Li Meng X, Keh Huan J
Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan.
J Phys Chem B. 2020 Nov 5;124(44):9967-9973. doi: 10.1021/acs.jpcb.0c07436. Epub 2020 Oct 21.
The start-up of electrophoretic motion of a charged circular cylindrical particle in an unbounded solution of arbitrary electrolytes is analytically investigated. The modified Stokes equation for the transient fluid flow field is solved by using the Laplace transform. Analytical formulas for the time-evolving electrophoretic velocities of the dielectric cylinder are determined for the transversely and axially imposed electric fields, and they can be superimposed linearly for an imposed electric field of arbitrary direction. The transient electrophoretic velocities normalized by their respective steady-state values increase monotonically with an increase in the ratio of the particle radius to the Debye screening length but decrease monotonically with an increase in the particle-to-fluid density ratio, keeping the other parameter unchanged. The normalized electrophoretic acceleration of the particle decreases monotonically with the elapsed time. In general, the electrophoretic velocity of the cylindrical particle is not collinear with the arbitrarily oriented imposed electric field. The effect of the relaxation time for the transient electrophoresis is much more important for a cylindrical particle than for a spherical particle.
对带电荷的圆柱形粒子在任意电解质的无界溶液中的电泳运动启动进行了分析研究。利用拉普拉斯变换求解了瞬态流体流场的修正斯托克斯方程。确定了横向和轴向施加电场时电介质圆柱体随时间变化的电泳速度的解析公式，对于任意方向的施加电场，它们可以线性叠加。通过各自稳态值归一化的瞬态电泳速度随粒子半径与德拜屏蔽长度之比的增加而单调增加，但随粒子与流体密度比的增加而单调减少，其他参数保持不变。粒子的归一化电泳加速度随时间单调减小。一般来说，圆柱形粒子的电泳速度与任意取向的施加电场不共线。瞬态电泳弛豫时间的影响对圆柱形粒子比对球形粒子重要得多。
