We consider a modified electrokinetic model to study the electrophoresis of a hydrophobic particle by considering the finite sized ions. The mathematical model adopted in this study incorporates the ion steric repulsion, ion-solvent interactions as well as Maxwell stress on the electrolyte. The dielectric permittivity and viscosity of the electrolyte is considered to vary with the local ionic volume fraction. Based on this modified model for the electrokinetics we have analyzed the electrophoresis in a single as well as mixture of electrolytes of monovalent and non-$z:z$ electrolytes. The dependence of viscosity on local ionic volume fraction modifies the hydrodynamic drag as well as diffusivity of ions, which are ignored in existing studies on electrophoresis. A simplified model for electrophoresis of a hydrophobic particle incorporating the ion steric repulsion and ion-solvent interactions is developed based on the first-order perturbation on applied electric field. This simplified model is established to be efficient for a Debye layer thinner than the particle size and a smaller range of slip length. This model can be implemented for any number of ionic species as well as non-$z:z$ electrolytes. It is established that the ion steric interactions and dielectric decrement creates a counterion saturation in the Debye layer leading to an enhanced mobility compared to the standard model. However, experimental data for non-dilute cases often under predicts the theoretically determined mobility. The present modified model fills this lacuna and demonstrate that the consideration of finite ion size modifies the medium viscosity and hence, ionic mobility, which in combination lowers the mobility value.

中文翻译：

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结合有限离子尺寸效应和离子-溶剂相互作用的疏水胶体电泳简化模型的数值研究

我们考虑修改后的电动模型，通过考虑有限大小的离子来研究疏水粒子的电泳。本研究采用的数学模型结合了离子空间排斥、离子-溶剂相互作用以及电解质上的麦克斯韦应力。电解质的介电常数和粘度被认为随局部离子体积分数而变化。基于这种修改后的电动力学模型，我们分析了单价和非单价电解质以及混合电解质中的电泳$z:z$电解质。粘度对局部离子体积分数的依赖性会改变离子的流体动力阻力和扩散系数，这在现有的电泳研究中被忽略了。基于对施加电场的一阶扰动，开发了结合离子空间排斥和离子-溶剂相互作用的疏水性粒子电泳的简化模型。建立此简化模型是为了对比粒径更薄的德拜层和更小的滑移长度范围有效。该模型可用于任意数量的离子种类以及非$z:z$电解质。已确定，与标准模型相比，离子空间相互作用和介电衰减在德拜层中产生反离子饱和，从而导致迁移率增强。然而，非稀释情况下的实验数据往往低估了理论上确定的流动性。目前的修改模型填补了这个空白，并证明有限离子尺寸的考虑改变了介质粘度，因此改变了离子迁移率，这结合起来降低了迁移率值。