Electrowetting-induced oil film entrapment and instability

We investigate the spreading at variable rate of a water drop on a smooth hydrophobic substrate in an ambient oil bath driven by electrowetting. We find that a thin film of oil is entrapped under the drop. Its thickness is described by an extension of the Landau-Levich law of dip coating that includes the electrostatic pressure contribution. Once trapped, the thin film becomes unstable under the competing effects of the electrostatic pressure and surface tension and dewets into microscopic droplets, in agreement with a linear stability analysis. Our results recommend electrowetting as an efficient experimental approach to the fundamental problem of dynamic wetting in the presence of a tunable substrate-liquid interaction.

Restructuring and break-up of two-dimensional aggregates in shear flow

We consider single two-dimensional aggregates, containing glass particles, placed at a water/air interface. We have investigated the critical shear rate for break-up of aggregates with different sizes in a simple shear flow. All aggregates break-up nearly at the same shear rate (1.8 +/- 0.2 s(-)(1)) independent of their size. The evolution of the aggregate structure before break-up was also investigated. With increasing shear rate, the aggregates adopt a more circular shape, and the particles order in a more dense, hexagonal structure. A simple theoretical model was developed to explain the experimentally observed break-up. In the model, the aggregate is considered as a solid circular disk that will break near its diameter. The capillary and drag force on the two parts of the aggregate were calculated, and from this force balance, the critical shear rate was found. The model shows a weak size dependence of the critical shear rate for the considered aggregates. This is consistent with the experimental observations.

Microrheology of aggregated emulsion droplet networks, studied with AFM-CSLM

We studied the mechanical behavior of densely packed (up to approximately 30% v/v), sedimented layers of (1 microm) water-in-oil W/O emulsion droplets, upon indentation with a (10 microm) large spherical probe. In the presence of attractive forces, the droplets form solid like networks which can resist deformation. Adding a polymer to the oil phase was used to control droplet attraction. The droplet layers were assembled via normal gravity settling. Considering that both the network structure and the droplet interactions play a key role, we used a combination of atomic force microscopy (AFM) and confocal scanning laser microscopy (CSLM) to characterize the mechanical behavior. Here the AFM was used both as indentation tool and as force sensor. Indentation experiments were performed via a protocol consisting of approach, waiting, and retract stages. CSLM was used to observe the network structure at micron resolution in real time. Use of refractive index matched fluorescent droplets allowed the visualization of the entire layer. Upon compression with the probe, a markedly nonhomogeneous deformation occurred, evidenced by the formation of a dense corona (containing practically all of the displaced droplets) in the direct vicinity of the probe, as well as more subtle deformations of force-chains at larger distances. Upon decompression, both the imprint of the indenter and the corona remained, even long after the load was released. The force-distance curves recorded with the AFM correspond well to these observations. For each deformation cycle performed on fresh material, the retract curve was much steeper than the approach curve, thus corroborating the occurrence of irreversible compaction. Contrary to classic linear viscoelastic materials, this hysteresis did not show any dependence on the deformation speed. Our force-indentation approach curves were seen to scale roughly as F approximately delta(3/2). The pre-factor was found to increase with the polymer concentration and with the density of the network. These findings suggest that this new AFM-CSLM method could be used for rheological characterization of small volumes of "granular networks" in liquid. Our hypothesis that the mechanical resistance of the networks originates from interdroplet friction forces, which in turn are set by the interdroplet potential forces, is supported by the predictions from a new mechanical model in which the interdroplet bonds are represented by stick-slip elements.

Electrical discharge in capillary breakup: controlling the charge of a droplet

We studied the detachment of sessile droplets of conductive liquids from an immersed wire by reducing the contact angle using ac electrowetting. Upon detachment, the droplets acquire a certain amount of charge, which is shown to be controlled by a dimensionless parameter alpha. Alpha describes the interplay between the diverging Ohmic resistance of the breaking capillary neck and the ac frequency. In the specific configuration of the present experiment, discharging at high frequency leads to self-excited oscillations in which the droplets periodically detach from and reattach to the wire.

Capillary forces between spherical particles floating at a liquid-liquid interface

We study the capillary forces acting on sub-millimeter particles (0.02-0.6 mm) trapped at a liquid-liquid interface due to gravity-induced interface deformations. An analytical procedure is developed to solve the linearized capillary (Young-Laplace) equation and calculate the forces for an arbitrary number of particles, allowing also for a background curvature of the interface. The full solution is expressed in a series of Bessel functions with coefficients determined by the contact angle at the particle surface. For sub-millimeter spherical particles, it is shown that the forces calculated using the lowest order term of the full solution (linear superposition approximation; LSA) are accurate to within a few percents. Consequently the many particle capillary force is simply the sum of the isolated pair interactions. To test these theoretical results, we use video microscopy to follow the motion of individual particles and pairs of interacting particles at a liquid-liquid interface with a slight macroscopic background curvature. Particle velocities are determined by the balance of capillary forces and viscous drag. The measured velocities (and thus the capillary forces) are well described by the LSA solution with a single fitting parameter.

