Nadine Aubry

Linear stability of a two-fluid interface for electrohydrodynamic mixing in a channel

We study the electrohydrodynamic stability of the interface between two superposed viscous fluids in a channel subjected to a normal electric field. The two fluids can have different densities, viscosities, permittivities and conductivities. The interface allows surface charges, and there exists an electrical tangential shear stress at the interface owing to the finite conductivities of the two fluids. The long-wave linear stability analysis is performed within the generic Orr–Sommerfeld framework for both perfect and leaky dielectrics. In the framework of the long-wave linear stability analysis, the wave speed is expressed in terms of the ratio of viscosities, densities, permittivities and conductivities of the two fluids. For perfect dielectrics, the electric field always has a destabilizing effect, whereas for leaky dielectrics, the electric field can have either a destabilizing or a stabilizing effect depending on the ratios of permittivities and conductivities of the two fluids. In addition, the linear stability analysis for all wavenumbers is carried out numerically using the Chebyshev spectral method, and the various types of neutral stability curves (NSC) obtained are discussed.

Micro- and nanoparticles self-assembly for virtually defect-free, adjustable monolayers

As chips further shrink toward smaller scales, fabrication processes based on the self-assembly of individual particles into patterns or structures are often sought. One of the most popular techniques for two-dimensional assembly (self-assembled monolayers) is based on capillary forces acting on particles placed at a liquid interface. Capillarity-induced clustering, however, has several limitations: it applies to relatively large (radius > ≈10 μm) particles only, the clustering is usually non-defect-free and lacks long-range order, and the lattice spacing cannot be adjusted. The goal of the present article is to show that these shortcomings can be addressed by using an external electric field normal to the interface. The resulting self-assembly is capable of controlling the lattice spacing statically or dynamically, forming virtually defect-free monolayers, and manipulating a broad range of particle sizes and types including nanoparticles and electrically neutral particles.

Transient and steady state of a rising bubble in a viscoelastic fluid

A finite element code based on the level-set method is used to perform direct numerical simulations (DNS) of the transient and steady-state motion of bubbles rising in a viscoelastic liquid modelled by the Oldroyd-B constitutive equation. The role of the governing dimensionless parameters, the capillary number (Ca), the Deborah number (De) and the polymer concentration parameter c, in both the rising speed and the deformation of the bubbles is studied. Simulations show that there exists a critical bubble volume at which there is a sharp increase in the terminal velocity with increasing bubble volume, similar to the behaviour observed in experiments, and that the shape of both the bubble and its wake structure changes fundamentally at that critical volume value. The bubbles with volumes smaller than the critical volume are prolate shaped while those with volumes larger than the critical volume have cusp-like trailing ends. In the latter situation, we show that there is a net force in the upward direction because the surface tension no longer integrates to zero. In addition, the structure of the wake of a bubble with a volume smaller than the critical volume is similar to that of a bubble rising in a Newtonian fluid, whereas the wake structure of a bubble with a volume larger than the critical value is strikingly different. Specifically, in addition to the vortex ring located at the equator of the bubble similar to the one present for a Newtonian fluid, a vortex ring is also present in the wake of a larger bubble, with a circulation of opposite sign, thus corresponding to the formation of a negative wake. This not only coincides with the appearance of a cusp-like trailing end of the rising bubble but also propels the bubble, the direction of the fluid velocity behind the bubble being in the opposite direction to that of the bubble. These DNS results are in agreement with experiments.

Dispersion and attraction of particles floating on fluid–liquid surfaces

In this review, we summarize the current state of understanding of the mechanisms that are important in determining the distribution of particles on fluid–liquid interfaces and of a technique that uses an externally applied electric field to control the microstructure of monolayers on interfaces. When particles come in contact with an interface they first disperse and cause particles already trapped on the interface to move away. The initial dispersion, which can be explosive for small particles on the surface of mobile liquids like water, is due to the fact that the capillary force pulls particles into the interface causing them to accelerate to a relatively large velocity. Since the motion of the particles is inertia dominated, they oscillate about the equilibrium position before coming to a stop under viscous drag. The observed spontaneous dispersion is a result of repulsive hydrodynamic forces that arise because of these oscillations. Then, after the forces causing dispersion subside, particles either cluster into monolayers under the action of attractive lateral forces or remain dispersed. The former scenario takes place for particles larger than about 10 µm for which attractive capillary forces can be significant and therefore such particles usually form tightly packed monolayers that normally contain defects and lack long-range order. The spacing between the particles of a monolayer can be controlled and defects eliminated by applying an electric field normal to the interface. This technique, in fact, also allows for the formation of monolayers of particles smaller than about 10 µm, as in the presence of the electric field the particles experience a force normal to the surface which gives rise to attractive lateral capillary forces. We also discuss the direct numerical simulation (DNS) and analytical approaches which have been used to understand and model these physical phenomena.

