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A Focus on Two Electrokinetics Issues
Micromachines ( IF 3.4 ) Pub Date : 2020-11-24 , DOI: 10.3390/mi11121028
Cheng Dai , Ping Sheng

This review article intends to communicate the new understanding and viewpoints on two fundamental electrokinetics topics that have only become available recently. The first is on the holistic approach to the Poisson–Boltzmann equation that can account for the effects arising from the interaction between the mobile ions in the Debye layer and the surface charge. The second is on the physical picture of the inner electro-hydrodynamic flow field of an electrophoretic particle and its drag coefficient. For the first issue, the traditional Poisson–Boltzmann equation focuses only on the mobile ions in the Debye layer; effects such as charge regulation and the isoelectronic point arising from the interaction between the mobile ions in the Debye layer and the surface charge are left to supplemental measures. However, a holistic treatment is entirely possible in which the whole electrical double layer—the Debye layer and the surface charge—is treated consistently from the beginning. While the derived form of the Poisson–Boltzmann equation remains unchanged, the zeta potential boundary condition becomes a calculated quantity that can reflect the various effects due to the interaction between the surface charges and the mobile ions in the liquid. The second issue, regarding the drag coefficient of a spherical electrophoretic particle, has existed ever since the breakthrough by Smoluchowski a century ago that linked the zeta potential of the particle to its mobility. Due to the highly nonlinear mathematics involved in the electro-hydrodynamics inside the Debye layer, there has been a lack of an exact solution for the electrophoretic flow field. Recent numerical simulation results show that the flow field comprises an inner region and an outer region, separated by a rather sharp interface. As the inner flow field is carried along by the particle, the measured drag is that at the inner/outer interface rather than at the solid/liquid interface. This identification and its associated physical picture of the inner flow field resolves a long-standing puzzle regarding the electrophoretic drag coefficient.

中文翻译:

专注于两个电动学问题

本文旨在就最近才出现的两个基本电动学主题交流新的理解和观点。第一个是对Poisson-Boltzmann方程的整体方法,该方法可以解释由Debye层中的移动离子与表面电荷之间的相互作用引起的影响。第二个是电泳粒子内部电动流体流场及其阻力系数的物理图。对于第一个问题,传统的泊松-玻尔兹曼方程只关注德拜层中的移动离子。由德拜层中的移动离子与表面电荷之间的相互作用引起的电荷调节和等电点等效应留待补充措施。然而,从一开始就对整个电气双层(德拜层和表面电荷)进行统一处理是完全有可能的。尽管泊松-玻尔兹曼方程的推导形式保持不变,但由于表面电荷与液体中的移动离子之间的相互作用,ζ电势边界条件成为计算量,可以反映各种影响。自一个世纪前Smoluchowski的突破以来,关于球形电泳粒子的阻力系数的第二个问题就存在了,该突破将粒子的Zeta电位与其迁移率联系起来。由于涉及德拜层内部电流体动力学的高度非线性数学,对于电泳流场一直缺乏精确的解决方案。最近的数值模拟结果表明,流场包括一个内部区域和一个外部区域,由一个相当尖锐的界面隔开。当内部流场被颗粒带走时,测得的阻力是在内/外界面处而不是在固/液界面处。这种识别及其内部流场的相关物理图景解决了有关电泳阻力系数的长期难题。
更新日期:2020-11-25
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