Department of Mathematics, National Institute of Technology Patna, Patna, India.
Department of Mathematics, National Institute of Technology Durgapur, Durgapur, India.
Electrophoresis. 2019 May;40(9):1282-1292. doi: 10.1002/elps.201800427. Epub 2019 Feb 12.
This article deals with a semi-analytical study on the electrophoresis of charged spherical rigid colloid by considering the effects of relaxation and ion size. The particle surface is taken to be either hydrophilic or hydrophobic in nature. In order to consider the ion size effect we have invoked the Carnahan and Starling model (J. Chem. Phys. 1969, 51, 635-636). The mathematical model is based on Stokes equation for fluid flow, modified Boltzmann equation for spatial distribution of ionic species and Poisson equation for electric potential. We adopt a linear perturbation technique under a weak electric field assumption. An iterative numerical technique in employed to solve the coupled set of perturbed equations. We have validated the numerically obtained electrophoretic mobility with the corresponding analytical solution derived under low potential limit. Going beyond the widely employed Debye-Hückel linearization, we have presented the results for a wide range of surface charge density, electrolyte concentration, and slip length to Debye length ratio. We have also identified several interesting features including occurrence of local maxima and minima in the mobility for critical choice of pertinent parameters.
本文通过考虑松弛和离子大小的影响，对半解析研究了带电球形刚性胶体的电泳。颗粒表面的性质可以是亲水的也可以是疏水的。为了考虑离子大小的影响，我们采用了卡哈南-斯塔林模型（J. Chem. Phys. 1969, 51, 635-636）。该数学模型基于流体流动的斯托克斯方程、离子空间分布的修正玻尔兹曼方程和电势的泊松方程。我们在弱电场假设下采用线性微扰技术。通过迭代数值技术来求解耦合的扰动方程组。我们已经验证了在低电势极限下从相应的解析解中得出的数值得到的电泳迁移率。与广泛采用的德拜-休克尔线性化不同，我们给出了一系列表面电荷密度、电解质浓度和滑移长度与德拜长度比的广泛参数范围内的结果。我们还确定了几个有趣的特征，包括在相关参数的临界选择下，迁移率出现局部最大值和最小值的情况。
