Hierarchical Colloidal Vortex Rings in a Constant Electric Field

Despite nearly two centuries of study, the response of charged particles dispersed in water to the influence of electric fields can be quite surprising, particularly when the particles also interact strongly with each other. This article describes a previously unrecognized class of hierarchically organized dynamical patterns that arise in the bulk of charge-stabilized colloidal suspensions when electrohydrodynamic forces due to constant applied fields complete with gravity. Our system, shown schematically in Fig. 1(a), resembles that previously used [1, 2] to study interfacial colloidal electrokinetic phenomena. An aqueous suspension of monodisperse colloidal silica spheres 3.0 μm in diameter (Bangs Laboratories, Lot No. 4740) is confined to a 4×1.5 cm horizontal layer H = 200±5 μm thick between a glass cover slip and a glass microscope slide. Both inner glass surfaces are coated with 10 nm thick gold electrodes on 10 nm thick titanium wetting layers. While still optically thin, these electrodes have a resistivity of less than 50 Ω/¤ and allow us to apply uniform vertical electric fields to the confined suspension. Once equilibrated to pH 5.5 in air, the colloidal silica spheres have a surface charge density of roughly −0.4 mC/m [3]. Given their density of 2 g/cm, they sediment rapidly onto the lower electrode. Positively biasing the upper electrode by less than 2.4 V has little effect because ions in solution screen out the electric field. Sustained upward forces only occur at higher biases for which hydrolysis at the electrodes feeds steady-state ionic fluxes, which in turn exert electroviscous forces on the charged spheres [2, 4]. These fluxes are spatially uniform in the parallel plate geometry, so that the drag they exert on an isolated sphere is independent of height, h, in the cell. Consequently, well separated spheres (< 0.01 monolayer) rise straight to the upper electrode at biases high enough to overcome gravity. Charged spheres not only respond to ionic fluxes, but also distort them, and the distortions mediate long-range inter-sphere interactions [2]. These interactions drive new cooperative behavior appears in denser monolayers. Increasing the bias beyond 2.6 V levitates the sedimented monolayer of spheres into hundreds of extraordinary flower-like clusters such as the example in Fig. 1(a), all floating freely at h = 40 μm above the lower electrode. Each cluster consists of a rapidly circulating toroidal vortex in which spheres travel downward along the inner surface and return upward along the outside, completing one cycle in a few seconds. Most often, the dense ring of 30