Faculty of Pharmaceutical Sciences, Tokyo University of Science, 2641 Yamazaki, Noda, Chiba 278-8510, Japan.
Molecules. 2022 Aug 11;27(16):5108. doi: 10.3390/molecules27165108.
The general expression is derived for the Laplace transform of the time-dependent transient electrophoretic mobility (with respect to time) of a spherical colloidal particle when a step electric field is applied. The transient electrophoretic mobility can be obtained by the numerical inverse Laplace transformation method. The obtained expression is applicable for arbitrary particle zeta potential and arbitrary thickness of the electrical double layer around the particle. For the low potential case, this expression gives the result obtained by Huang and Keh. On the basis of the obtained general expression for the Laplace transform of the transient electrophoretic mobility, we present an approximation method to avoid the numerical inverse Laplace transformation and derive a simple approximate analytic mobility expression for a weakly charged particle without involving numerical inverse Laplace transformations. The transient electrophoretic mobility can be obtained directly from this approximate mobility expression without recourse to the numerical inverse Laplace transformation. The results are found to be in excellent agreement with the exact numerical results obtained by Huang and Keh.
当施加阶跃电场时，导出了球形胶体颗粒的时变瞬态电泳迁移率（相对于时间）的拉普拉斯变换的一般表达式。瞬态电泳迁移率可以通过数值反拉普拉斯变换方法获得。所得到的表达式适用于任意的颗粒zeta 电位和颗粒周围的电双层的任意厚度。对于低电位情况，该表达式给出了 Huang 和 Keh 得到的结果。基于瞬态电泳迁移率的拉普拉斯变换的一般表达式，我们提出了一种近似方法来避免数值反拉普拉斯变换，并为无数值反拉普拉斯变换的弱电荷颗粒推导了一个简单的近似分析迁移率表达式。无需诉诸数值反拉普拉斯变换，就可以从这个近似迁移率表达式中直接获得瞬态电泳迁移率。结果与 Huang 和 Keh 通过数值方法得到的精确结果非常吻合。
