Droplet Profiles Research Articles

Development of aperture total internal reflection (A-TIR) for micro droplets and fingerprint patterns characterization

This study proposes and demonstrates a new approach using aperture total internal reflection (A-TIR) by means an aperture in front of a detector to characterize micro droplet and fingerprint patterns on different surface coatings. A microcontact printing using PDMS stamp is employed to prepare micro droplet patterns on differently coated glass surfaces with synthetic sebum liquids. An aperture in front of a detector in TIR configuration generates unique reflectance curve by blocking aberrated beams from the top curved profiles of droplets and liquid–air interfaces due to the quantum phenomenon of Goos–Hänchen (G–H) shift. The Fresnel equation is modified with a modeling to consider geometric features of droplets and G–H shift. The measurement by A-TIR is compared with the simulation based on the modified Fresnel equation to show a good agreement. A-TIR reflectance curves show that the area fraction covered by droplets is linearly proportional to the measured reflectance and the oleophobicities of the coating surfaces. For practical application, A-TIR is employed to characterize human fingerprint patterns consisting of hundreds of micro droplets to show a good agreement between the measurement and the simulation. G–H shift is experimentally verified to cause the ray aberration at the liquid–air interface of micro droplets in fingerprint patterns, resulting in the reflectance decrease and the curved profile near the critical angles. This result can be used to characterize uneven surface features for surface coating condition monitoring.

Effect of time-varying magnetic field on metal droplet profiles

A nonmagnetic metal droplet with dynamic interfaces under a time-varying magnetic field was considered. Considering that the thermal effect of the magnetic field and the droplet evaporation were disregarded, we obtained the magnetically augmented Young–Laplace equation theoretically according to the normal stress balance principles. The droplet contact angle was further determined according to the droplet volume conservation. According to the curvature and contact angle, the droplet profile was mathematically determined. Results showed that a downward magnetic force caused droplet contraction and an upward force caused expansion. The increase in surface tension hindered the droplet spreading without affecting the change trend of droplet shape parameters. The increase in angular frequency (ω) decreased the variation amplitude of the droplet curvature and contact angle, and the increase in damping factor (τ) slowed down the decay of the droplet curvature and contact angle.

Fabrication of Wettability Mesh with Quasi-Rectangular-Restraining Capacity to Water.

A water droplet placed on a surface is usually round owing to surface tension. Restraining a droplet to a rectangle shape has been rarely reported. Herein, we fabricated three meshes with diverse wettability including ordinary mesh, superhydropilic mesh, and quasi-rectangular-restraining mesh. The profiles of water droplets on these three meshes were entirely different from the top view, especially for the quasi-rectangular-restraining mesh, which enables the water droplet on it to achieve the rectangular shape. The surface morphologies and chemical compositions of the meshes were characterized by scanning electron microscopy, energy dispersive spectroscopy, and X-ray diffraction. Moreover, the influences of processing parameters of the quasi-rectangular-restraining mesh on the quasi-rectangular quality of the water droplet on it were investigated to obtain the relatively optimum processing parameters. The dynamic properties of water droplets on the three meshes were compared, and forces acting on the water droplets during the spreading and shrinking processes on the three meshes were qualitatively analyzed. Additionally, we studied the influences of falling height and water volume on the quasi-rectangular quality of the water droplet on the quasi-rectangular-restraining mesh. Water droplets on the quasi-rectangular-restraining mesh demonstrated good stability under vibration and the droplet could maintain the quasi-rectangular quality on the quasi-rectangular-restraining mesh for about 7 days, revealing a good durability. Further, the large-scaled fabrication of the quasi-rectangular-restraining mesh was realized.

Sessile droplets shape response to complex body forces

The majority of studies on forced wetting of sessile droplets refers to application of a steadily increasing normal or tangential force or to a specific combination of these forces arising from tilting the substrate. The above constitute well-defined test conditions but are not representative of what is encountered in most industrial applications. To approach realistic industrial conditions and so also expand existing wetting theories, an evaluation of droplet shape deformation under the influence of a complicated evolution of body forces, is performed herein. To this aim, two sets of experiments are carried out in Kerberos device creating force fields by combination of gravitational and centrifugal forces: i) by oscillations of the tilting angle at constant rotation speed and ii) by alternating small step-increases of the rotation speed and the tilting angle, one after the other, so as to trail the symmetric side profile (SSP) curve of a droplet. The latter is done in three or six steps following two different paths: increasing first either the rotation speed or the tilting angle. The aim of the experiments is, on one hand, to explore droplet deformation under cycles of increasing/decreasing tangential forces and, on the other hand, to analyze the effect of residual tangential forces on droplet shape. Several features related to the droplet shape evolution are investigated such as contact angles, side and top contour profiles and droplet 3-dimensional shape. The resulting droplet profiles are analyzed using numerical solutions of the Young-Laplace equation. It is found that the 3-dimensional Young Laplace equation can describe very accurately the experimental profiles.

