本研究以假性光譜法數值模擬密集硬球在高分子溶液中的電泳行為,以單位晶格模型描述密集硬球、以均勻介質模型結合Debye-Bueche-Brinkman理論方程式描述非均相多孔系統中的流動行為,並求解電動力學方程組。 本研究的影響參數甚多,包含:電雙層厚度、表面電位、密集度、高分子溶液摩擦係數,影響效應則包含:電雙層重疊效應、極化效應、密集度,電力與流力競合關係極為複雜。 綜合而言,電雙層厚度與溶液中離子強度有關,電雙層厚度愈薄,溶液離子強度愈強,電場的梯度愈強,驅動力較強使得電泳動度愈快;當電雙層厚度愈厚,溶液離子強度愈弱,密集度成為決定電泳動度的主要參數,密集度愈高,電雙層重疊效應愈顯著,使得電泳動度愈慢。 在電雙層厚度與單位晶格半徑相同附近會有高低電位的電泳動度順序變化,來自於電雙層重疊效應與極化效應的消長;高分子溶液貢獻的摩擦也將減緩粒子電泳動度,且密集度與高分子溶液摩擦係數增加皆會抑制離子對流引起的極化效應。 本研究提供廣效亨利公式(generalized Henry formula),以電泳動度對電雙層厚度圖形表示,針對不同濃度及不同電位之粒子在不同特性的高分子溶液中提供理論預測之電泳動度,亦探討表面調節(charge-regulation)粒子之行為。 本研究在使用高分子溶液之微流體系統(microfluidic systems),例如生物晶片等等,有廣泛的應用潛力。
Electrophoretic behavior of rigid particles in polymeric electrolyte solutions, described by Debye-Bueche-Brinkman (DBB) model, is investigated theoretically in this study. Standard electrokinetic equations governing the particle motion are solved numerically with pseudo-spectral method. Parameters of electrokinetic interest, such as the double layer thickness, κa, the particle zeta potential, ζ, concentration, H, and the extra retardation force of the polymeric solutions, λa, are examined respectively to understand their specific impact on the particle motion. It is found that the higher the polymeric retarding force is, the lower the particle mobility. The involvement of polarization and overlapping effects of the double layer further complicates the electrophoretic behavior of the particle, which is discussed in detail. General mobility charts expressed as a function of the reciprocal of dimensionless Debye length are established for various particle zeta potential and suspension concentrations. These original charts are very useful for the prediction of particle mobility in DBB polymeric solutions. Moreover, particles with charge regulated surface are explored as well, which is often encountered in bio-colloids such as human cells. This study extends the conventional aqueous electrolyte systems to polymeric ones, which find potential applications in microfluidic operations involving polymeric solutions in particular.
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