葛煥彰臺灣大學：化學工程學研究所黃友清Huang, You-ChingYou-ChingHuang2007-11-262018-06-282007-11-262018-06-282005http://ntur.lib.ntu.edu.tw//handle/246246/52368本文以解析方法探討一具有任意厚度電雙層之球形帶電粒子置於一廣大不可壓縮牛頓流體之電解質溶液中，受到外加電場作用之暫態電泳運動現象。在Debye-Huckel之低電位假設，低Reynolds數及系統相對於平衡狀態為微小擾動之情況下，利用微擾法將電動力主導方程式線性化以求解流場，得到任意電雙層厚度粒子之電泳速度半解析半數值解以及在電雙層極薄與極厚情況下的粒子電泳速度解析解。研究結果顯示，在固定粒子與流體之密度比值下，粒子電泳速度隨時間之增加隨著粒子表面電雙層厚度愈薄而愈快；而在同樣電雙層厚度下，相對愈重粒子的電泳速度隨時間之增加比較輕的粒子為慢。但不論在何種情況下，粒子之加速度同樣呈現單調遞減。研究結果發現粒子進行電泳運動之暫態時間相當短小，僅約 秒，所以在一般情況下，此暫態效應應可忽略。A theoretical study is presented for the dynamic electrophoretic response of a charged spherical particle in an unbounded electrolyte solution to a step change in the applied electric field. The electric double layer surrounding the particle may have an arbitrary thickness relative to the particle radius. The transient Stokes equations modified with the electrostatic effect which govern the fluid velocity field is linearized by assuming that the system is only slightly distorted from equilibrium. Semi-analytical results for the transient electrophoretic mobility of the particle are obtained as a function of relevant parameters by using the Debye-Huckel approximation. The results demonstrate that the electrophoretic mobility of a particle with a constant density at a specified dimensionless time normalized by its steady-state quantity decreases monotonically with a decrease in the parameter , where is the Debye screening length and a is the particle radius. For a given value of , a heavier particle lags behind a lighter one in the development of the electrophoretic mobility. In the limits of and , our results reduce to the corresponding analytical solutions available in the section 2.2 and 2.3. The electrophoretic acceleration of the particle is a monotonic decreasing function of the time for any fixed value of . In practical applications, the effect of the relaxation time for transient electrophoresis is negligible, regardless of the value of or the relative density of the particle.Chapter 1 Introduction 1 Chapter 2 Analysis 4 2.1 Transient Electrophoresis of a Spherical Particle of an Arbitrary Double-Layer Thickness 4 2.2 Transient Electrophoresis of a Spherical Particle with a Very Thin Double Layer 12 2.3 Transient Electrophoresis of a Spherical Particle with a Very Thick Double Layer 15 Chapter 3 Results and Discussion 20 3.1 Transient Electrophoretic Velocity of a Spherical Particle 20 3.2 Transient Acceleration of an Electrophoretic Sphere 21 Chapter 4 Concluding Remarks 35 Notation 37 References 40 Biographical Sketch 43383243 bytesapplication/pdfen-US暫態電泳Transientelectrophoresisthesishttp://ntur.lib.ntu.edu.tw/bitstream/246246/52368/1/ntu-94-R92524042-1.pdf