Intelligent droplet tracking with correlation filters for digital microfluidics

Tracking the movement of droplets in digital microfluidics is essential to improve its control stability and obtain dynamic information for its applications such as point-of-care testing, environment monitoring and chemical synthesis. Herein, an intelligent, accurate and fast droplet tracking method based on machine vision is developed for applications of digital microfluidics. To continuously recognize the transparent droplets in real-time and avoid the interferes from background patterns or inhomogeneous illumination, we introduced the correlation filter tracker, enabling online learning of the multi-features of the droplets in Fourier domain. Results show the proposed droplet tracking method could accurately locate the droplets. We also demonstrated the capacity of the proposed method for estimation of the droplet velocity as faster as 20 mm/s, and its application in online monitoring the Griess reaction for both colorimetric assay of nitrite and study of reaction kinetics.     

Analysis of the relationship between liquid droplet size and contact angle

The purpose of this paper is to present a consistent theoretical concept that can explain the various physical phenomena associated with the effect of droplet size on contact angle for droplets on solid surfaces, and with the geometry of the liquid/gas/solid contact line in general. Two droplet geometries have been considered: uniformly elongated droplets and axisymmetric droplets. It has been shown that the contact angle for elongated droplets is size-independent and, thus, satisfies the Young equation for constant material and interfacial properties. On the other hand, whereas the contact angle for axisymmetric droplets is size-dependent and does not satisfy the original Young equation, it is shown that this contact angle can still be predicted for any combination of droplet and substrate materials, and a given mass of the droplet. The theoretical work has been combined with the development of numerical schemes of solving the Laplace-Young equation for various droplet geometries. The proposed approach has been applied to different material/substrate combinations and validated against several sets of experimental data. As a result, a method has been developed for predicting the contact angle of both long and axisymmetric sessile droplets of arbitrary sizes for given liquid/solid/gas properties.     

Fusion and sorting of two parallel trains of droplets using a railroad-like channel network and guiding tracks

We propose a robust droplet fusion and sorting method for two parallel trains of droplets that is relatively insensitive to frequency and phase mismatch. Conventional methods of droplet fusion require an extremely precise control of aqueous/oil flows for perfect frequency matching between two trains of droplets. In this work, by combining our previous two methods (i.e., droplet synchronization using railroad-like channels and manipulation of shape-dependent droplets using guiding tracks), we realized an error-free droplet fusion/sorting device for the two parallel trains of droplets. If droplet pairs are synchronized through a railroad-like channel, they are electrically fused and the fused droplets transit to a middle guiding track to flow in a middle channel; otherwise non-synchronized non-fused droplets will be discarded into the side waste channels by flowing through their own guiding tracks. The simple droplet synchronization, fusion, and sorting technology will have widespread application in droplet-based chemical or biological experiments, where two trains of the chemically or biologically treated or pre-formed droplets yield a train of 100% one-to-one fused droplets at the desired outlet channel by sorting all the non-synchronized non-fused droplets into waste outlets.     

Adsorption of protein-coated lipid droplets to mixed biopolymer hydrogel surfaces: role of biopolymer diffusion

The adsorption of charged particles to hydrogel surfaces is important in a number of natural and industrial processes. In this study, the adsorption of cationic lipid droplets to the surfaces of anionic hydrogels was examined. An oil-in-water emulsion containing cationic beta-lactoglobulin-coated lipid droplets was prepared (d32=0.24 microm, zeta=+74 mV, pH 3.0). An anionic hydrogel containing 0.1 wt % beet pectin and 1.5 wt % agar (pH 3.0) was prepared. Emulsions containing different lipid droplet concentrations (0.3-5 wt %) were brought into contact with the hydrogel surfaces for different times (0-24 h). The adsorption of lipid droplets to the hydrogel surfaces could not be explained by a typical adsorption isotherm. We found that the electrical charge on the nonadsorbed lipid droplets became less positive or even became negative in the presence of the hydrogel and that extensive droplet aggregation occurred, which was attributed to the ability of pectin molecules to diffuse through the hydrogels and interact with the lipid droplets. These results may have important consequences for understanding certain industrial and biological processes, as well as for the design of controlled or triggered release systems.     

Methodology for calculating the volume of condensate droplets on topographically modified, microgrooved surfaces

Liquid droplets on micropatterned surfaces consisting of parallel grooves tens of micrometers in width and depth are considered, and a method for calculating the droplet volume on these surfaces is presented. This model, which utilizes the elongated and parallel-sided nature of droplets condensed on these microgrooved surfaces, requires inputs from two droplet images at ? = 0° and ? = 90°--namely, the droplet major axis, minor axis, height, and two contact angles. In this method, a circular cross-sectional area is extruded the length of the droplet where the chord of the extruded circle is fixed by the width of the droplet. The maximum apparent contact angle is assumed to occur along the side of the droplet because of the surface energy barrier to wetting imposed by the grooves--a behavior that was observed experimentally. When applied to water droplets condensed onto a microgrooved aluminum surface, this method was shown to calculate the actual droplet volume to within 10% for 88% of the droplets analyzed. This method is useful for estimating the volume of retained droplets on topographically modified, anisotropic surfaces where both heat and mass transfer occur and the surface microchannels are aligned parallel to gravity to assist in condensate drainage.     

