Physics underlying controlled self-assembly of micro- and nanoparticles at a two-fluid interface using an electric field

Deformation of confined liquid interfaces by inhomogeneous electric fields and localized particle forces

HYPOTHESIS

Oil-water interfaces that are created by confining a certain amount of oil in a square shaped pixel (∼200 x 200 μm2 with a height of ∼10 μm) topped by a layer of water, have a curvature that depends on the amount of oil that happens to be present in the confining area. Under the application of an electric field normal to the interface, the interface will deform due to inhomogeneities in the electric field. These inhomogeneities are expected to arise from the initial curvature of the meniscus, from fringe fields that emerge at the confining pixel walls and, if applicable, from interfacially adsorbed particles.

MODELING AND EXPERIMENTS

We model the shape of the confined oil-water interface invoking capillarity and electrostatics. Furthermore, we measure the initial curvature by tracking the position of interfacially adsorbed particles depending on sample tilt.

FINDINGS

We found that the pixels exhibited meniscus curvature radii ranging from 0.6-7 mm. The corresponding model based minimum oil film thicknesses range between 0.7 and 9 μm. Furthermore, the model shows that the initial meniscus curvature can increase up to 76 percent relative to the initial curvature by the electric field before the oil film becomes unstable. The pixel wall and particles are shown to have minimal impact on the interface deformation.

Electric-Field-Induced Pattern Formation in Layers of DNA Molecules at the Interface between Two Immiscible Liquids

The concentration patterns of DNA molecules attached to the interface between two immiscible aqueous phases forming under an electric field are studied. The pattern formation is driven by hydrodynamic interactions between the molecules originating from the electro-osmotic flow due to the Debye layer around a molecule. A nonlinear integrodifferential equation is derived describing the time evolution of the concentration field at the liquid-liquid interface. A linear stability analysis of this equation shows that a mode of given wavelength is initially stable, but destabilizes after a critical time which is inversely proportional to the wavelength. The scaling behavior of the critical time with electric field strength and viscosity found in the experiments agrees with the predictions by the theoretical model.

Wave-based liquid-interface metamaterials

The control of matter motion at liquid–gas interfaces opens an opportunity to create two-dimensional materials with remotely tunable properties. In analogy with optical lattices used in ultra-cold atom physics, such materials can be created by a wave field capable of dynamically guiding matter into periodic spatial structures. Here we show experimentally that such structures can be realized at the macroscopic scale on a liquid surface by using rotating waves. The wave angular momentum is transferred to floating micro-particles, guiding them along closed trajectories. These orbits form stable spatially periodic patterns, the unit cells of a two-dimensional wave-based material. Such dynamic patterns, a mirror image of the concept of metamaterials, are scalable and biocompatible. They can be used in assembly applications, conversion of wave energy into mean two-dimensional flows and for organising motion of active swimmers.

Here, Francois et al. propose a method of remotely shaping particle trajectories by using rotating waves on a liquid gas interface. The superposition of orthogonal standing waves creates angular momentum which is transferred from waves to floating microparticles, guiding them along closed trajectories.

Controlled capillary assembly of magnetic Janus particles at fluid-fluid interfaces

Capillary interactions can be used to direct assembly of particles adsorbed at fluid-fluid interfaces. Precisely controlling the magnitude and direction of capillary interactions to assemble particles into favoured structures for materials science purposes is desirable but challenging. In this paper, we investigate capillary interactions between magnetic Janus particles adsorbed at fluid-fluid interfaces. We develop a pair-interaction model that predicts that these particles should arrange into a side-side configuration, and carry out simulations that confirm the predictions of our model. Finally, we investigate the monolayer structures that form when many magnetic Janus particles adsorb at the interface. We find that the particles arrange into long, straight chains exhibiting little curvature, in contrast with capillary interactions between ellipsoidal particles. We further find a regime in which highly ordered, lattice-like monolayer structures form, which can be tuned dynamically using an external magnetic field.

Electrohydrodynamic manipulation of particles adsorbed on the surface of a drop

In our previous studies we have shown that particles adsorbed on the surface of a drop can be concentrated at its poles or equator by applying a uniform electric field. This happens because even when the applied electric field is uniform the electric field on the surface of the drop is nonuniform, and so particles adsorbed on the surface are subjected to dielectrophoretic (DEP) forces. In this paper, we study the behavior of adsorbed particles at low electric field frequencies when the drop and ambient liquids are weakly conducting dielectric liquids, and model it using a leaky dielectric model. The electrohydrodynamic (EHD) flow which arises because of the accumulation of charge on the surface of the drop can be from pole-to-equator or equator-to-pole depending on the properties of the drop and ambient liquids. The flow however diminishes with increasing frequency and there is a critical frequency at which the drag force on a particle due to the EHD flow becomes equal to the DEP force, and above this critical frequency the DEP force dominates. When the fluid and particles properties are such that the EHD and DEP forces are in the opposite directions, particles can be collected at the poles or the equator, and also can be moved from the poles to the equator, or vice versa, by varying the frequency. Also, it is possible to separate the particles of a binary mixture when the critical frequencies of the two types of particles are different.