Wetting of pristine and functionalized nanocrystalline cellulose

Molecular dynamic simulations were used to investigate the wetting behavior of nanocrystalline cellulose allomorphs. Three 40ns independent MD simulations using CHARMM force field gave droplet profiles, whose contact angles were obtained with LBADSA plugin for ImageJ. Surface hydrophilicity was related to hydroxyl group availability for hydrogen bonding. Oxidation of C6 hydroxyl groups significantly boosts surface hydrophilicity, and even low levels of modification (~7%) leads to contact angles close to zero degrees. These data can be useful for biotechnological applications.

Quasi-static simulation of droplet morphologies using a smoothed particle hydrodynamics multiphase model

Numerical simulation of the morphology of a droplet deposited on a solid surface requires an efficient description of the three-phase contact line. In this study, a simple method of implementing the contact angle is proposed, combined with a robust smoothed particle hydrodynamics multiphase algorithm (Zhang 2015). The first step of the method is the creation of the virtual liquid–gas interface across the solid surface by means of dummy particles, thus the calculated surface tension near the triple point serves to automatically modulate the dynamic contact line towards the equilibrium state. We simulate the evolution process of initially square liquid lumps on flat and curved surfaces. The predictions of droplet profiles are in good agreement with the analytical solutions provided that the macroscopic contact angle is accurately implemented. Compared to the normal correction method, the present method is straightforward without the need to manually alter the normal vectors. This study presents a robust algorithm capable of capturing the physics of the static wetting. It may hold great potentials in bio-inspired superhydrophobic surfaces, oil displacement, microfluidics, ore floatation, etc.

Comparison of micro- and macro-wettability measurements and evaluation of micro-scale imbibition rates for unconventional reservoirs: Implications for modeling multi-phase flow at the micro-scale

Significant advances have been made in the evaluation of micro- and nano-scale variations of pore structure in low-permeability (unconventional) reservoirs using imaging techniques. In parallel, digital rock physics (DRP) methods have been advanced so that pore structure information extracted from these images may be used, in combination with pore-scale modeling, to predict critical petrophysical rock properties such as porosity and permeability. Recent work using DRP applied to multi-phase flow of unconventional reservoirs has suggested that wettability variations at the micro-scale caused by mineralogical heterogeneity or aging can have a profound effect on simulated capillary pressure and relative permeability curves. However, wettability is typically measured at the macro-scale, with the resulting contact angles used for populating DRP models. Further, fluid imbibition rates are usually measured at the macro-scale to compare, for example, the impact of fracturing fluid additives on oil recovery.This study compares water contact angle measurements made at the micro-scale, using an environmental field emission scanning electron microscope (E-FESEM) combined with innovative procedures for contact-angle extraction, with a conventional macro-scale approach (sessile drop) for low-permeability samples obtained from the Montney Formation in Western Canada. For the first time, quantification of imbibition rates at the micro-scale is demonstrated. Two micro-wettability evaluation procedures developed previously are applied to these samples to evaluate water micro-contact angles: 1) imaging of condensation/evaporation experiments and 2) imaging of injected fluids using a micro-injection system. Micro contact angles were first estimated by extracting sessile droplet profiles (with user-guided software developed in-house) and then fitting a parameterized Young-Laplace equation to the droplet profile. For some of the micro-injection experiments, the geometry of the micro-droplet, as captured with the parameterized Young-Laplace equation, was used to compute the volume of the micro-droplet at different stages of imbibition, which in turn was used to evaluate imbibition rates at this scale. Macro contact angles were evaluated using the parameterized Young-Laplace equation and commercial software.This study suggests that laboratory-derived macro-droplet contact angles cannot be confidently and consistently applied at the micro-scale for use in DRP models for tight heterogeneous formations such as the Montney. Significant errors in simulating fluid displacement processes, fluid saturation distributions, capillary pressure and relative permeability curves using DRP methods will result if micro-scale variations in wettability are not taken into account. Finally, the study demonstrates that fluid imbibition measurements may be performed at the micro-scale, enabling fine-scale rock composition/pore structure controls on fluid imbibition to be explored.

