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.     

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.     

A numerical study on viscoelastic droplet migration on a solid substrate due to wettability gradient

This study investigates the viscoelastic effects on droplet migration induced by a wettability gradient on a rigid substrate by a numerical simulation based on OpenFOAM with the volume‐of‐fluid method. The droplets are set with different rheological properties to investigate the effect of the elastic parameters. The Oldroyd‐B model was employed. Quantitative differences in the migration and deformation between Newtonian and viscoelastic droplets were investigated by changing the degree of elasticity. The droplet migration shows conspicuously higher mobility for high elasticity, especially during the accelerating period. Moreover, the displacement and velocity increased with the decrease of a viscoelasticity parameter, and the velocity enhancement was regulated by the elastic instability shown at a high Weissenberg number. In addition, the velocity of the droplet changes more significantly over the range of contact angles of 130° to 60° compared to other wettability‐gradient surfaces.     

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.     

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.     

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.     

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.     

Experimental investigation of droplet acceleration and collision in the gas phase in a microchannel

We developed a novel microfluidic system, termed a micro-droplet collider, by utilizing the spatial-temporal localized liquid energy to realize chemical processes, which achieved rapid mixing between droplets having a large volume ratio by collision. In this paper, in order to clarify the characteristics of the micro-droplet collider, dynamics of droplet acceleration, stationary motion and collision in the gas phase in a microchannel were experimentally investigated with visualized images using a microscope equipped with a high-speed camera. The maximum velocity of 450 mm s(-1) and acceleration of 1500 m s(-2) of a 1.6 nL water droplet were achieved at an air pressure of 100 kPa. Measurement results of dynamic contact angles of droplets indicated that wettability of the surface played an important role in the stability of droplet acceleration and collision. We found that the bullet droplet penetrated into the target droplet at collision, which differed from bulk scale. The deformation of the droplet was strongly suppressed by the channel structure, thus stable collision and efficient utilization of the droplet energy were possible. These results are useful for estimating the localized energy, for improving the system in order to realize extreme performance, and for extending the applications of microfluidic devices.     

Observation and modelling of barrel droplets on vertical fibres subjected to gravitational and drag forces

Extensive experimental investigation of the wetting processes of fibre/liquid systems during air filtration (when drag and gravitational forces are acting) has shown many important features, including droplet extension, oscillatory motion, and detachment or flow of drops from fibres as airflow velocity increases. A detailed experimental study of the aforementioned processes was conducted using glass filter fibres and H(2)O aerosol, which coalesce on the fibre to form barrel droplets with small contact angles. The droplets were predominantly observed in the Reynolds transition (or unsteady laminar) flow region. The droplet oscillation appears to be induced by the onset of vortexes in the flow field around the droplet as the increasing droplet size increases the Reynolds number. Flow in this region is usually modelled using the classical two-dimensional Karman vortex street, and there exist no 3D equivalents. Therefore to model such oscillation it was necessary to create a new conceptual model to account for the forces both inducing and inhibiting such oscillation. The agreement between the model and experimental results is acceptable for both the radial and transverse oscillations.     

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.     

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.     

Evaporation of sessile droplets of dilute aqueous solutions containing sodium n-alkylates from polymer surfaces: influences of alkyl length and concentration of solute

The evaporation of sessile droplets placed on polymer surfaces was studied by microscopic observation of the changes in shape of aqueous solution droplets in which the alkyl lengths and the initial concentrations of sodium n-alkylates were varied. Although the initial contact angles of the droplets were not significantly different, the evaporation process varied significantly with the alkyl length of the sodium n-alkylate employed. For the sodium dodecanoate (C 12), showing the highest surface activity, the concentration was found to have a significant effect on the evaporation process of the droplets. In the evaporation of water droplets, variations in the three distinct stages were caused by the different concentration of solutes distributed near or at the air/water interface. It is revealed that the concentration of droplet solute near the air/water interface requires not only solvent evaporation but also some affinity of the solute for the interface. The initial C 12 concentration-dependence of the evaporation of C 12 solution droplets is discussed with particular emphasis on the sudden spreading or sudden contraction of the contact area near the end of evaporation. It is suggested that the cluster formation by C 12 molecules at the air/liquid interface during the evaporation causes Marangoni instability in an evaporating droplet, and the clusters are expected to move dynamically, depending on the droplet concentration of C 12, from the droplet center to the contact line and vice versa, showing Marangoni flow along the air/water interface.     

Several surfaces with special wettability: Influence on spreading and motion of W/O emulsion droplets

Physical and chemical modifications were made on the surface of the aluminum sheet to change the surface properties and superhydrophobic–hydrophilic wettability gradient surface was made on the perspex surface by using microstructure-pattering technique and self-assembled-monolayer method. By using high-speed video camera system and optical tensiometer, this paper discusses the influence of special surfaces with different wettability on spreading and motion of water, oil, and W/O emulsion droplets both experimentally and theoretically. In addition, the paper also discusses the influence of the superhydrophobic–hydrophilic wettability gradient on fluidity of W/O emulsion droplets and the coalescence process of droplets. The results showed that the contact angle of W/O emulsion droplets on the modified surfaces was related to the water and oil distribution at the three-phase line. On the wettability gradient surface, the droplet moved spontaneously when the droplet was located at the junction of the gradient. A quasi-steady theoretical model was used to analyze the driving and resistant forces acting on a droplet to improve the understanding of the self-transport behavior of the droplets.     

