Department of Chemical Engineering, Faculty of Chemistry, Sofia University, 1164 Sofia, Bulgaria.
J Colloid Interface Sci. 2010 May 15;345(2):505-14. doi: 10.1016/j.jcis.2010.02.017. Epub 2010 Feb 13.
The electric field of charged particles, which are adsorbed at a liquid interface, induces interfacial deformations (capillary menisci). The overlap of such deformations gives rise to electrocapillary force of interaction between the particles. Our goal is to quantify this interaction on the basis of a force approach, which is different from the approaches (mostly based on energy calculations) used by other authors. The fact that the electric field of adsorbed particles has a dipolar asymptotics (due to the image-charge effect) is utilized to derive an analytical expression for the meniscus profile. The comparison of the calculated profile with experimental data indicates that the results based on the dipolar approximation agree excellently with the data, except some small deviations near the contact line. The effect of the interfacial deformation on the electrostatic pressure is also taken into account. The two-particle electrocapillary problem is solved in bipolar coordinates without using the superposition approximation. It turns out that for uniform distribution of the surface charges, the electrocapillary attraction is weaker than the electrostatic repulsion at interparticle distances at which the dipolar approximation is applicable, so that the net force is repulsive. This result is in agreement with the conclusions of other authors obtained by using different theoretical approaches and with available experimental data. The analytical expressions for the electrocapillary and electrodipping forces derived in the present article provide a simple and convenient way for estimation of these forces.
带电粒子在液体界面上被吸附时，会产生电场，从而导致界面变形（毛细弯月面）。这些变形的重叠会导致粒子之间的电动毛细相互作用力。我们的目标是基于力的方法来量化这种相互作用，这种方法与其他作者使用的方法（主要基于能量计算）不同。吸附粒子的电场具有偶极子渐近线（由于镜像电荷效应），这一事实被用来推导出弯月面轮廓的解析表达式。计算轮廓与实验数据的比较表明，除了在接触线附近的一些小偏差外，基于偶极子近似的结果与数据非常吻合。还考虑了界面变形对静电压力的影响。在不使用叠加近似的情况下，在双极坐标中解决了两个粒子的电动毛细问题。事实证明，对于表面电荷的均匀分布，在适用偶极子近似的粒子间距离处，电动毛细吸引力比静电排斥力弱，因此净力是排斥的。这一结果与其他作者使用不同理论方法得出的结论以及现有的实验数据一致。本文推导出的电动毛细力和电动浸渍力的解析表达式为估计这些力提供了一种简单方便的方法。