Prediction of Contact Angles and Density Profiles of Sessile Droplets Using Classical Density Functional Theory Based on the PCP-SAFT Equation of State.

This study demonstrates the capability of the density functional theory (DFT) formalism to predict contact angles and density profiles of model fluids and of real substances in good quantitative agreement with molecular simulations and experimental data. The DFT problem is written in cylindrical coordinates, and the solid-fluid interactions are defined as external potentials toward the fluid phase. Monte Carlo (MC) molecular simulations are conducted in order to assess the density profiles resulting from the Helmholtz energy functional used in the DFT formalism. Good quantitative agreement between DFT predictions and MC results for Lennard-Jones and ethane nanodroplets is observed, both for density profiles and for contact angles. That comparison suggests, first, that the Helmholtz energy functional proposed in a previous study [ Sauer , E. ; Gross , J. Ind. Eng. Chem. Res. 56 , 2017 , 4119 - 4135 ] is suitable for three-phase contact lines and, second, that Lagrange multipliers can be used to constrain the number of molecules, similar to a canonical ensemble. Experiments of sessile droplets on solid surfaces are performed to assess whether a real solid with its microscopic roughness can be described through a simple model potential. Comparison of DFT results to experimental data is done for a Teflon surface because Teflon can be regarded as a substrate exhibiting only attractive interactions of van der Waals type. It is shown that the real solid can be described as a perfectly planar solid with effective solvent-to-solid interactions, defined through a single adjustable parameter for the solid. Subsequent predictions for the contact angle of eight solvents, including polar components such as water, are found in very good agreement to experimental data using simple Berthelot-Lorentz combining rules. For the eight investigated solvents, we find mean absolute deviations of 3.77°.

Droplet size distributions in dropwise condensation heat transfer: Consideration of droplet overlapping and multiple re-nucleation

Evolution and distribution of condensate droplets are the most important information in dropwise condensation. For surfaces with larger contact angles, droplet interactions and distributions become more complicated due to their three dimensional profiles. In this study, the effect of droplet overlapping and multiple re-nucleation on droplet size distribution and heat transfer are analyzed quantificationally by numerical simulations. Experimental droplet images obtained by environmental scanning electronic microscope are also presented to support the analyses. The simulated droplet size distributions show that droplet overlapping and multiple re-nucleation can improve the spatial distribution of small droplets for larger contact angle surfaces, and the difference in droplet size distributions decreases as droplet radius is increased. The distributions of larger droplets with radii larger than the critical coalescence size are also affected by the overlapping and multiple re-nucleation effect. The difference between droplet size distributions finally diminish for different contact angles when droplet radius is increased to dozens of microns and the effect of overlapping and multiple re-nucleation become less important in that size range. As contact angle is increasing, surface coverage decreases, while the number density of small droplets is greatly increased, and the overall effect leads to an improved heat transfer performance. The present simulations reveal the effect of droplet overlapping and multiple re-nucleation quantificationally from the perspective of three dimensional droplet profiles, which provide insight into the better understanding of droplet size distributions and extend the dropwise condensation theory.

Experimental study on the droplet formation around pins of different geometry for the design of a compact falling-droplet absorber

Absorber downsizing for the development of compact absorption chillers is a known challenge of this type of refrigerator. Past studies have revealed how a droplet flow regime can increase the interface area and enhance absorption rates, especially during the droplet formation. This study proposes a space-efficient design for an adiabatic absorber based on a bank of solid pins coupled with a droplet flow regime. Manufacturing through 3D printing technique is used to study the effect of different fin shapes during droplet formation. Droplet behavior is firstly studied analytically through a variational approach. Experiments on pure water are then carried out to validate the model and produce design guidelines for a H2O-LiBr absorber. Results show that the analytical model is more accurate in the regions close to the droplet bottom. The rhomboidal geometry with 120° returned the smallest droplet volume without allowing coalescence of more droplets, ensuring the maintenance of droplet flow and a high surface area for mass transfer. Disturbances in the droplet profiles were observed, caused by the pin-droplet interaction. A map has been then created to allow a quick sizing of the absorber and find its main geometrical and operational features.

