic Potential Distribution..................................................................... 47
3.1.1 General analysis........................................................................................... 47
3.1.2 Case of low surface potential....................................................................... 51
3.2 Fluid Velocity Distribution................................................................................. 51
3.2.1 General analysis........................................................................................... 51
3.2.2 Case of low surface potential without relaxation effect............................... 52
3.3 Results and Discussion....................................................................................... 55
3.3.1 Induced electric field.................................................................................... 55
3.3.2 Diffusioosmotic velocity.............................................................................. 61
3.3.3 Diffusioosmosis for the case of low surface potential without relaxation
effect…………………………………..........…………………………….. 71

Chapter 4 Diffusioosmosis in a Capillary Tube...................................................... 81
4.1 Electrostatic Potential Distribution..................................................................... 81
4.2 Fluid Velocity Distribution................................................................................. 87
4.2.1 General analysis........................................................................................... 87
4.2.2 Case of low surface potential without relaxation effect.............................. 90
4.3 Results and Discussion....................................................................................... 92
4.3.1 Induced electric field.................................................................................... 92
4.3.2 Diffusioosmotic velocity.............................................................................. 98
4.3.3 Diffusioosmosis for the case of low surface potential without
relaxation effect........................................................................................ .110

Chapter 5 Diffusioosmosis in a Capillary Slit with Surface Charge Layers…...119
5.1 Electrostatic Potential Distribution................................................................... 122
5.1.1 General analysis......................................................................................... 122
5.1.2 Case of low surface potential..................................................................... 126
5.2 Fluid Velocity Distribution............................................................................... 128
5.2.1 General analysis......................................................................................... 129
5.2.2 Case of low surface potential without relaxation effect............................. 134
5.3 Results and Discussion..................................................................................... 138
5.3.1 Induced electric field.................................................................................. 138
5.3.2 Diffusioosmotic velocity............................................................................ 144
5.3.3 Diffusioosmosis for the case of low surface potential without
relaxation effect........................................................................................ 163

Chapter 6 Concluding Remarks............................................................................. 187

Lists of Symbols.......................................................................................................... 191
References.................................................................................................................... 197
Appendix...................................................................................................................... 205
Biographical Sketch.................................................................................................... 208

