Journal of Colloid and Interface Science 257 (2003) 250–257 www.elsevier.com/locate/jcis Electrophoresis of concentrated mercury drops Eric Lee, Jin-Kan Hu, and Jyh-Ping Hsu ∗ Department of Chemical Engineering, National Taiwan University, Taipei, Taiwan 10617,ROC Received 16 April 2002; accepted 22 October 2002 Abstract The electrophoretic behavior of concentrated monodispersed, positively charged mercury drops is investigated theoretically. The present study extends previous analyses by considering arbitrary surface potentials, double-layer polarization, and the interaction between adjacent double layers. The coupled equations describing the spatial variations in the flow field, the electric field, and the concentration field are solved by a pseudo-spectral method. For a low surface potential φ r , the mobility increases monotonically with κa; κ and a are respectively the reciprocal Debye length and the radius of a mercury drop. For medium and high φ r , the mobility curve has a reflection point, which arises from the interaction of adjacent double layers, for κa. Also, if φ r is high, the mobility curve may exhibit a local minimum as κa varies. This phenomenon is pronounced if the concentration of the dispersed phase is high. If the double layer is thick, the mobility increases with φ r , and the reverse is true if it is thin. We show that the higher the concentration of the dispersed phase the smaller the mobility, and as κa becomes large the mobility approaches a constant value, which is independent of the concentration of the dispersed phase. The mobility of mercury drops is larger than that of the corresponding rigid particles.  2003 Elsevier Science (USA). All rights reserved. Keywords: Mercury drops; Electrophoresis; Pseudo-spectral method; Double layer polarization; Mobility 1. Introduction The electrokinetic phenomenon is one of the important branches of colloidal science. The phenomenon, which in- cludes electrophoresis, electroosmosis, sedimentation poten- tial, streaming potential, and electric conductivity, is closely related to the properties of a particle, in particular, the charged conditions on its surface. Unfortunately, this can only be characterized approximately by the electrical po- tential or charge density on the shear plane of the double layer surrounding a particle, and the exact surface properties remain unknown. Furthermore, limited by the available ex- perimental apparatus, the reliability of the experimental data gathered often deserves further observation. The mercury–liquid interface provides an ideal model for the simulation of charged conditions on a colloidal surface and the electrokinetic phenomenon of colloidal particles. A mercury drop is electrically conductive and can have a flow field inside. Due to these specific properties many phenomena of rigid colloidal particles are pronounced in the case of mercury drops. It was observed that when an electric * Corresponding author. E-mail address: jphsu@ccms.ntu.edu.tw (J.-P. Hsu). current is applied on a mercury drop placed in a capillary, the potential drop at the mercury–liquid interface varies with the current [1]. If the mercury drop is positively charged, its surface tension near the cathode is larger than that near the anode, and therefore, it moves toward the cathode, the so-called electrocapillary motion. Other experimental work that involves a mercury–liquid interface, can also be found in standard textbooks [2–4]. The charged condition on a mercury surface, the adsorption of molecules on the surface, and the structure of the double layer are investigated. The theoretical analysis of the motion of a mercury drop in an electric field was originated by Craxford et al. [1]. It was concluded that the force experienced by a mercury drop could be expressed as the product of the strength of the electric field and the amount of charges in the electrical double layer surrounding the drop. Although this is incorrect when the total amount of charges vanishes, the result derived under the condition of low potential gradient provides valuable reference for electrophoresis. Levich and Frumkin investigated the electrokinetic phenomenon of a charged mercury drop under the condition of a thin double layer by solving the Lippmann equation subject to some simplified boundary conditions on a mercury surface [1]. Ohshima et al. [5] analyzed theoretically the electrokinetic 0021-9797/03/$ – see front matter  2003 Elsevier Science (USA). All rights reserved. doi:10.1016/S0021-9797(02)00039-5