軸對稱膠體粒子於非電解質溶液中沿其對稱軸且垂直於雙平板之擴散泳動

Diffusiophoretic Motion of an Axially Symmetric Colloidal Particle in Nonelectrolyte Gradients along Its Axis of Revolution and Perpendicular to Two Plane Walls

萬義偉(Yi-Wei Wan)

指導教授 ： 葛煥彰

國立臺灣大學/工學院/化學工程學研究所/博士(2011年)

https://doi.org/10.6342/NTU.2011.02762

摘要

本論文主要為探討一軸對稱膠體粒子於非電解質溶液中垂直於單一平板或兩平行平板之軸對稱擴散泳動現象，所考慮之系統為擬穩態且皮克數及雷諾數極小，而外加溶質之濃度梯度均勻且垂直於平板。吾人假設粒子與溶質之間之交互作用層相較於粒子半徑及粒子與平板間距離為極薄，然而在此極薄的擴散層中溶質極化現象卻可存在。平板之邊界效應對於粒子速度可產生兩種影響，一為粒子表面之濃度梯度會因邊界效應產生變化，進而造成粒子速度增加或減少；另一為邊界效應會增強流體黏性阻力，進而減緩粒子移動速度。
本論文利用半解析半數值方法來求解系統中濃度場及流場之主導方程式，先以球型奇點分佈法沿長形軸對稱粒子內對稱軸上或於扁形軸對稱粒子內基礎面上分佈一組球形奇點以求得粒子之濃度分佈及流速場通解，再利用邊界取點法解出通解中之未知係數，所解出之粒子擴散泳速度之數值結果於各種不同條件下皆可獲得良好的收斂性。對於球形粒子所受之平板邊界效應，吾人亦以反射法求得近似解析解，發現此解與利用邊界取點法所求得之數值解十分吻合。平板邊界效應在各種粒子表面特性或粒子與平板之相對距離情形下皆會減緩球形粒子之運動速度。
對於橢球粒子軸對稱擴散泳動所受到之平板邊界效應，吾人發現於大多數情況下，擴散泳速度會隨粒子長短軸比值上升而增加，然而此現象並非絕對。此外平板邊界效應可能會增加或降低橢球粒子之運動速度，主要取決於粒子表面擴散層內溶質分子之極化係數、粒子長短軸比以及粒子與平板間相對距離等因素。當兩平板距離固定時，橢球粒子於兩平板正中間位置具有最大擴散泳可動度，而隨著粒子接近任一平板，皆會造成擴散泳可動度減緩。當粒子與第一個平板之距離固定且較近時，隨著另一平板從無窮遠處接近，會造成擴散泳可動度先增加至一極大值後再遞減，直到第二個平板與粒子之間之距離等同於第一個平板與粒子之間之距離則到達一極小值。

關鍵字

擴散泳 ； 軸對稱粒子 ； 橢球粒子 ； 邊界效應 ； 平板邊界

並列摘要

The axisymmetric diffusiophoretic motion of a colloidal particle of revolution in a nonelectrolyte solution situated between two infinite parallel plane walls are studied theoretically in the quasisteady limit with small Peclet and Reynolds numbers. The applied solute concentration gradient is uniform and perpendicular to the plane walls. The particle-solute interaction layer at the particle surface is assumed to be thin relative to the particle size and to the particle-wall gaps, but the polarization effect of the solute is incorporated in the thin interfacial layer caused by the strong adsorption of the solute. The presence of the confining walls causes two basic effects on the particle velocity: first, the local solute concentration gradient on the particle surface is altered by the walls, thereby speeding up or slowing down the particle; secondly, the walls enhance the viscous retardation of the moving particle.
To solve the solutal and hydrodynamic governing equations of the system, a method of distribution of a set of spherical singularities along the axis of revolution within a prolate particle or on the fundamental plane within an oblate particle is used to find the general solutions for the solute concentration distribution and fluid velocity field. The apparent slip condition on the particle surface is satisfied by applying a boundary collocation technique to these general solutions. Numerical results for the diffusiophoretic velocity of the colloid particle relative to that under identical conditions in an unbounded fluid solution are presented for various cases. The collocation results of a spherical particle agree well with the approximate analytical solutions obtained by using the method of reflections. The presence of the walls always reduces the spherical particle velocity, irrespective of the surface properties of the particle or the relative particle-wall distances.
The diffusiophoretic velocity of a confined spheroid along its axis of revolution in general increases with an increase in its axial-to-radial aspect ratio, but there are exceptions. The presence of the walls can reduce or enhance the spheroid velocity, depending upon the polarization parameter and aspect ratio of the particle as well as the relative particle-wall separation distances. For a constant relative separation between the two plane walls, the diffusiophoretic mobility of the spheroid has a maximum when it is located midway between the walls and decreases as it approaches either of the walls. When a spheroid with a fixed aspect ratio is located near a first plane wall, the approach of a second wall far from the particle can first increase the diffusiophoretic mobility to a maximum, then reduce this mobility when the second wall is close to the particle, and finally lead to a minimum mobility when it reaches to the same distance from the particle as the first wall.

並列關鍵字

Diffusiophersis ； Axisymmetric particle ； Colloid spheroid ； Boundary effects ； Plane walls

參考文獻

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