Effect of an encapsulated bubble in inhibiting droplet sliding

The transport of liquid droplets on surfaces carrying reactants offers advantages in the creation of fluidic devices crucial for life science applications. In a majority of situations, a selection of these droplets on a surface, rather than all of them, will need to be moved at any one time. It is a formidable challenge to deliver the motive energy source only to specific droplets while leaving the others unmoved. Here, we describe an alternative novel solution of momentarily pinning specific droplets to the surface while allowing the rest to be moved. We demonstrate this concept via the injection of a sizable bubble that is attached to a PTFE surface within a droplet. This then affects the contact line of the droplet, pinning it despite the introduction of an incline that will normally result in sliding. The use of bubbles offers easy release of pinning at will by simple rupture using mechanical means.     

An empirically validated analytical model of droplet dynamics in electrowetting on dielectric devices

Explicit analytical models that describe the capillary force on confined droplets actuated in electrowetting on dielectric devices and the reduction in that force by contact angle hysteresis as a function of the three-dimensional shape of the droplet interface are presented. These models are used to develop an analytical model for the transient position and velocity of the droplet. An order of magnitude analysis showed that droplet motion could be modeled using the driving capillary force opposed by contact angle hysteresis, wall shear, and contact line friction. Droplet dynamics were found to be a function of gap height, droplet radius, surface tension, fluid density, the initial and deformed contact angles, contact angle hysteresis, and friction coefficients pertaining to viscous wall friction and contact line friction. The first four parameters describe the device geometry and fluid properties; the remaining parameters were determined experimentally. Images of the droplet during motion were used to determine the evolution of the shape, position, and velocity of the droplet with time. Comparisons between the measured and predicted results show that the proposed model provides good accuracy over a range of practical voltages and droplet aspect ratios.     

Sliding/rolling phobic droplets along a fiber: measurement of interfacial forces

Phobic droplet-fiber systems possess complex geometries, which have made full characterization of such systems difficult. This work has used atomic force microscopy (AFM) to measure droplet-fiber forces for oil droplets on oleophobic fibers over a range of fiber diameters. The work adapted a previous method and a theoretical model developed by the authors for philic droplet-fiber systems. A Bayesian statistical model was also used to account for the influence of surface roughness on the droplet-fiber force. In general, it has been found that the force required to move a liquid droplet along an oleophobic filter fiber will be less than that required to move a droplet along an oleophilic fiber. However, because of the effects of pinning and/or wetting behavior, this difference may be less than would otherwise be expected. Droplets with a greater contact angle (~110°) were observed to roll along the fiber, whereas droplets with a lesser contact angle (<90°) would slide.     

Two-dimensional fluidics based on differential lyophobicity and gravity

We have prepared planar fluidics devices using binary chemical patterns consisting of hydrophobic "roads" on which water droplets slide easily and more hydrophobic "curbs" that direct droplet motion. Contact angle and contact angle hysteresis both control the motion of liquid droplets on surfaces. The difference between the advancing contact angles of the two regions prevents the liquid from crossing the interface between them. The low hysteresis of the roads allows facile movement. Gravity (slight tilting of samples) forces droplets to move effortlessly in defined pathways even though the difference in contact angles is not large and both regions are hydrophobic.     

Displacement of liquid droplets on a surface by a shearing air flow

The motion of droplets on surfaces is crucial to the performance of a wide range of processes; this study examines the initiation of droplet motion through a shearing mechanism generated here by a controlled air flow. Systematic experiments are carried out for a range of fluids and well defined surfaces. A model is postulated that balances surface tension forces at the contact line and the drag force due to the air motion. Experiments reveal that the critical velocity at which droplet motion is initiated depends on the contact angle and the droplet size. Visualizations highlight three modes of motion: (I) the droplet retains a footprint similar to that at the point of motion; (II) a tail exists at the rear of the droplet; (III) a trail remains behind the droplet (that can shed smaller droplets). The predictions of droplet initiation velocity are good for type I motion, in accordance with the assumptions inherent within the model. This model confirms the dominant physics associated with the initiation of droplet motion and provides a useful predictive expression.     