1. Anderson, J. L., Diffusiophoresis caused by gradients of strongly adsorbing. Langmuir 1991, 7, 403.
2.Dukhin, S. S.; Derjaguin, B. V., Surface and Colloid Science; Matijevic, E., Ed.; Wiley: New York, 1974; Vol. 7.
3.Prieve, D. C.; Anderson, J. L.; Ebel, J. P., Motion of a particle generated by chemical gradients. part 2. electrolytes. Journal of Fluid Mechanics 1984, 148, 247.
4.Ebel, J. P.; Anderson, J. L.; Prieve, D. C., Diffusiophoresis of latex-particles in electrolyte gradients. Langmuir 1988, 4, 396.
5.Staffeld, P. O.; Quinn, J. A., Diffusion-induced banding of colloid particles via diffusiophoresis. 2. Non-electrolytes. Journal of Colloid and Interface Science 1989, 130, 88.
6.Smith, R. E.; Prieve, D. C., Accelerated deposition of latex-particles onto a rapidly dissolving steel surface. Chemical Engineering Science 1982, 37, 1213.
7.Prieve, D. C., Migration of a colloidal particle in a gradient of electrolyte concentration. Advances in Colloid and Interface Science 1982, 16, 352.
8.Prieve, D. C.; Roman, R. J., Diffusiophoresis of a rigid sphere through a viscous electrolyte solution. Journal of the Chemical Society. Faraday Transactions II 1987, 283, 1287.
9.Chen, P. Y.; Keh, H. J., Diffusiophoresis and electrophoresis of a charged sphere parallel to one or two plane walls. Journal of Colloid and Interface Science 2005, 286, 774.
10.Keh, H. J.; Chen, S. B., Diffusiophoresis and electrophoresis of colloidal cylinders. Langmuir 1993, 9, 1142.
11.Keh, H. J.; Jan, J. S., Boundary effects on diffusiophoresis and electrophoresis: Motion of a colloidal sphere normal to a plane wall. Journal of Colloid and Interface Science 1996, 183, 458.
12.Keh, H. J.; Luo, S. C., Particle interactions in diffusiophoresis: Axisymmetric motion of multiple spheres in electrolyte gradients. Langmuir 1996, 12, 657.
13.Pawar, Y.; Solomentsev, Y. E.; Anderson, J. L., Polarization effects on diffusiophoresis in electrolyte gradients. Journal of Colloid and Interface Science 1993, 155, 488.
14.Tu, H. J.; Keh, H. J., Particle interactions in diffusiophoresis and electrophoresis of colloidal spheres with thin but polarized double layers. Journal of Colloid and Interface Science 2000, 231, 265.
15.Wei, Y. K.; Keh, H. J., Diffusiophoresis and electrophoresis in concentrated suspensions of charged colloidal spheres. Langmuir 2001, 17, 1437.
16.Keh, H. J.; Wei, Y. K., Diffusioosmosis and electroosmosis of electrolyte solutions in fibrous porous media. Journal of Colloid and Interface Science 2002, 252, 354.
17.Keh, H. J.; Huang, T. Y., Diffusiophoresis and electrophoresis of colloidal spheroids. Journal of Colloid and Interface Science 1993, 160, 354.
18.Keh, H. J.; Wei, Y. K., Diffusiophoretic mobility of spherical particles at low potential and arbitrary double-layer thickness Langmuir 2000, 16, 5289.
19.Wei, Y. K.; Keh, H. J., Diffusiophoresis in a suspension of spherical particles with arbitrary double-layer thickness. Journal of Colloid and Interface Science 2002, 248, 76.
20.Wei, Y. K.; Keh, H. J., Diffusiophoretic mobility of charged porous spheres in electrolyte gradients. Journal of Colloid and Interface Science 2004, 269, 240.
21.Wei, Y. K.; Keh, H. J., Theory of electrokinetic phenomena in fibrous porous media caused by gradients of electrolyte concentration. Colloids and Surfaces A-Physicochemical and Engineering Aspects 2003, 222, 301.
22.Keh, H. J.; Wei, Y. K., Osmosis through a fibrous medium caused by transverse electrolyte concentration gradients Langmuir 2002, 18, 10475.
23.Keh, H. J.; Ding, J. M., Electrokinetic flow in a capillary with a charge-regulating surface polymer layer. Journal Colloid Interface Science 2003, 263, 645.
24.Keh, H. J.; Liu, Y. C., Electrokinetic flow in a circular capillary with a surface-charge layer. Journal of Colloid and Interface Science 1995, 172, 222.
25.Keh, H. J.; Tseng, H. C., Transient electrokinetic flow in fine capillaries. Journal Colloid Interface Science 2001, 242, 450.
26.Helmholtz, H., Studies of electric boundary layers. Annual Physical Chemistry 1879, 7, 337.
27.Smoluchowski, M., Elektrische endosmose und stromungsstrome. In Handbuch del Elektrizitat und des Magnetismus, Graetz, L., Ed. Barth: Leipzig, Germany, 1921; Vol. 2, p 336.
28.Burgreen, D.; Nakache, F. R., Electrokinetic flow in ultrafine capillary slits. Journal of Physical Chemistry 1964, 68, 1084.
29.Levine, S.; Marriott, J. R.; Neale, G.; Epstein, N., Theory of electrokinetic flow in fine cylindrical capillaries at high zeta-potentials. Journal of Colloid and Interface Science 1975, 52, 136.
30.Masliyah, J. H., Electrokinetic transprot phenomena. AOSTRA: Edmonton, Alberta, Canada, 1994.
