Dielectric force and relative motion between two spherical particles in electrophoresis
Dielectric force and relative motion between two spherical particles in electrophoresis
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作者：
Kang, KH;Li, DQ
当两个相互靠近的粒子进行电泳运动时，每个粒子都受到另一个粒子产生的不均匀电场的影响。两个粒子可能由于介电力而相互吸引或排斥，这取决于它们在非均匀电场中的位置。在这项工作中，介电相互作用和随后的相对运动的两个任意取向的球形粒子进行了分析。介电力通过积分麦克斯韦应力得到。在薄双电层假设下，该结果对任意取向的粒子都是有效的。将介电力的大小与所谓的惯性感应力进行比较，这表明介电力通常比惯性感应力大得多。粒子的相对速度由介电力和斯托克斯阻力之间的力平衡决定。定义了吸引和排斥的区域。结果表明，一对粒子最终平行于外部施加的电场，除了在两个粒子最初取向垂直于电场的情况下。一个封闭形式的分析解决方案，获得的粒子轨迹，通过使用的近似表达式的介电力有效的位置不太接近的粒子。
When two particles close to each other are in electrophoretic motion, each particle is under the influence of the nonuniform electric field generated by the other particle. Two particles may attract or repel each other due to the dielectric force, depending on their positions in the nonuniform electric field. In this work, the dielectric interaction and the subsequent relative motion of the two arbitrarily oriented spherical particles are analyzed. The dielectric force is obtained by integrating the Maxwell stress. The result is valid for arbitrary orientations of the particles under the thin electrical-double-layer assumption. The magnitude of the dielectric force is compared to the so-called inertia-induced force, which shows that the dielectric force is normally much greater than the inertia-induced force. The relative velocity of particles is determined by the force balance between the dielectric force and the Stokes drag. The regions of attraction and repulsion are defined. It is shown that a pair of particles eventually aligns parallel to the externally applied electric field, except in the case where the two particles are initially oriented perpendicular to the electric field. A closed-form analytical solution is obtained for the particle trajectory by using the approximate expression for the dielectric force valid for not-too-closely located particles.