Heterogeneous uptake of 8-2 fluorotelomer alcohol on liquid water and 1-octanol droplets

The heterogeneous uptake of the 8-2 fluorotelomer alcohol, F(CF2)8CH2CH2OH, on liquid water surfaces over the temperature range 256-273 K and on 1-octanol surfaces over the temperature range 264-295 K has been investigated with a droplet train flow reactor. The uptake coefficient on water droplets is zero within the error of the measurement (+/-0.01) and is independent of droplet temperature. In contrast, significant uptake onto 1-octanol is observed. Measured uptake coefficients for 1-octanol showed a negative temperature dependence, varying from 0.034 +/- 0.005 (1sigma) at 295 K to 0.103 +/- 0.009 at 264 K. The measured uptake coefficients on 1-octanol were independent of gas-liquid contact time, for typical contact times varying between 3 and 15 ms, and independent of the 8-2 fluorotelomer alcohol gas-phase concentration, indicating that the uptake coefficients are equivalent to mass accommodation coefficients. The uptake coefficients on 1-octanol were also independent of relative humidity. These results show that the uptake of FTOHs on or into the aqueous component of cloud/fog droplets or aqueous aerosol particles is not likely to be an important atmospheric sink for these compounds. In these experiments, 1-octanol was used as a model compound for organic-containing atmospheric particles. The larger uptake coefficient measured for 1-octanol surfaces indicates that FTOH partitioning to organic-containing cloud/fog droplets and aerosol particles may be an atmospheric loss mechanism.     

Behavior of evaporating droplets at nonsoluble and soluble surfaces: Modeling with molecular resolution

Liquid droplets in equilibrium with vapor are simulated at solidlike surfaces using the cooperative motion algorithm (CMA). These droplets behave like real droplets, i.e., the densities of the coexistent liquid and vapor phases obey empirical relations such as rho l - rho v proportional, variant (1 - T/Tc)(1/3). Droplet evaporation was studied under various interaction conditions, i.e., nonsoluble and soluble substrates. In the last case, substrate particles migrate toward the liquid-vapor interface to minimize the droplet surface energy. This leads to the formation of a microwell surrounded by a ringlike deposit on the substrate surface. It is shown that the ring formation in the first stages of evaporation results in pinning of the droplet contact area.     

Droplet-based microfluidics with nonaqueous solvents and solutions

In droplet-based ("digital") microfluidics, liquid droplets in contact with dielectric surfaces are created, moved, merged and mixed by applying AC or DC potentials across electrodes patterned beneath the dielectric. We show for the first time that it is possible to manipulate droplets of organic solvents, ionic liquids, and aqueous surfactant solutions in air by these mechanisms using only modest voltages (<100 V) and frequencies (<10 kHz). The feasibility of moving any liquid can be predicted empirically from its frequency-dependent complex permittivity, epsilon*. The threshold for droplet actuation in air with our two-plate device configuration is /epsilon*/>8x10(-11). The mechanistic implications of these results are discussed, along with the greatly expanded range of applications for digital microfluidics that these results suggest are now feasible.     

Evaporation of two solution droplets and a droplet located near a flat liquid surface

The mutual influence of two moderate-sized droplets of a dilute nonvolatile substance solution on the processes of their evaporation or condensation is theoretically analyzed under the assumption of a uniform concentration distribution inside the droplets. The conditions for the applicability of this approach are revealed. The evaporation or condensation of a droplet near a flat liquid surface is considered as a limiting case. The fluxes of water molecules to and from the surface of aqueous glycerol solution droplets occurring in air are numerically estimated depending on the droplet radii, distances between their surfaces, and air humidity. Analogous estimates are obtained for an aqueous glycerol solution droplet growing near a flat water surface.     

Contact angle dependence of the resonant frequency of sessile water droplets

The resonant vibrations of small (microliter) sessile water droplets supported on solid substrates were monitored using a simple optical detection technique. A small puff of air was used to apply an impulse to the droplets and their time dependent oscillations were monitored by passing a laser beam through the droplet and measuring the variations of the intensity of the scattered light using a simple photodiode arrangement. The resulting time dependent intensity changes were then Fourier transformed to obtain information about the vibrational frequencies of the droplets. The resonant frequencies of droplets with masses in the range 0.005-0.03 g were obtained on surfaces with water contact angles ranging from 12 ± 4° to 160 ± 5°. The contact angle dependence of the resonant frequency of the droplets was found to be in good agreement with a simple theory which considers standing wave states along the meridian profile length of the droplets.     

Observation and modelling of clamshell droplets on vertical fibres subjected to gravitational and drag forces

Extensive experimental investigation of the wetting processes of fibre-liquid systems during air filtration (when drag and gravitational forces are acting) has shown many important features, including droplet extension, oscillatory motion, and detachment of drops from fibres as airflow velocity increases, and also movement or flow of droplets along fibres. A detailed experimental study of the processes was conducted using stainless steel filter fibres and H2O aerosol, which coalesce on the fibre to form clamshell droplets. The droplets were predominantly observed in the Reynolds transition flow region, since this is the region where most of the above features occur. The droplet oscillation is believed to be induced by the onset of the transition from laminar to turbulent flow as the increasing droplet size increases Reynolds number for the flow around the droplet. Two-dimensional flow in this region is usually modelled using the classical Karman vortex street, however there exist no 3D equivalents. Therefore to model such oscillation it was necessary to create a new conceptual model to account for the forces both inducing and preventing such oscillation. The agreement between the model and experimental results is very good for both the radial and transverse oscillations.