Kundu Dipankar, Bhattacharyya Somnath
Department of Mathematics, Indian Institute of Technology Kharagpur, 721302, Kharagpur, India.
Eur Phys J E Soft Matter. 2020 May 27;43(5):27. doi: 10.1140/epje/i2020-11957-8.
Nonlinear effects on the electrophoresis of a soft particle, consisting of a rigid hydrophobic core coated with a diffuse polymer layer (PEL) suspended in an electrolyte medium, are studied. The impact of the ion partitioning effect arising due to the Born energy difference between the PEL and the electrolyte is approximated based on the equilibrium Boltzmann equation, with which the ion distribution and hence, the charge density is modified. The equations describing the electrokinetic transport comprising the Darcy-Brinkman extended Navier-Stokes equations which includes the ion partitioning effect coupled with the modified Nernst-Planck equations and Poisson equations for electric field are solved numerically. The present numerical model for the soft particle compares well with the existing theoretical solutions and experimental results in the limiting cases. A deviation from existing simplified models based on the Boltzmann distribution of ions occurs when the Debye layer polarization, relaxation and the electroosmosis induced by the PEL immobile charge become significant. The hydrophobicity of the inner core strongly influences the nonlinear electrokinetic effects by modifying the Debye layer, electroosmotic flow in the PEL and surface conduction. The results indicate that the ion partitioning can significantly increase the electrophoretic mobility of the soft particle by attenuating the shielding effect. When the Debye layer is in the order of the particle size the hydrophobicity of the core surface and the ion partitioning effect manifest the surface conduction, which implies that the Boltzmann distribution of ions is no longer valid. The core hydrophobicity and ion partitioning effect have influence on the condensation of the PEL immobile charge, which creates a significant impact on the mobility.
研究了对软颗粒电泳的非线性效应，该软颗粒由悬浮在电解质介质中的刚性疏水核和包裹着扩散聚合物层（PEL）组成。基于平衡玻尔兹曼方程近似计算了由于PEL与电解质之间的玻恩能量差而产生的离子分配效应的影响，利用该方程修正了离子分布，进而修正了电荷密度。对描述电动输运的方程进行了数值求解，这些方程包括达西-布林克曼扩展纳维-斯托克斯方程（其中包含离子分配效应），并与修正的能斯特-普朗克方程以及电场的泊松方程相耦合。在极限情况下，本文针对软颗粒的数值模型与现有的理论解和实验结果吻合良好。当德拜层极化、弛豫以及由PEL固定电荷引起的电渗变得显著时，会出现与基于离子玻尔兹曼分布的现有简化模型的偏差。内核的疏水性通过改变德拜层、PEL中的电渗流和表面传导，强烈影响非线性电动效应。结果表明，离子分配可通过减弱屏蔽效应显著提高软颗粒的电泳迁移率。当德拜层与颗粒尺寸相当时，核心表面的疏水性和离子分配效应表现出表面传导，这意味着离子的玻尔兹曼分布不再有效。核心疏水性和离子分配效应会影响PEL固定电荷的凝聚，这对迁移率产生重大影响。