Quantifying the linear stability of a flowing electrified two-fluid layer in a channel for fast electric times for normal and parallel electric fields

Motivated by the destabilization of a two-fluid layer flowing in a microchannel for efficient mixing or droplet formation, we study quantitatively the linear stability of the interface between two liquids subjected to an electric field parallel or normal to the flat interface. In the case of fast electric charge relaxation times, the equations for the perturbation can be significantly reduced [A. K. Uguz, O. Ozen, and N. Aubry, Phys. Fluids 20, 031702 (2008)]. Using a simple argument and without solving the equations, Uguz et al. determined the range of parameters over which the electric field is destabilizing, which is narrower for the parallel compared to the normal electric field. However, the argument of Uguz et al. was not amenable to the calculation of growth rates and neutral stability curves. In this paper, by solving the equations, we not only confirm the previous findings but also determine the quantitative linear stability properties, namely, the growth rates and neutral stability curves. Depen...

Electric field effect on a two-fluid interface instability in channel flow for fast electric times

The application of an electric field to a two-fluid layer in channel flow has been shown to be an effective way to destabilize microscale interfacial flows. Here, we perform a linear stability analysis of a flat interface between two leaky dielectric liquids flowing in a channel while also subjected to an electric field parallel to the interface. It is shown that the analysis simplifies for fast electric charge relaxation times, in which case conditions for the electric field to be either stabilizing or destabilizing are derived analytically. These results are compared to those previously obtained for a normal electric field.

Concentrating particles on drop surfaces using external electric fields

We propose to use an externally applied uniform electric field to alter the distribution of particles on the surface of a drop immersed in another immiscible liquid. Specifically, we seek to generate well‐defined concentrated regions at the drop surface while leaving the rest of the surface particle free. Experiments show that when the dielectric constant of the drop is greater than that of the ambient liquid the particles for which the Clausius–Mossotti factor is positive move along the drop surface to the two poles of the drop. Particles with a negative Clausius–Mossotti factor, on the other hand, move along the drop surface to form a ring near the drop equator. The opposite takes place when the dielectric constant of the drop is smaller than that of the ambient liquid, namely particles for which the Clausius–Mossotti factor is positive form a ring near the equator while those for which such a factor is negative move to the poles. This motion is due to the dielectrophoretic force that acts upon particles because the electric field on the surface of the drop is nonuniform, despite the uniformity of the applied electric field. Experiments also show that when small particles collect at the poles of a deformed drop the electric field needed to break the drop is smaller than without particles. These phenomena could be useful to concentrate particles at a drop surface within well‐defined regions (poles and equator), separate two types of particles at the surface of a drop or increase the drop deformation to accelerate drop breakup.

Destabilization of Pickering emulsions using external electric fields.

It is known that emulsions can be stabilized by the presence of particles that get trapped at fluid–fluid interfaces and prevent adjacent drops from coalescing with one another. We show here that such emulsions, or Pickering emulsions, can be destabilized by applying external electric fields. This is demonstrated experimentally by studying water drops in decane and silicone oil drops in corn oil in the presence of micro‐sized particles. It is shown that the primary phenomenon responsible for the destabilization is the motion of particles on the surface of drops in the presence of a uniform electric field. Although there should be no electrostatic forces acting on neutral particles in a uniform electric field, the presence of the drop itself introduces nonuniformity, which leads to dielectrophoretic forces acting on the particles and is thus responsible for particle motions along the drop surface. Particles translate to either the poles or the equator of the drop, depending on the relative dielectric constants of the particles, the surrounding fluid and the fluid within the drop. Such motions break the particle barrier, thus allowing for drops to merge with one another and therefore destabilizing the emulsion.

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.

Effect of parameters on redistribution and removal of particles from drop surfaces

It was recently shown by us that particles distributed on the surface of a drop can be concentrated at the poles or the equator of the drop by subjecting the latter to a uniform electric field and that such concentrated particles can then be removed from the drop by increasing the electric field intensity. In this paper, we present experimental results for the dependence of the dielectrophoretic force on the parameters of the system such as the particles and drops radii and the dielectric properties of the fluids and particles, and define a dimensionless parameter regime for which the technique can work. Specifically, we show that if the drop radius is larger than a critical value, that depends on the physical properties of the drop and ambient fluids and those of the particles, it is not possible to concentrate particles and thus clean the drop of the particles it carries at its surface because the drop breaks or tip-streams at an electric field intensity smaller than that needed for concentrating particles. However, since the dielectrophoretic force varies inversely with the drop radius, the effectiveness of the concentration mechanism increases with decreasing drop size, and therefore the technique (particles concentration followed by drop clean-up or delivery) is guaranteed to work provided the drop radius is sufficiently small. We also show that this concentration method can be used to separate particles experiencing positive dielectrophoresis on the surface of a drop from those experiencing negative dielectrophoresis, and form a composite (Janus) drop by aggregating particles of one type near the poles and of another near the equator. Furthermore, after the two types of particles are separated on the surface of the drop, it is possible to remove the particles concentrated near the poles from the drop by increasing the electric field intensity so that the drop tip-streams, thus leaving only one type of particles at the surface of the drop. This could be useful for having drops selectively deliver, or get rid of, some particles while keeping others.