Stability and dynamics of magnetocapillary interactions

Recent experiments have shown that floating ferromagnetic beads, under the influence of an oscillating background magnetic field, can move along a liquid-air interface in a sustained periodic locomotion [Lumay et al., Soft Matter, 2013, 9, 2420]. Dynamic activity arises from a periodically induced dipole-dipole repulsion between the beads acting in concert with capillary attraction. We investigate analytically and numerically the stability and dynamics of this magnetocapillary swimming, and explore other related topics including the steady and periodic equilibrium configurations of two and three beads, and bead collisions. The swimming speed and system stability depend on a dimensionless measure of the relative repulsive and attractive forces which we term the magnetocapillary number. An oscillatory magnetic field may stabilize an otherwise unstable collinear configuration, and striking behaviors are observed in fast transitions to and from locomotory states, offering insight into the behavior and self-assembly of interface-bound micro-particles.

Molecular-like hierarchical self-assembly of monolayers of mixtures of particles

We present a technique that uses an externally applied electric field to self-assemble monolayers of mixtures of particles into molecular-like hierarchical arrangements on fluid-liquid interfaces. The arrangements consist of composite particles (analogous to molecules) which are arranged in a pattern. The structure of a composite particle depends on factors such as the relative sizes of the particles and their polarizabilities, and the electric field intensity. If the particles sizes differ by a factor of two or more, the composite particle has a larger particle at its core and several smaller particles form a ring around it. The number of particles in the ring and the spacing between the composite particles depend on their polarizabilities and the electric field intensity. Approximately same sized particles form chains (analogous to polymeric molecules) in which positively and negatively polarized particles alternate.

Capillary interactions in Pickering emulsions

The effective capillary interaction potentials for small colloidal particles trapped at the surface of liquid droplets are calculated analytically. Pair potentials between capillary monopoles and dipoles, corresponding to particles floating on a droplet with a fixed center of mass and subjected to external forces and torques, respectively, exhibit a repulsion at large angular separations and an attraction at smaller separations, with the latter resembling the typical behavior for flat interfaces. This change of character is not observed for quadrupoles, corresponding to free particles on a mechanically isolated droplet. The analytical results are compared with the numerical minimization of the surface free energy of the droplet in the presence of spherical or ellipsoidal particles.

Electric field-induced self-assembly of micro- and nanoparticles of various shapes at two-fluid interfaces

Particle lithography which explores the capability of particles to self-assemble offers an attractive means to manufacture nanostructured materials. Although traditional techniques typically lead to the formation of dense crystals, adjustable non-close-packed crystals are crucial in a number of applications. We have recently proposed a novel method to assemble spherical micro- and nanoparticles into monolayers. The technique consists of trapping particles at a liquid-fluid interface and applying an electric field normal to the interface. Particles rearrange themselves under the influence of interfacial and electrostatic forces to form 2-D hexagonal arrays of long-range order and whose lattice constant depends on the electric field strength and frequency. Furthermore, the existence of an electric field-induced capillary force makes the technique applicable to submicron and nanosized particles. Although spherical particles are often used, non-spherical particles can be beneficial in practice. Here, we review the method, discuss its applicability to particles of various shapes, and present results for particles self-assembly on air-liquid and liquid-liquid interfaces. In the case of non-spherical particles, the self-assembly process, while still taking place, is more complex as particles experience a torque which causes them to rotate relative to one another. This leads to a final arrangement displaying either a dominant orientation or no well-defined orientation. We also discuss the possibility of dislodging the particles from the interface by applying a strong electric field such that the Weber number is of order 1 or larger, a phenomenon which can be utilized to clean particles from liquid-fluid surfaces.

Dynamics of colloidal particles with capillary interactions

We investigate the dynamics of colloids at a fluid interface driven by attractive capillary interactions. At submillimeter length scales, the capillary attraction is formally analogous to two-dimensional gravity. In particular it is a nonintegrable interaction and it can be actually relevant for collective phenomena in spite of its weakness at the level of the pair potential. We introduce a mean-field model for the dynamical evolution of the particle number density at the interface. For generic values of the physical parameters the homogeneous distribution is found to be unstable against large-scale clustering driven by the capillary attraction. We also show that for the instability to be observable, the appropriate values for the relevant parameters (colloid radius, surface charge, external electric field, etc.) are experimentally well accessible. Our analysis contributes to current studies of the structure and dynamics of systems governed by long-ranged interactions and points toward their experimental realizations via colloidal suspensions.

Electrohydrodynamic removal of particles from drop surfaces

A uniform electric field is used for cleaning drops of the particles they often carry on their surface. In a first step, particles migrate to either the drop's poles or equator. This is due to the presence of an electrostatic force for which an analytical expression is derived. In a second step, particles concentrated near the poles are released into the ambient liquid via tip streaming, and those near the equator are removed by stretching the drop and breaking it into several droplets. In the latter case, particles are all concentrated in a small middle daughter droplet.