本篇主要研究在低電位中,受外加電場作用之下,對於不同粒徑比的橢球粒子,沿著一圓柱狀的毛孔之泳動現象做討論。泳動率的大小常隨著不同的形狀因子或是管壁的邊界效應等因素而改變。首先,我們先固定所有粒子的體積大小,然後再改變不同的電雙層厚度、粒子與邊界本身帶電與否、管徑的大小以及粒子或邊界本身帶電情形的不同,分別將這些因素作用在不同橢球粒子上,並根據其相對所產生的泳動率之大小做討論。在研究過程中,我們可以發現到幾個有趣的現象,例如:在固定粒子體積,以及粒子與邊界都帶固定電位的條件下,隨著電雙層厚度的變動,粒子的泳動率會產生出一極值的現象。另外,不論邊界條件如何改變,扁橢球粒子所受到靜電力的作用都要比長橢球粒子所受到靜電力的作用來得大。至於其他的特殊現象,我們將會在本文中一一的詳細解說。

The electrophoretic behavior of a spheroidal particle along the axis of a cylindrical pore is investigated under the conditions of weak applied electric field and low surface potential.  For a fixed particle volume, the influences of the key parameters of the system under consideration, including the thickness of double layer, the aspect ratio of a particle, the relative size of a cylindrical pore, and the charged conditions on the particle and pore surfaces, on the on the mobility of the particle are discussed.  Several interesting phenomena are observed.  For example, the mobility of a particle has a local minimum as the thickness of double layer varies.  Also, the electric force acting on an oblate is greater than that on a prolate.

目錄             
第一章 序論                               1
  第一節 膠體系統                         1
  第二節 膠體表面帶電因素                 1
  第三節 膠體表面帶電情形                 2
  第四節 電動力學的基本理論               3
第二章 文獻回顧與研究動機                 5
第三章 理論分析                           8
第四章 結果與討論                         15
  第一節 固定電位                         15
    1.1 粒子帶正電zeta_p=1和邊界不帶電zeta_w=0           15
    1.2 粒子不帶電zeta_p=0和邊界帶正電zeta_w=1           17
    1.3 粒子zeta_p=1和邊界zeta_w=1皆帶正電               19
  第二節 固定電荷密度                     20           
    2.1粒子sigma_p=-1(固定電荷密度)且邊界zeta_w=0(固定電位)                                       20
    2.2粒子sigma_p=-1(固定電荷密度)且邊界zeta_w=1(固定電位)                                       21
    2.3粒子sigma_p=-1(固定電荷密度)且邊界zeta_w=-1(固定電位)                                       22
第五章 結論                               23
附錄(Appendix A)                          42
參考文獻                                  44
圖目錄
圖1   橢球粒子在圓柱中受外加電場作用      24
圖2(a)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,S=(1/3)a_0,隨著ka_0的變動粒子泳動率w的變化情形       25
圖2(b)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,S=(1/3)a_0,隨著ka_0的變動粒子D^*的變化情形           25
圖2(c)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,S=(1/3)a_0,隨著ka_0的變動粒子F^*_D,2的變化情形       26
圖2(d)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,S=(1/3)a_0,隨著ka_0的變動粒子F^*_E的變化情形         26
圖3 曲線1是表示橢球平行於z軸方向的截面積大小               
    曲線2是表示橢球垂直於z軸方向的截面積大小            27
圖4(a)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,ka_0=1,隨著管徑(S/a_0)的變動粒子泳動率w的變化情形                  28
圖4(b)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,ka_0=1,隨著管徑(S/a_0)的變動粒子D^*的變化情形                      28
圖4(c)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_D,2的變化情形                  29
圖4(d)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=0,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_E的變化情形                    29
圖5(a)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子泳動率w的變化情形                     30
圖5(b)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子F^*_D,2的變化情形                     30
圖5(c)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子F^*_E的變化情形                       31
圖6(a)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子泳動率w的變化情形                  32
圖6(b)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_D,2的變化情形                  32
圖6(c)在固定粒子體積之下,E=1,zeta_p=0,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_E的變化情形                    33
圖7(a)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子泳動率w的變化情形                     34
圖7(b)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子F^*_D,2的變化情形                     34
圖7(c)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,S=(1/3)a_0,隨著ka_0的變動粒子F^*_E的變化情形                       35
圖8(a)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子泳動率w的變化情形                  36
圖8(b)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_D,2的變化情形                  36
圖8(c)在固定粒子體積之下,E=1,zeta_p=1,zeta_w=1,ka_0=1,隨著管徑(S/a_0)的變動粒子F^*_E的變化情形                    37
圖9(a)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=0,S=(1/3)a_0之下,隨著ka_0的變動粒子泳動率w的變化情形                                                    38
圖9(b)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=0,S=(1/3)a_0之下,隨著ka_0的變動粒子D^*的變化情形                                                      38
圖9(c)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=0,S=(1/3)a_0之下,隨著ka_0的變動粒子F^*_D,2的變化情形                                                    39
圖9(d)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=0,S=(1/3)a_0之下,隨著ka_0的變動粒子F^*_E的變化情形                                                      39
圖10(a)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=1,S=(1/3)a_0之下,隨著ka_0的變動粒子泳動率w的變化情形                                                    40
圖10(b)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=1,S=(1/3)a_0之下,隨著ka_0的變動粒子F^*_D,2的變化情形                                                    40
圖11(a)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=-1,S=(1/3)a_0之下,隨著ka_0的變動粒子泳動率w的變化情形    41
圖11(b)在固定粒子體積,E=1,sigma_p=-1(固定電荷密度),zeta_w=-1,S=(1/3)a_0之下,隨著ka_0的變動粒子F^*_D,2的變化情形     41

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