Dynamic behavior of water droplets on solid surfaces with pillar-type nanostructures

In the present study, we investigated the static and dynamic behavior of water droplets on solid surfaces featuring pillar-type nanostructures by using molecular dynamics simulations. We carried out the computation in two stages. As a result of the first computational stage, an initial water cube reached an equilibrium state at which the water droplet showed different shapes depending on the height and the lateral and gap dimensions of the pillars. In the second computational stage, we applied a constant body force to the static water droplet obtained from the first computational stage and evaluated the dynamic behavior of the water droplet as it slid along the pillar-type surface. The dynamic behavior of the water droplet, which could be classified into three different groups, depended on the static state of the water droplet, the pillar characteristics (e.g., height and the lateral and gap dimensions of the pillars), and the magnitude of the applied body force. We obtained the advancing and receding contact angles and the corresponding contact angle hysteresis of the water droplets, which helped classify the water droplets into the three different groups.     

Dynamics of droplet motion under electrowetting actuation

The static shape of droplets under electrowetting actuation is well understood. The steady-state shape of the droplet is obtained on the basis of the balance of surface tension and electrowetting forces, and the change in the apparent contact angle is well characterized by the Young-Lippmann equation. However, the transient droplet shape behavior when a voltage is suddenly applied across a droplet has received less attention. Additional dynamic frictional forces are at play during this transient process. We present a model to predict this transient behavior of the droplet shape under electrowetting actuation. The droplet shape is modeled using the volume of fluid method. The electrowetting and dynamic frictional forces are included as an effective dynamic contact angle through a force balance at the contact line. The model is used to predict the transient behavior of water droplets on smooth hydrophobic surfaces under electrowetting actuation. The predictions of the transient behavior of droplet shape and contact radius are in excellent agreement with our experimental measurements. The internal fluid motion is explained, and the droplet motion is shown to initiate from the contact line. An approximate mathematical model is also developed to understand the physics of the droplet motion and to describe the overall droplet motion and the contact line velocities.     

Nonequilibrium bubbles in a flowing langmuir monolayer

We investigate the nonequilibrium behavior of two-dimensional gas bubbles in Langmuir monolayers. A cavitation bubble is induced in liquid expanded phase by locally heating a Langmuir monolayer with an IR-laser. At low IR-laser power the cavitation bubble is immersed in quiescent liquid expanded monolayer. At higher IR-laser power thermo capillary flow around the laser-induced cavitation bubble sets in. The thermo capillary flow is caused by a temperature dependence of the gas/liquid line tension. The slope of the line tension with temperature is determined by measuring the thermo capillary flow velocity. Thermodynamically stable satellite bubbles are generated by increasing the surface area of the monolayer. Those satellite bubbles collide with the cavitation bubble. Upon collision the satellite bubbles either coalesce with the cavitation bubble or slide past the cavitation bubble. Moreover we show that the satellite bubbles can also be produced by the emission from the laser-induced cavitation bubbles.     

Sliding of water droplets on hydrophobic surfaces with various hydrophilic region sizes

Four patterned surfaces with hydrophilic areas of different sizes were prepared using photolithography with a smooth octadecyltrimethoxysilane (ODS) hydrophobic coating. The hydrophilic area in the surfaces was aligned hexagonally with a constant area fraction. The sliding angle and contact angle hysteresis of the water droplets increased concomitantly with increasing pattern size. The increase of the contact line distortion between defects at the receding side plays an important role in this trend. The droplet sliding velocity also increased concomitantly with increasing pattern size. This trend was simulated by a simple flow model. The contribution of the interface between the ODS region and the hydrophilic area was deduced from this trend. This study demonstrated the different size dependency of the chemical surface defects for sliding behavior between the critical moment at which a droplet slides down and the period when a droplet is sliding.     