Wetting phenomena on micro-grooved aluminum surfaces and modeling of the critical droplet size

The behavior of water droplets on aluminum surfaces with parallel grooves tens of microns in width and depth is considered, and a mechanistic model is developed for predicting the critical droplet size-droplets at incipient sliding due to gravity. The critical droplet size is nearly 50% smaller on micro-grooved surfaces than on the same surface without micro-grooves. The application of existing models fails to predict this behavior, and a new model based on empiricism is developed. The new model provides reasonable predictions of the critical droplet size for a given inclination angle, advancing contact angle, and maximum contact angle. When the grooves are aligned parallel to gravity, the maximum apparent contact angle does not occur at the advancing front but rather along the side of the droplet because of contact-line pinning. Droplets on these surfaces are elongated and possess a parallel-sided base contour shape. Novel data are provided for droplets in a Wenzel state, a Cassie-Baxter state, and combined state on micro-grooved surfaces, and the ability of the empirical model to handle these variations is explored. These findings may be important to a broad range of engineering applications.     

Charge limits on droplets during evaporation

We have examined charge stability limits of single evaporating microdroplets that were suspended in an electrodynamic balance. A high precision light scattering technique based on optical resonances was used to determine the size and the size change of a droplet at a charge instability induced breakup. The charge level and the charge loss at the breakup were obtained from the dc voltages required to balance the droplet prior to and following the breakup. The results on droplets of diethyl phthalate (DEP), diethylene glycol (DEG), triethylene glycol (TEG), and hexadecane show that breakups due to the charge instability occur at the Rayleigh charge limit. The observed charge losses during breakups range from about 15.3% for hexadecane droplets to about 41.1% for TEG droplets. Hexadecane droplets lose about 1.5% of their mass, while DEP droplets, about 2.3%. Within the detectable limit of 0.03%, no mass losses were observed during breakups of DEG and TEG droplets. The observation of extremely low mass losses that accompany high charge losses from DEG and TEG droplets suggests that the process of breakups of DEG and TEG droplets is distinct from that of DEP and hexadecane droplets. An analysis of the results indicates that breakups of DEP and hexadecane droplets result in the formation of a few large progeny droplets, while TEG and DEG droplets produce thousands of fine progeny droplets.     

Cross-scale electric manipulations of cells and droplets by frequency-modulated dielectrophoresis and electrowetting

Two important electric forces, dielectrophoresis (DEP) and electrowetting-on-dielectric (EWOD), are demonstrated by dielectric-coated electrodes on a single chip to manipulate objects on different scales, which results in a dielectrophoretic concentrator in an EWOD-actuated droplet. By applying appropriate electric signals with different frequencies on identical electrodes, EWOD and DEP can be selectively generated on the proposed chip. At low frequencies, the applied voltage is consumed mostly in the dielectric layer and causes EWOD to pump liquid droplets on the millimetre scale. However, high frequency signals establish electric fields in the liquid and generate DEP forces to actuate cells or particles on the micrometre scale inside the droplet. For better performance of EWOD and DEP, square and strip electrodes are designed, respectively. Mammalian cells (Neuro-2a) and polystyrene beads are successfully actuated by a 2 MHz signal in a droplet by positive DEP and negative DEP, respectively. Droplet splitting is achieved by EWOD with a 1 kHz signal after moving cells or beads to one side of the droplet. Cell concentration, measured by a cell count chamber before and after experiments, increases 1.6 times from 8.6 x 10(5) cells ml(-1) to 1.4 x 10(6) cells ml(-1) with a single cycle of positive DEP attraction. By comparing the cutoff frequency of the voltage drop in the dielectric layer and the cross-over frequency of Re(fCM) of the suspended particles, we can estimate the frequency-modulated behaviors between EWOD, positive DEP, and negative DEP. A proposed weighted Re(fCM) facilitates analysis of the DEP phenomenon on dielectric-coated electrodes.     

