Electrophoresis of two spheres: Influence of double layer and van der Waals interactions Shiojenn Tseng a , Chih-Hua Huang b , Jyh-Ping Hsu b,⇑ a Department of Mathematics, Tamkang University, Tamsui, Taipei 25137, Taiwan b Department of Chemical Engineering, National Taiwan University, Taipei 10617, Taiwan graphical abstract article info Article history: Received 1 March 2015 Accepted 31 March 2015 Available online 8 April 2015 Keywords: Electrophoresis Two spheres Electric double layer force Van der Waals force abstract Considering recent applications of electrophoresis conduced in nanoscaled devices, where particle–par- ticle interaction can play a role, we studied for the first time the electrophoresis of two rigid spheres along their center line, taking account of the hydrodynamic, electric, and van der Waals interactions between them. Under the conditions of constant surface potential and surface charge density, the influ- ences of the level of surface potential/charge density, the bulk salt concentration, and the particle–parti- cle distance on their electrokinetic behaviors are examined. Numerical simulation reveals that these behaviors are much more complicated and interesting than those of isolated particles. In particular, we show that care must be taken in choosing an appropriate particle concentration in relevant experi- ment to avoid obtaining unreliable mobility data. Ó 2015 Elsevier Inc. All rights reserved. 1. Introduction Electrophoresis has been applied widely as a separation tech- nique and as a powerful analytical tool in areas such as biology, chemistry, and medical science, to name a few. Recent advances in material science and fabrication technique further extend its applications to submicron and nano scaled devices such as those used in DNA sequencing [1–4]. Previous electrophoresis analyses are almost always based on isolated particles. For example, the derivations of the Smoluchowski’, Huckel’s, and Henry’s formulas [5] widely used in electrophoresis instruments all neglect the presence of nearby par- ticles. Some studies considered the electrophoresis of a swarm of uniformly distributed particles by adopting a cell model, where http://dx.doi.org/10.1016/j.jcis.2015.03.060 0021-9797/Ó 2015 Elsevier Inc. All rights reserved. ⇑ Corresponding author. Fax: +886 2 23623040. E-mail address: jphsu@ntu.edu.tw (J.-P. Hsu). Journal of Colloid and Interface Science 451 (2015) 170–176 Contents lists available at ScienceDirect Journal of Colloid and Interface Science www.elsevier.com/locate/jcis