Capillary bridges in electric fields

We analyzed the morphology of droplets of conductive liquids placed between two parallel plate electrodes as a function of the two control parameters electrode separation and applied voltage. Both electrodes were covered by thin insulating layers, as in conventional electrowetting experiments. Depending on the values of the control parameters, three different states of the system were found: stationary capillary bridges, stationary separated droplets, and periodic self-excited oscillations between both morphologies, which appear only above a certain threshold voltage. In the two stationary states, the morphology of the liquid is modified by the electric fields due to electrowetting and due to mutual electrostatic attraction, respectively. We determined a complete phase diagram within the two-dimensional phase space given by the control parameters. We discuss a model based on the interfacial and electrostatic contributions to the free energy. Numerical solutions of the model are in quantitative agreement with the phase boundaries found in the experiments. The dynamics in the oscillatory state are governed by electric charge relaxation and by contact angle hysteresis.

Trends in Microfluidics with Complex Fluids

The rapid developments in biotechnology create a great demand for fluid handling systems on the nano- and picoliter scale. The characterization of minute quantities of DNA or protein samples requires highly integrated, automated, and miniaturized "total analysis systems" (mu-TAS). The small scales necessitate new concepts for devices both from a technological and from a fundamental physical point of view. Here, we describe recent trends in both areas. New technologies include soft lithography, chemical, and topographical structuring of surfaces in order to define pathways for liquids, as well as electro-wetting for manipulation purposes. Fundamentally, the interplay between geometric confinement and the size of biological macromolecules gives rise to complex dynamic behavior. The combination of both fluorescence imaging and scattering techniques allows for detailed insight into the dynamics of individual molecules and into their self-assembly into supramolecular aggregates.

Nanofluidics: viscous dissipation in layered liquid films

We studied the layer-by-layer collapse of molecularly thin films of a model lubricant confined between two atomically smooth substrates. The dynamics of the consecutive expulsion of four molecular layers were found to slow down with decreasing film thickness but showed no evidence for confinement-induced solidification. Using a hydrodynamic model, we show that the sliding friction of liquid layers on top of the solid substrates is approximately 18 times higher than the mutual friction between adjacent liquid layers. The latter was independent of film thickness and in close agreement with the bulk viscosity.

Interface profiles near three-phase contact lines in electric fields

Long-range electrostatic fields deform the surface profile of a conductive liquid in the vicinity of the contact line. We have investigated the equilibrium profiles by balancing electrostatic and capillary forces locally at the liquid vapor interface. Numerical results show that the contact angle at the contact line approaches Young's angle. Simultaneously, the local curvature displays a weak algebraic divergence. Furthermore, we present an asymptotic analytical model, which confirms these results and elucidates the scaling behavior of the profile close to the contact line.

Mixing and condensation in a wet granular medium

We have studied the effect of small amounts of added liquid on the dynamic behavior of a granular system consisting of a mixture of glass beads of two different sizes. Segregation of the large beads to the top of the sample is found to depend in a nontrivial way on the liquid content. A transition to viscoplastic behavior occurs at a critical liquid content, which depends upon the bead size. We show that this transition can be interpreted as a condensation due to the hysteretic liquid bridge forces connecting the beads, and we provide the corresponding phase diagram.

Nonlocal dynamics of spontaneous imbibition fronts

We have studied spontaneous imbibition fronts generated by capillary rise between two roughened glass plates, the separation d of which varied between 10 and 50 microm. Perfect agreement with Washburn's law was obtained. We have determined the roughness exponent chi of the fronts, and found chi=0.81+/-0.01 for small length scales. Above a certain crossover length xi, it reached chi=0.58+/-0.04, as predicted by the quenched noise Kardar-Parisi-Zhang equation. The crossover length is found to scale with the plate separation as sqrt[d], as predicted by recent models which properly include nonlocal dynamics effects on the front. We believe this to be the first clear identification of crossover from nonlocal to local dynamics.

Boundary lubrication: dynamics of squeeze-out

The dynamics of the expulsion of the last liquid monolayer of molecules confined between two surfaces (measured recently for the first time) has been analyzed by solving the two-dimensional Navier-Stokes equation combined with kinetic Monte Carlo simulations. Instabilities in the boundary line of the expelled film were observed. We show that the instabilities produce a rough boundary for all length scales above a critical value and a smooth boundary for shorter lengths. The squeezing out of all but a few trapped islands of liquid is shown to be the result of the pressure gradient in the contact area.

Dynamics of layering transitions in confined liquids

Multiple beam interferometry and video microscopy were used to investigate the layering transition of thin liquid films of 1-undecanol confined between atomically smooth mica surfaces. The expulsion of a molecularly thin lubricant layer was followed directly in two dimensions. Overall, the dynamics of the transition follows theoretical predictions based on two-dimensional hydrodynamics. Frequently, pockets of liquid remain trapped inside the contact area at the end of the transition. The trapped pockets undergo shape transformations to minimize elastic and interfacial energy.