切應力不連續對軟球粒子電動力學現象的影響

Abstract

本研究是以數值方法討論軟球粒子中軟球層表面發生切應力不連續(stress jump)的情形，並且在不同的系統下(cavity、cell model)，軟球粒子發生沉降或電泳等電動力學現象時，對沉降速度或電泳動度產生的影響。 所謂的軟球粒子，是在一個膠體硬球上包覆一層多孔性物質，我們稱為軟球層，軟球層允許電解質離子自由進出，而在軟球層的切線方向，我們加入了切應力不連續(stress jump)的條件，在球形孔洞(cavity)與懸浮密集溶液(cell model)的系統中，觀察其對沉降及電泳所造成的影響。 我們利用非線性的流場、電場、及濃度場之方程式耦合，先經過基本假設之後，線性化此三大主控方程式，再利用假性光譜法進行數值模擬，在此所要探討的結果重點集中在軟球層表面考慮切應力不連續(stress jump)所造成的改變，以切應力不連續係數(stress jump coefficient)為系統主要變因，觀察當電雙層厚度、軟球層摩擦係數、軟球層帶電量變化時，對沉降速度、沉降電位及電泳動度所造成的影響。

In this study, we use pseudo-spectral method to investigate the external layer of a soft particle under stress jump condition. When the soft particle exhibit sedimentation or electrophoresis, we want to know how the stress jump condition affect the corresponding mobility. The soft particle consists of a layer of porous substance around an inner hard particle. The external ion-penetrable layer allows ions moves in and out. On the tangent direction of ion-penetrable layer, we apply the stress jump boundary condition. We examine its effects on sedimentation and electrophoresis, respectively, for both cavity and cell model system. The resulting non-linear hydrodynamic, electrical potential and ion-conservation equations are coupled. Under some assumptions, these equations are linearized and solved with pseudo-spectral method. The major point of interest is the impact on ion-penetrable layer surface under the application of stress jump condition. The stress jump coefficient is the key variable in this system. The effect on sedimentation velocity, sedimentation potential and electrophoresis of various variable such as double layer thickness, ion-penetrable layer friction coefficient, and fixed charges density are examined and discussed.