Droplet compression and relaxation by a superhydrophobic surface: contact angle hysteresis

In this article, the contact angle hysteresis (CAH) of acrylic glass is experimentally and theoretically studied through the compression-relaxation process of droplets by using a superhydrophobic surface with negligible CAH effect. In contrast to the existing technique in which the volume of the droplet changes during the measurement of CAH, this procedure is carried out at a constant volume of the droplet. By observing the base diameter (BD) and the contact angle (CA) of the droplet during the compression-relaxation process, the wetting behavior of the droplet can be divided into two regimes, the contact line withdrawal and the contact line pinning regimes, depending on the gap thickness (H) at the end of the compression process. During the compression process, both regimes possess similar droplet behavior; the contact line will move outward and the BD will expand while the CA remains at the advancing angle. During the relaxation process, the two regimes are significantly different. In the contact line withdrawal regime, the contact line will withdraw with the CA remaining at the receding angle. In the contact line pinning regime, however, the contact line will be pinned at the final position and the CA will decline to a certain value higher than the receding angle. Furthermore, the advancing pinning behavior can also be realized through a successive compression-relaxation process. On the basis of the liquid-induced defects model, Surface Evolver simulations are performed to reproduce the behavior of the droplet during the compression-relaxation process; both contact line withdrawal and pinning regimes can also be identified. The results of the experiment and simulation agree with each other very well.     

Contact angle hysteresis in multiphase systems

Contact angle (CA) hysteresis is the difference between the maximum (advancing) and minimum (receding) water CA. Hysteresis is caused by adhesion hysteresis in the solid–water contact area (2D effect) and by pinning of the solid–water–air triple line due to the surface roughness (1D effect). In this work, we show that CA hysteresis is present also in more complex systems, such as an organic liquid (oil) in contact with a solid immersed in water. In order to decouple the 1D and 2D effects, we study CA hysteresis in solid–water–air (droplet), solid–air–water (bubble), solid–water–oil, and solid–water–air–oil systems involving rough and microstructured surfaces. The comparative analysis of these systems allows decoupling the 1D and 2D effects as well as hydrogen bonding and entropic forces (water–air tension) and dispersion forces (oil–air tension).     

Sonic wave separation of invertase from a dilute solution to generated droplets

It has previously been shown that a droplet fractionation process, simulated by shaking a separatory funnel containing a dilute protein solution, can generate droplets richer in protein than present in the original dilute solution. In this article, we describe an alternative method that can increase the amount of protein transferred to the droplets. The new metho uses ultrasonic waves, enhanced by a bubble gas stream to create the droplets. The amount of protein in these droplets increases by about 50%. In this method, the top layer of the dilute protein solution (of the solution-air interface) becomes enriched in protein when air is bubbled into the solution. This concentrating procedure is called bubble fractionation. Once the protein has passed through the initial buildup, this enriched protein layer is transferred into droplets with the aid of a vacuum above the solution at the same time that ultrasonic waves are introduced. The droplets are then carried over to a condenser and coalesced. We found that this new method provides an easier way to remove the protein-enriched top layer of the dilute solution and generates more droplet within a shorter period than the separatory funnel droplet generation method. The added air creates the bubbles and carries the droplets, and the vacuum helps remove the effluent airstream from the condenser. The maximum partition coefficient, the ratio of the protein concentration in the droplets to that in the residual solution (approx 8.5), occurred at pH 5.0.     

Directing droplets using microstructured surfaces

Systematic variation of microscale structures has been employed to create a rough superhydrophobic surface with a contact angle gradient. Droplets are propelled down these gradients, overcoming contact angle hysteresis using energy supplied by mechanical vibration. The rough hydrophobic surfaces have been designed to maintain air traps beneath the droplet by stabilizing its Fakir state. Dimensions and spacing of the microfabricated pillars in silicon control the solid-liquid contact area and are varied to create a gradient in the apparent contact angle. This work introduces the solid-liquid contact area fraction as a new control variable in any scheme of manipulating droplets, presenting theory, fabricated structures, and experimental results that validate the approach.     

