中空多孔帶電粒子在電解質梯度中之擴散泳

Abstract

本論文探討一帶電之多孔中空球形粒子懸浮於一對稱電解質溶液中，受到一外加均勻濃度梯度驅動下，所進行之擴散泳運動。中空多孔球形粒子是由溶劑與微小離子皆可穿透之帶電凝聚體或微囊所構成，其所帶的固定電荷密度以及對流體之摩擦阻力密度皆為定值，且粒子周圍之電雙層可為任意厚度。在濃度梯度較小的情況下，主導電解質溶液的電位、電化學位能及流場分佈之電動力方程式可藉由假設相對於平衡狀態，系統只受到微小的擾動來線性化。在多孔粒子的固定電荷密度較小的情況下，利用正規微擾法，可對待定的擾動項以無因次化的固定電荷密度作冪級數的展開，並配合適當的邊界條件求得解析解。多孔粒子的擴散泳速度可以利用在穩定狀態下，作用在粒子上之靜電力及流體拖曳力之合力為零的條件來求解，可精確求得至固定電荷密度二階之項。結果顯示粒子電泳速度(一階)及化學泳速度(二階)皆會單調地隨著粒子的相對厚度變小而下降，惟此現象僅在粒子相對厚度很小的情況下才較顯著。然而粒子之擴散泳速度為電泳速度和化學泳速度相互競爭合併之結果，其淨速度和粒子相對厚度不一定為單調之函數關係。隨著粒子之固定電荷密度從負電荷到正電荷的變化，可能導致擴散泳之速度方向產生超過一次的改變。

The diffusiophoresis of a charged spherical porous shell or permeable microcapsule with arbitrary inner and outer radii, fluid permeability, and electric double layer thickness in an ionic solution is analyzed. With the assumption that the imposed electrolyte concentration gradient is relatively weak and the transport system is only perturbed slightly from equilibrium, the electrostatic potential, ionic concentration (electrochemical potential energy), and fluid velocity fields are determined as power-series expansions of the small fixed charge density of the porous shell by solving the relevant linearized electrokinetic equations. An explicit expression for the diffusiophoretic velocity of the porous shell correct to the second order of the fixed charge density results from balancing the exerted electrostatic and hydrodynamic forces. Both the electrophoretic (first-order) and chemiphoretic (second-order) mobilities increase with an increase in the normalized thickness of the porous shell, and these increases are significant when the porous shell is thin. However, the diffusiophoretic velocity of the porous shell, which is the sum of the electrophoretic and chemiphoretic velocities, may not be a monotonic function of its normalized thickness. The variation in the normalized fixed charge density of the porous shell from negative to positive values can lead to more than one reversals in the direction of the diffusiophoretic velocity.