Miloh Touvia, Avital Eldad J
School of Mechanical Engineering, Tel Aviv University, Tel-Aviv 69978, Israel.
School of Engineering and Materials Science, Queen Mary University of London, London E1 4NS, UK.
Micromachines (Basel). 2022 Jul 25;13(8):1173. doi: 10.3390/mi13081173.
A theoretical framework is presented for calculating the polarization, electro-rotation, travelling-wave dielectrophoresis, electro-hydrodynamics and induced-charge electroosmotic flow fields around a freely suspended conducting dimer (two touching spheres) exposed to non-uniform direct current (DC) or alternating current (AC) electric fields. The analysis is based on employing the classical (linearized) Poisson-Nernst-Planck (PNP) formulation under the standard linearized 'weak-field' assumption and using the tangent-sphere coordinate system. Explicit expressions are first derived for the axisymmetric AC electric potential governed by the Robin (mixed) boundary condition applied on the dimer surface depending on the resistance-capacitance circuit (RC) forcing frequency. Dimer electro-rotation due to two orthogonal (out-of-phase) uniform AC fields and the corresponding mobility problem of a polarizable dimer exposed to a travelling-wave electric excitation are also analyzed. We present an explicit solution for the non-linear induced-charge electroosmotic (ICEO) flow problem of a free polarized dimer in terms of the corresponding Stokes stream function determined by the Helmholtz-Smoluchowski velocity slip. Next, we demonstrate how the same framework can be used to obtain an exact solution for the electro-hydrodynamic (EHD) problem of a polarizable sphere lying next to a conducting planar electrode. Finally, we present a new solution for the induced-charge mobility of a Janus dimer composed of two fused spherical colloids, one perfectly conducting and one dielectrically coated. So far, most of the available electrokinetic theoretical studies involving polarizable nano/micro shapes dealt with convex configurations (e.g., spheres, spheroids, ellipsoids) and as such the newly obtained electrostatic AC solution for a dimer provides a useful extension for similar concave colloids and engineered particles.
本文提出了一个理论框架，用于计算自由悬浮的导电二聚体（两个相切球体）周围的极化、电旋转、行波介电泳、电流体动力学和感应电荷电渗流场，该二聚体暴露于非均匀直流（DC）或交流（AC）电场中。分析基于在标准线性化“弱场”假设下采用经典（线性化）泊松 - 能斯特 - 普朗克（PNP）公式，并使用切球坐标系。首先根据施加在二聚体表面的罗宾（混合）边界条件，针对取决于电阻 - 电容电路（RC）强迫频率的轴对称交流电势，推导出显式表达式。还分析了由两个正交（异相）均匀交流场引起的二聚体电旋转以及可极化二聚体在行波电激励下的相应迁移率问题。我们根据由亥姆霍兹 - 斯莫卢霍夫斯基速度滑移确定的相应斯托克斯流函数，给出了自由极化二聚体的非线性感应电荷电渗（ICEO）流动问题的显式解。接下来，我们展示了如何使用相同的框架来获得位于导电平面电极旁边的可极化球体的电流体动力学（EHD）问题的精确解。最后，我们给出了由两个融合的球形胶体组成的Janus二聚体的感应电荷迁移率的新解，其中一个是完美导电的，另一个涂有介电层。到目前为止，大多数涉及可极化纳米/微形状的可用电动理论研究都处理凸形配置（例如球体、椭球体、椭圆体），因此新获得的二聚体静电交流解为类似的凹形胶体和工程颗粒提供了有用的扩展。