Dynamics of water droplets detached from porous surfaces of relevance to PEM fuel cells

The detachment of liquid droplets from porous material surfaces used with proton exchange membrane (PEM) fuel cells under the influence of a cross-flowing air is investigated computationally and experimentally. CCD images taken on a purpose-built transparent fuel cell have revealed that the water produced within the PEM is forming droplets on the surface of the gas-diffusion layer. These droplets are swept away if the velocity of the flowing air is above a critical value for a given droplet size. Static and dynamic contact angle measurements for three different carbon gas-diffusion layer materials obtained inside a transparent air-channel test model have been used as input to the numerical model; the latter is based on a Navier–Stokes equations flow solver incorporating the volume of fluid (VOF) two-phase flow methodology. Variable contact angle values around the gas–liquid–solid contact-line as well as their dynamic change during the droplet shape deformation process, have allowed estimation of the adhesion force between the liquid droplet and the solid surface and successful prediction of the separation line at which droplets loose their contact from the solid surface under the influence of the air stream flowing around them. Parametric studies highlight the relevant importance of various factors affecting the detachment of the liquid droplets from the solid surface.     

Aeration of emulsions by whipping

During aeration of food emulsions such as dairy cream and ice cream, small gas bubbles are introduced, which are often stabilized by a layer of adsorbed emulsion droplets. It is shown that the maximum achievable volume of gas bubbles that can be incorporated by whipping depends on the effectiveness of the introduction of gas during the first stage of whipping and is furthermore limited by packing constraints. The main factors relevant for the latter limitation are the thickness of the coating of emulsion droplets at the bubble surface, the ratio between the droplet and bubble radii, and the fat content of the emulsion. It is hypothesized that, during whipping, a dynamic process of bubble break-up and coalescence adjusts the average bubble size and the volume of gas incorporated in the foam to the constraint of close packing of the bubbles. The consequences of this mechanism for whipping of emulsions are discussed.     

Nanoparticle flotation collectors: mechanisms behind a new technology

This is the first report describing a new technology where hydrophobic nanoparticles adsorb onto much larger, hydrophilic mineral particle surfaces to facilitate attachment to air bubbles in flotation. The adsorption of 46 nm cationic polystyrene nanoparticles onto 43 μm diameter glass beads, a mineral model, facilitates virtually complete removal of the beads by flotation. As little as 5% coverage of the bead surfaces with nanoparticles promotes high flotation efficiencies. The maximum force required to pull a glass bead from an air bubble interface into the aqueous phase was measured by micromechanics. The pull-off force was 1.9 μN for glass beads coated with nanoparticles, compared to 0.0086 μN for clean beads. The pull-off forces were modeled using Scheludko's classical expression. We propose that the bubble/bead contact area may not be dry (completely dewetted). Instead, for hydrophobic nanoparticles sitting on a hydrophilic surface, it is possible that only the nanoparticles penetrate the air/water interface to form a three-phase contact line. We present a new model for pull-off forces for such a wet contact patch between the bead and the air bubble. Contact angle measurements of both nanoparticle coated glass and smooth films from dissolved nanoparticles were performed to support the modeling.     

Hysteresis controlled water droplet splitting on superhydrophobic paper

Fabrication of surfaces with heterogeneous contact angle hysteresis enables extraction of droplet samples from bulk liquid volumes. These surfaces are created by printing high hysteresis wax islands onto low hysteresis superhydrophobic paper. The volume of the sampled droplets depends on the hysteresis of the printed islands, which can be controlled through both physical and chemical means. Physically, hysteresis is modified through the addition of surface roughness. Chemical hysteresis is tuned by changing the active chemical groups present on the wax surface. The observed control of the volume of sampled droplets, which is necessary for quantitative biochemical or chemical assays, extends to scenarios in which multiple droplet samples are extracted simultaneously from a single bulk droplet. Demonstration of the capacity of this technique to perform colorimetric glucose immunoassays is described. The ability to obtain well-defined microliter sample volumes and to extract several samples simultaneously from the same source enables the development of two-dimensional paper-based microfluidic devices for biomedical testing.     