31.Ohshima, H.; Kondo, T., Electrokinetic flow between 2 parallel plates with surface-charge layers - elctroosmosis and streaming potential. Journal of Colloid and Interface Science 1990, 135, 443.
32.Rice, C. L.; Whitehead, R., Electrokinetic flow in a narrow capillary. Journal of Physical Chemistry 1965, 69, 4017.
33.Szymczyk, A.; Aoubiza, B.; Fievet, P.; Pagetti, J., Electrokinetic phenomena in homogeneous cylindrical pores. Journal Colloid Interface Science 1999, 216, 285.
34.Yang, C.; Li, D., Electrokinetic effects on pressure-driven liquid flows in rectangular microchannels. Journal Colloid Interface Science 1997, 194, 95.
35.Anderson, J. L.; Idol, W. K., Electroosmosis through pores with nonuniformly charged walls. Chemical Engineering Communications 1985, 38, (3-6), 93-106.
36.Long, D.; Stone, H. A.; Ajdari, A., Electroosmotic flows created by surface defects in capillary electrophoresis. Journal of Colloid and Interface Science 1999, 212, 338.
37.Anderson, J. L., Colloid transport by interfacial forces. Annual Review of Fluid Mechanics 1989, 21, 61.
38.Derjaguin, B. V.; Dukhin, S. S.; Korotkova, A. A., Kolloidnyĭ Zhurnal 1961, 23, 53.
39.Keh, H. J.; Ma, H. C., Diffusioosmosis of electrolyte solutions along a charged plane wall. Langmuir 2005, 21, 5461.
40.Anderson, J. L.; Lowell, M. E.; Prieve, D. C., Motion of a particle generated by chemical gradients. 1. Non-electrolytes. Journal of Fluid Mechanics 1982, 117, 107.
41.Fair, J. C.; Osterle, J. F., Reverse electrodialysis in charged capillary membranes. Journal of Chemical Physics 1971, 54, 3307.
42.Keh, H. J.; Wu, J. H., Electrokinetic flow in fine capillaries caused by gradients of electrolyte concentration Langmuir 2001, 17, 4216.
43.Sasidhar, V.; Ruckenstein, E., Anomalous effects during electrolyte osmosis across charged porous membranes Journal Colloid Interface Science 1982, 85, 332.
44.Westermann-Clark, G. B.; Anderson, J. L., Experimental verification of the space-charge model for electrokinetics in charged microporous membranes. Journal of the Electrochemical Society 1983, 130, 839.
45.Wu, J. H.; Keh, H. J., Diffusioosmosis and electroosmosis in a capillary slit with surface charge layers. Colloids and Surfaces A-Physicochemical and Engineering Aspects 2003, 212, 27.
46.Ma, H. C.; Keh, H. J., Diffusioosmosis of electrolyte solutions in a capillary slit with surface charge layers. Colloids and Surfaces a-Physicochemical and Engineering Aspects 2005, 267, 4.
47.Keh, H. J.; Ma, H. C., Diffusioosmosis of electrolyte solutions in fine capillaries. Colloids and Surfaces a-Physicochemical and Engineering Aspects 2004, 233, 87.
48.Dukhin, S. S., Non-equilibrium electric surface phenomena. Advances in Colloid and Interface Science 1993, 44, 1.
49.Starov, V. M.; Bowen, W. R.; Welfoot, J. S., Flow of multicomponent electrolyte solutions through narrow pores of nanofiltration membranes. Journal of Colloid and Interface Science 2001, 240, 509.
50.Ma, H. C.; Keh, H. J., Diffusioosmosis of electrolyte solutions in a fine capillary slit. Journal of Colloid and Interface Science 2006, 298, 476.
51.Prudnikov, A. P.; Brychkov, Y. A.; Marichev, O. I., More special functions. In Integrals and Series, Gordon and Breach Science Publishers: New York, 1990; Vol. 3.
52.Philip, J. R.; Wooding, R. A., Solution of Poisson-Boltzmann equation about a cylindrical particle. Journal of Chemical Physics 1970, 52, 953.
53.Donath, E.; Voigt, A., Streaming current and streaming potential on structured surfaces. Journal of Colloid and Interface Science 1986, 109, 122.
54.Starov, V. M.; Solomentsev, Y. E., Influence of gel Layers on electrokinetic phenomena .2. Effect of ions interaction with the gel layer. Journal of Colloid and Interface Science 1993, 158, 166.
55.Sharp, K. A.; Brook, D. E., Calculation of the electrophoretic mobility of a particle bearing bound polyelectrolyte using the nonlinear Poisson-Boltzmann equation. Biophysical Journal 1985, 47, 563.
56.Morita, K.; Muramatsu, N.; Ohshima, H.; Kondo, T., Electrophoretic behavior of rat lymphocyte subpopulations. Journal of Colloid and Interface Science 1991, 147, 457.
57.Aoyanagi, O.; Muramatsu, N.; Ohshima, H.; Kondo, T., Electrophoretic Behavior of Polya-Graft-Polyb-Type Microcapsules. Journal of Colloid and Interface Science 1994, 162, 222.
58.Adamson, A. W., Physical Chemistry of Surfaces. 5th ed.; Wiley: New York, 1990.
59.Dukhin, S. S.; Zimmermann, R.; Werner, C., Intrinsic charge and Donnan potentials of grafted polyelectrolyte layers determined by surface conductivity data. Journal of Colloid and Interface Science 2004, 274, 309.
60.Delgado, A. V., Measurement and interpretation of electrokinetic phenomena. Pure and Applied Chemistry 2005, 77, 1753.