Liquid crystal orientation in elliptic droplets in nematic emulsions

Elliptic droplets of nematic liquid crystal dispersed in a fluid organic monomer were obtained by phase separation from an isotropic mixture consisting of an organic monomer and a nematic liquid crystal contained in a poly(ethylene terephthalate) cell with inner surfaces treated with rubbed polyimide. The elliptic shape is a consequence of the constraint upon droplet growth along the direction perpendicular to the cell surfaces owing to the small thickness. Then, the resulting droplets will have a contact area with the inner surfaces of the cell treated with polyimide, which will impart a planar orientation on the liquid crystal in the droplet. By means of an optical microscope, using a simple pin hole of 5 μm, we have selected single droplets for a series of samples having different contact areas. By polarized infrared spectroscopy we have also studied the liquid crystal orientation in selected areas of the droplets. We then report the dependence of the order parameter of the liquid crystal on different contact areas with the alignment surface of the cell. The good degree of planar alignment of the liquid crystal in the elliptic droplets allows the use of such a technique for realizing electro-optical films operating in the reverse mode. We report the electro-optical transmission of reverse mode films with different sizes of elliptic droplet.     

Viscosity based droplet size controlling in negative pressure driven droplets generator for large‐scale particle synthesis

The poor control and regulation of droplets limit the applications of negative pressure driven droplet generator (NPDDG). Here, we present a simple method to control droplet size in NPDDG via varying the oil viscosity. Depending on the infinite intersolubility of high viscous mineral oil and low viscous hexadecane, we obtain a series of oils with kinematic viscosities linearly varied from 4.2 to 194.6 mm²/s. By using these oils as continuous phases, monodisperse droplets are fabricated with controllable size in NPDDG. This viscosity‐based droplet regulation method is effective, reliable, and compatible with scale‐up processes. Compared with droplet generator driven by positive pressure, the presented method can fabricate hydrogel particles massively, without complicated multilayer chip structure and complex fluid controlling, which may extend the potential of NPDDG in droplets based high‐throughput assay or large‐scale materials synthesis.     

Sliding variability of droplets on a hydrophobic incline due to surface entrained air bubbles

The ability of a liquid droplet to move on an incline has important ramifications in discrete volume fluidic devices. By taking advantage of the spontaneous and copious formation of visible air bubbles within water droplets on a polytetrafluoroethylene (PTFE) surface, we uncovered a direct correlation between their presence and the ability of droplets to slide down an incline. We forward two possible mechanisms to account for this behavior. The first is attributed to the air bubbles creating regions where additional solid-liquid-vapor phase interfaces are present; wherein due to the buoyancy force acting upwards, the orientation of the contact angles of each bubble (which should also be in hysteresis but in the opposite direction of the hysteresis at the droplet rim contact lines) dictate that the net force of the bubbles in the droplet act down an incline. We show here that this mechanism cannot fully account for the bubble enhanced sliding behavior. The second mechanism is based on the occurrence of the droplet front advancing first, causing the droplet to elongate and thus allowing the receding contact line to partially sweep inwards over the bubbles. This causes a series of point-wise disruptions on the contact line that permits the droplet to slide down more readily. The relatively short time of ～180s during which these micron sized bubbles decrease in size indicates a possibility of this mechanism contributing to a transient means to reduce the retention force of droplets that reside on hydrophobic surfaces.     

Contact-angle hysteresis on super-hydrophobic surfaces

The relationship between perturbations to contact angles on a rough or textured surface and the super-hydrophobic enhancement of the equilibrium contact angle is discussed theoretically. Two models are considered. In the first (Wenzel) case, the super-hydrophobic surface has a very high contact angle and the droplet completely contacts the surface upon which it rests. In the second (Cassie-Baxter) case, the super-hydrophobic surface has a very high contact angle, but the droplet bridges across surface protrusions. The theoretical treatment emphasizes the concept of contact-angle amplification or attenuation and distinguishes between the increases in contact angles due to roughening or texturing surfaces and perturbations to the resulting contact angles. The theory is applied to predicting contact-angle hysteresis on rough surfaces from the hysteresis observable on smooth surfaces and is therefore relevant to predicting roll-off angles for droplets on tilted surfaces. The theory quantitatively predicts a "sticky" surface for Wenzel-type surfaces and a "slippy" surface for Cassie-Baxter-type surfaces.     

Liquid crystal orientation in elliptic droplets in nematic emulsions

Elliptic droplets of nematic liquid crystal dispersed in a fluid organic monomer were obtained by phase separation from an isotropic mixture consisting of an organic monomer and a nematic liquid crystal contained in a poly(ethylene terephthalate) cell with inner surfaces treated with rubbed polyimide. The elliptic shape is a consequence of the constraint upon droplet growth along the direction perpendicular to the cell surfaces owing to the small thickness. Then, the resulting droplets will have a contact area with the inner surfaces of the cell treated with polyimide, which will impart a planar orientation on the liquid crystal in the droplet. By means of an optical microscope, using a simple pin hole of 5 μ m, we have selected single droplets for a series of samples having different contact areas. By polarized infrared spectroscopy we have also studied the liquid crystal orientation in selected areas of the droplets. We then report the dependence of the order parameter of the liquid crystal on different contact areas with the alignment surface of the cell. The good degree of planar alignment of the liquid crystal in the elliptic droplets allows the use of such a technique for realizing electro-optical films operating in the reverse mode. We report the electro-optical transmission of reverse mode films with different sizes of elliptic droplet.     

