Attraction between Particles at a Liquid Interface Due to the Interplay of Gravity- and Electric-Field-Induced Interfacial Deformations

Abstract

In a previous study, we established that the attraction between electrically charged particles attached to a water/tetradecane interface is stronger than predicted on the basis of the gravity-induced lateral capillary force. Here, our goal is to explain this effect. The investigated particles are hydrophobized glass spheres of radii between 240 and 320 microm. Their weight is large enough to deform the liquid interface. The interfacial deformation is considerably greater for charged particles because of the electrodipping force that pushes the particles toward the water phase. By independent experiments with particles placed between two electrodes, we confirmed the presence of electric charges at the particle/tetradecane interface. The theoretical analysis shows that if the distribution of these surface charges is isotropic, the meniscus produced by the particle electric field decays too fast with distance and cannot explain the experimental observations. However, if the surface-charge distribution is anisotropic, it induces a saddle-shaped deformation in the liquid interface around each particle. This deformation, which is equivalent to a capillary quadrupole, decays relatively slow. Its interference with the gravity-induced isotropic meniscus around the other particle gives rise to a long-range attractive capillary force, F approximately 1/L3 (L=interparticle distance). The obtained agreement between the experimental and theoretical curves, and the reasonable values of the parameters determined from the fits, indicate that the observed stronger attraction in the investigated system can be really explained as a hybrid interaction between gravity-induced "capillary charges" and electric-field-induced "capillary quadrupoles".

Interaction between like-charged particles at a liquid interface: Electrostatic repulsion vs. electrocapillary attraction

“…(4.6) is applicable, the electrostatic repulsion between the two like-charged particles prevails over the capillary attraction. Note, however, that in other cases (anisotropic surface charge distribution) the capillary attraction may prevail [35]. In Table 1 Expressions for the coefficients A0; .…”

“…The approach used in Ref. [35] is further developed and applied to the case of isotropic charge distribution on the particle surface. The interaction force is calculated by integrating the interfacial tension along the particle contact line and the pressure tensor over the particle surface.…”

“…(1.1) accounts for the fact that the dipolar field occupies only the upper half-space (the nonpolar fluid), whereas the electric field in the aqueous phase is screened by the ions in water. The electric charges that create the electric field can be located at the particle/water interface [22,29,[36][37][38] and/or on the particle/nonpolar-fluid interface [9,10,[25][26][27]34,35,[39][40][41][42][43]. Eq.…”

A Feasible Routine for Large-Scale Nanopatterning via Nanosphere Lithography

“…On contact with the water, the PS spheres immediately form a momolayer and start to assemble. The inherent mechanism for the ordering of PS spheres at a liquid interface has been studied by several groups (Aubry & Singh, 2008;Boneva et al, 2009;Larsen & Grier, 1997;Nikolaides et al, 2002;Pieranski, 1980;Trau et al, 1996;Yeh et al, 1997). A reasonable model has been provided to account for the ordering of PS spheres at the interface (Nikolaides et al, 2002).…”

“…Considering the importance of the electrical field in self-assembling PS spheres at interface, it is natural to find ways to change the electric field to control the arrangement of PS spheres. One way is to apply an external electric field during the self-assembly of PS spheres at the interface (Aubry & Singh, 2008;Boneva et al, 2009;Nikolaides et al, 2002;Trau et al, 1996). This external electrical field will change the charge distribution on the surface of PS Spheres, leading to the change of the electric dipole field around PS spheres.…”