非全對稱情況下帶電邊界對粒子在牛頓與卡羅流體中電泳行為的影響

本論文以有限元素分析法研究不同幾何系統下帶電邊界的存在對於粒子於牛頓與非牛頓牛體中電泳行為的影響。之前的研究在此利用一較為符合實際條件的電泳靜電力算法重新給予修正，而此根據Maxwell應變張量推導出的靜電力式子可適用於任一系統全對稱或不全對稱問題與不同表面荷電行為的硬或軟核粒子。文中探討的問題包括單顆球形膠體粒子在一無窮圓管的軸心與一球殼中心泳動等全對稱系統問題，與雙顆球形膠體粒子在一無窮圓管的軸心、單顆球形膠體粒子朝一無窮圓盤與球殼中任一位置下泳動等不完全對稱系統問題。最後本文並在低表面電位與弱外加電場的假設下，研究上述提出的電泳問題。數值模擬的結果顯示，下列幾個因素對於膠體粒子電泳的定性行為皆有重大的影響：邊界存在的重要程度、粒子與邊界的幾何形狀、粒子與邊界的距離或粒子間的距離、電雙層厚度與系統內流體的本質。除了剪切稀釋對於粒子運動確實有幫助的效應外，還有許多結論如下。例如：根據不可滑動的邊界條件，邊界的存在會藉由增加粒子流體阻力的方式降低泳動速度；此外，降低粒子的電雙層厚度也會藉由增加粒子表面靜電力的方式增快泳動速度與增加非牛頓卡羅流體之剪切稀釋效應。但以上這些電泳行為在系統邊界帶正電但膠體粒子不帶電的系統下卻不一定，這是因為此系統下由於邊界帶電所造成的電滲透流與滲透壓力場扮演著舉足輕重的角色，如：電泳方向會隨著系統參數改變或存在一局部最大值的產生，此外，當電雙層厚度極大或極小時剪切稀釋效應也會變得重要。

關鍵字

電泳；泳動度；帶電邊界效應；固定表面電位；固定表面電荷；非牛頓流體；卡羅模式

並列摘要

The effect of the presence of a charged boundary on the electrophoretic behavior of an entity in a Newtonian fluid and a non-Newtonian fluid are investigated in this study for various types of problems through solving numerically the governing electrokinetic equations by a finite element method. Previous analyses are modified by using a more realistic electrostatic force formula. This expression derived, which is based on Maxwell stress tensor, is applicable to both rigid and soft particles for various types of surface conditions and to both totally symmetric and asymmetric geometries. These analyses considered in this study include that, for example, problems of total symmetric nature such as an isolated sphere moving along the axis of a cylindrical pore and at the center of a spherical cavity, and those of not total symmetric nature such as two spheres moving along the axis of a cylindrical pore, a sphere moving toward to a large disk, and a sphere at an arbitrary position in a spherical cavity. All of the above eletrophoetic problems investigated in this study are under the conditions of low surface potential and weak applied electric field. We shown that the qualitative behavior of a particle depends largely on how significant of the boundary effect is, the geometries of a particle and a boundary, the separation distance between a particle and a boundary or between two particles, the thickness of double layer, and the nature of a fluid. In addition to the fact that the effect of shear-thinning is advantageous to the movement of a sphere, several other results are also observed. For example, the presence of a boundary has the effect of increasing the conventional hydrodynamic drag on a particle through a non-slip condition on the former. Also, a decrease in the thickness of double layer surrounding a sphere has the effect of increasing the electrostatic force acting on its surface so that its mobility increases, and increases the effect of the shear-thinning for a Carreau fluid. However, this might not be the case when an uncharged particle is placed in a positively charged boundary, where the electroosmotic flow and/or osmotic pressure force plays a role, for example, the mobility can exhibit a local extreme and the direction of electrophoresis can change. Also, the effect of shear-thinning is important only if the thickness of double layer is either sufficiently thin or sufficiently thick.

並列關鍵字

Electrophoresis ； Mobility ； Effect of charged boundary ； Constant surface potential ； Constant surface charge ； Non-Newtonian fluid ； Carreau model

參考文獻

[1] von Smoluchowski, M. Z. Phys. Chem. 1918, 92, 129.

[2] Morrison, F. A.; Stukel, J. J. J. Colloid Interface Sci. 1970, 33, 88.

[3] Keh, H. J.; Anderson, J. L. J. Fluid Mech. 1985, 153, 417.

[5] Feng, J. J.; Wu, W. Y. J. Fluid Mech. 1994, 264, 41.

[6] Ennis, J.; Anderson, J. L. J. Colloid Interface Sci. 1997, 185, 497.

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非全對稱情況下帶電邊界對粒子在牛頓與卡羅流體中電泳行為的影響

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