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.     

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.     

Induced detachment of coalescing droplets on superhydrophobic surfaces

Coalescence of a falling droplet with a stationary sessile droplet on a superhydrophobic surface is investigated by a combined experimental and numerical study. In the experiments, the droplet diameter, the impact velocity, and the distance between the impacting droplets were controlled. The evolution of surface shape during the coalescence of two droplets on the superhydrophobic surface is captured using high speed imaging and compared with numerical results. A two-phase volume of fluid (VOF) method is used to determine the dynamics of droplet coalescence, shape evaluation, and contact line movement. The spread length of two coalesced droplets along their original center is also predicted by the model and compared well with the experimental results. The effect of different parameters such as impact velocity, center to center distance, and droplet size on contact time and restitution coefficient are studied and compared to the experimental results. Finally, the wetting and the self-cleaning properties of superhydrophobic surfaces have been investigated. It has been found that impinging water drops with very small amount of kinetic impact energy were able to thoroughly clean these surfaces.     

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.     

Simulation of Sessile Water-Droplet Evaporation on Superhydrophobic Polymer Surfaces

Evaporation of sessile water-droplets on superhydrophobic polymer surfaces has been simulated in recent research. Models based on the ellipsoidal cap geometry and spherical cap geometry, which were originally put forward to describe the profile of a droplet during its evaporation process on a solid surface with a contact angle <90±, are developed to reveal the issue with an initial contact angles larger than 150±. To verify the validity of the model, experiments on superhydrophobic polycarbonate, and °uorinated polyurethane and poly (methyl methacrylate) blend surfaces were carried out. It was observed that the change trends of contact angle and height of the droplet against evaporation time on the superhydrophobic surfaces experimentally are consistent with the simulated results by ellipsoidal and spherical cap models. The ellipsoidal cap model shows the better fits due to the shape distortions of droplets.     

Behavior of oil droplets on an electrified solid metal surface immersed in ionic surfactant solutions

The present study investigates the change in the shape of oil droplets immersed in an ionic surfactant solution when the droplets are in contact with metal surfaces to which an electrical potential is applied. The three-phase system of aqueous solution-oil-steel was subjected to low-voltage electric potentials, which resulted in sometimes dramatic changes in droplet shape and wetting. This electric potential was applied to the conductive steel surface directly, and the counter electrode was immersed in the solution. Changes in both the shape and wetting extent of hexadecane and phenylmethyl polysiloxane were observed for voltages between +/-3.0 V in both sodium dodecyl sulfate and cetyl trimethylammonium bromide solutions. The droplets' behavior was opposite to what would be expected for traditional electrowetting. In one instance, hexadecane droplets in sodium dodecyl sulfate solutions with a voltage of -3.0 V, a rapid and repeating droplet elongation and detachment was observed. Additionally, the impact of the observed phenomena on electrowetting enhanced ultrasonication is presented to demonstrate the potential improvements in industrial ultrasonic cleaning processes. The observations lead to the possibility of employing simple electrowetting techniques in the removal of oil from metal surfaces in a manner that could greatly improve the environmental and economic performance of aqueous cleaning techniques.     

Droplet evaporation study applied to DNA chip manufacturing

DNA chips are potentially powerful technologies for genotyping and gene expression profiling that rely on comparative analyses of up to thousands of "spots of analysis" on a glass support. The spot quality throughout the support influences spot-to-spot variations within an array and the repeatability of data across experiments. For glass slide DNA microarrays, droplets of DNA solution are deposited on functionalized glass slides and left to react through complete evaporation of the droplet. On hydrophobic flat surfaces, different modes of droplet evaporation can be attained. Under atmospheric pressure, water droplets tend to evaporate under two main regimes. Initially, the droplet flattens with a constant contact area, and then the droplet shrinks at a constant contact angle. As a result, the diameter and morphology of thousands of spots on microarrays are not uniform. This leads to poor and unreliable data processing results. In this work, we report the evaporation of an aqueous solution under a constant contact area mode. Evaporation under reduced pressure and the effect of reagent additives to the solution have been investigated. Video microscopy and digital image analysis techniques were applied to monitor the evaporation of the droplets. A mixture of surfactants was developed to maintain a constant area regime during evaporation and to form homogeneous spots. The control of some physicochemical properties (wetting, evaporation rate) of the droplet allows the formation of well-controlled spots compatible with DNA grafting. The influence of surfactant molecules on the mechanisms of evaporation is also discussed.