Colloid probe AFM investigation of the influence of cross-linking on the interaction behavior and nano-rheology of colloidal droplets

The repulsive forces between a glass sphere and immobilized colloidal droplets of poly(dimethylsiloxane) (PDMS) (with various levels of internal cross-linking) have been determined in aqueous solution using colloid probe atomic force microscopy. On initial surface approach, droplet deformation is negligible and interaction forces resemble those expected for electrical double layer interaction of rigid spheres. Upon further approach, droplet flattening results in forces that deviate below rigid body electrical double layer interaction. The extent of droplet deformation has been determined in terms of the deviation from hard-sphere interaction. Droplet deformability is strongly dependent on the droplet cross-linking level and hence controlled by some combination of the bulk rheological and interfacial properties of the droplets. Droplet nano-rheology has been determined from the extent of force curve hysteresis. For liquidlike droplets, with low levels of cross-linking, no force curve hysteresis is observed and the elastic deformation may be described by a single spring constant, which is controlled by the interfacial properties. For highly cross-linked droplets, the extent of deformation is controlled by the droplet's bulk rheology rather than the interfacial properties. Upon retraction of the surfaces, force curve hysteresis is observed and is due to the viscoelastic response of the PDMS. The extent of hysteresis is dependent on the rate of approach/retraction and the loading force and has been theoretically analyzed to determine nano-rheological parameters that describe droplet relaxation processes. Elastic moduli and relaxation times of the PDMS droplets vary over several orders of magnitude as a function of cross-linking.     

Spreading of triple line and dynamics of bubble growth inside nanoparticle dispersions on top of a substrate plate

This work investigates the feasibility of engineering surface wettability by using different nanoparticles. As an illustration, detailed formation of gas bubbles on top of a stainless steel substrate plate in a quiescent pool of aqueous gold and alumina nanofluids is studied. The presence of nanoparticles is shown to be able to modify the dynamics of triple line and bubble growth significantly. An early pinning of the bubble triple line is observed and a larger bubble contact angle is found for bubbles growing in a gold nanofluid, whereas an opposite phenomenon is observed for bubbles growing in an alumina nanofluid compared to those of pure water. Other bubble parameters such as departure volume, bubble frequency, and waiting time of bubble formation are also affected by the presence of nanoparticles. The variation of solid surface tensions due to the existence of nanoparticles and the resultant force at the triple line should be responsible for such differences. Such results illustrate the big potential of nanoparticle in engineering surface wettability of a solid-liquid-gas system.     

Size-selective sliding of sessile drops on a slightly inclined plane using low-frequency AC electrowetting

When placed on an inclined solid plane, drops often stick to the solid surface due to pinning forces caused by contact angle hysteresis. When the drop size or the plane's incline angle is small, the drop is difficult to slide due to a decrease in gravitational force. Here we demonstrate that small drops (0.4-9 μL) on a slightly inclined plane (~12°, Teflon and parylene-C surface) can be mobilized through patterned electrodes by applying low-frequency ac electrowetting under 400 Hz (110-180 V(rms)), which has a mechanism different from that of the high-frequency ac method that induces sliding by reducing contact angle hysteresis. We attribute the sliding motion of our method to a combination of contact angle hysteresis and interfacial oscillation driven by ac electrowetting instead of the minimization of contact angle hysteresis at a high frequency. We investigated the effects of ac frequency on the sliding motion and terminal sliding of drops; the terminal sliding velocity is greatest at resonance frequency. Varying the electrowetting number (0.21-0.56) at a fixed frequency (40 Hz) for 5 μL drops, we found an empirical relationship between the electrowetting number and the terminal sliding velocity. Using the relationship between the drop size and ac frequency, we can selectively slide drops of a specific size or merge two drops along an inclined plane. This simple method will help with constructing microfluidic platforms with sorting, merging, transporting, and mixing of drops without a programmable control of electrical signals. Also, this method has a potential in heat transfer applications because heat removal capacity can be enhanced significantly through drop oscillation.