葛煥彰臺灣大學：化學工程學研究所馬先正Ma, Hsien-ChenHsien-ChenMa2007-11-262018-06-282007-11-262018-06-282007http://ntur.lib.ntu.edu.tw//handle/246246/52107一般而言，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.................................................................................................... 208en-US擴散滲透電滲透任意電雙層厚度鬆弛效應細微孔隙孔隙表面吸附高分子電解質DiffusioosmosisElectroosmosisArbitrary double-layer thicknessRelaxation effectFine capillaryPolyelectrolyte-coated capillarythesis