多孔膠體粒子在切應力不連續條件下的電泳運動現象

Abstract

多孔物質與自由液體之間的邊界條件一直是學者們關注的難題，而近年來切應力不連續條件廣泛的使用於處理此一問題，因此，本研究以數值方法探討多孔膠體粒子在切應力不連續條件下的電泳運動現象。我們考慮電雙層極化效應，並且採用Brinkman所提出的多孔物質模型，以及於多孔物質界面引入應力不連續條件(stress-jump condition)。為了適當描述系統，我們使用球座標進行多區聯解，在外加弱電場的假設下，將相互耦合的電動力學方程組線性化，以Chebyshev擬譜方法求解線性化後的電動力學方程組。 我們針對電動力學的一些重要參數，如切應力不連續係數(stress-jump coefficient)、電雙層厚度、多孔粒子摩擦係數、懸浮液密集度、多孔粒子帶電量等對電泳動度所造成的影響加以研究，並且發現切應力不連續係數對於粒子電泳現象有非常大的影響。研究結果發現切應力不連續係數越大，粒子所受流體阻力越小，粒子泳動度越快，且切應力不連續係數能有效影響極化效應的強弱，這些特性會使整體粒子泳動趨勢變得更為複雜。我們的數值結果與相關實驗文獻有著非常良好的吻合，因此也確立我們理論的正確性以及切應力不連續的重要性。

The boundary condition for the flow field across a porous material-liquid interface has drawn the attention of many researchers. Stress-jump condition, proposed by Ochoa-Tapia and Whitaker, has been introduced to solve this type of problem. In this study, the electrophoretic behavior of a porous particle in stress-jump condition is investigated. The effect of double-layer polarization is taken into account. Brinkman model is adopted to simulate the porous structure, and stress-jump condition is introduced into porous material-liquid interface. We treat the problem by separating the physical region into two domains using spherical coordinates. The coupled electrokinetic equations are linearized assuming the applied electric field is weak. General electrokinetic equations are employed and solved with pseudo-spectral method based on Chebyshev polynomials and Newton-Raphson schemes. Key parameters of electrokinetic interest such as stress-jump coefficient, double layer thickness, friction coefficient of the porous particle, volume fraction, and fixed charge density are examined for their respective effect on the particle motion. We found, among other things, the stress-jump coefficient is a crucial factor in determining the particle electrophoretic behavior. As stress-jump coefficient increases, the electrophoretic motion becomes quicker, due to the friction force decreases. In addition, stress-jump coefficient has a significant influence on the degree of double-layer polarization. These properties make electrophoretic behavior becomes more complicated. Comparison with experimental data available in the literature is excellent, indicating the reliability of this analysis, as well as the importance of using stree-jump condition.