Cassie-Levitated Droplets for Distortion-Free Low-Energy Solid-Liquid Interactions.

Despite the rapid advent of superomniphobic materials, there is a lack of methodologies to accurately investigate the ultralow-energy interactions taking place on these interfaces. For instance, universally employed models such as the pendant droplet often fail to provide representative information on the wetting properties of superomniphobic surfaces. The delicate balance between the forces acting at the droplet-surface and droplet-needle interfaces can easily result in heavily distorted droplet profiles. Here, we introduce a Cassie-levitating droplet model which overcomes the limitations of the pendant droplet model, allowing a distortion-free assessment of the interactions between super(amphi)omniphobic materials and low surface tension liquids. Comparative analysis in wetting of low surface tension fluids such as hexadecane (∼27.47 mN/m) on superamphiphobic surfaces via the Cassie-levitating and pendant droplet models reveals up to 70° (800%) deviations in the estimated contact angle hysteresis. A theoretical framework is developed to assess experimentally observed profile distortions against ideal gravity-induced sagging of droplet shapes during dynamic droplet expansion and contraction cycles. Notably, pendant droplets resulted in up to 50% distortion while the Cassie-levitating ones achieved less than just 10%. We believe that the Cassie-levitating droplet model bears ample potential for the characterization of the rapidly emerging family of superomniphobic materials, setting the basis for their future engineering in numerous emerging applications.

Macondo oil in northern Gulf of Mexico waters – Part 2: Dispersant-accelerated PAH dissolution in the Deepwater Horizon plume

During the Deepwater Horizon blowout, unprecedented volumes of dispersant were applied both on the surface and at depth. Application at depth was intended to disperse the oil into smaller microdroplets that would increase biodegradation and also reduce the volumes buoyantly rising to the surface, thereby reducing surface exposures, recovery efforts, and potential stranding. In forensically examining 5300 offshore water samples for the Natural Resource Damage Assessment (NRDA) effort, profiles of deep-plume oil droplets (from filtered water samples) were compared with those also containing dispersant indicators to reveal a previously hypothesized but undocumented, accelerated dissolution of the polycyclic aromatic hydrocarbons (PAH) in the plume samples. We interpret these data in a fate-and-transport context and conclude that dispersant applications were functionally effective at depth.

Optimization of a compact falling-droplet absorber for cooling power generation

Refrigeration has become a necessary component for comfort living. Absorption refrigeration is a valid option for waste-heat-to cool conversion. Coupling this technology with cheap heat energy sources is an interesting prospect, however downsizing of this type or chiller for small environments has been proven difficult, especially regarding the absorber. Large interface area between the two operating fluids returns higher absorption rates, but lack of control on the fluid distribution results in an inefficient use of the space available. This study proposes a space-efficient design based on finned-plate technology coupled with a droplet flow regime. Manufacturing through 3D printing technique is used to study the effect of fins shape. Droplet behaviour is firstly studied with an analytical model based on the variational approach. Experimental results were obtained using a high speed camera employed to validate the analytical results and obtain qualitative and quantitative data to complete the analysis. The results show that the analytical model reproduces with sufficient accuracy the droplet dynamics in some regions. The rhomboidal geometry with 120° angle proved able to produce the smallest droplets without allowing merging of more droplets, ensuring the maintenance of droplet flow. Disturbances in the droplet profiles were observed, caused by the pin-droplet interaction. Further study is required to refine the model (to account for these disturbances) and obtain a more precise prediction of the droplet sizes.

Doping of Green Fluorescent Protein into Superfluid Helium Droplets: Size and Velocity of Doped Droplets.

We report doping of green fluorescent protein from an electrospray ionization (ESI) source into superfluid helium droplets. From analyses of the time profiles of the doped droplets, we identify two distinct groups of droplets. The faster group has a smaller average size, on the order of 106 helium atoms/droplet, and the slower group is much larger, by at least an order of magnitude. The relative populations of these two groups depend on the temperature of the droplet source: from 11 to 5 K, the signal intensity of the slower droplet group gradually increases, from near the detection limit to comparable to that of the faster group. We postulate that the smaller droplets are formed via condensation of gaseous helium upon expansion from the pulsed valve, while the larger droplets develop from fragmentation of ejected liquid helium. Our results on the size and velocity of the condensation peak at higher source temperatures (>7 K) agree with previous reports, but those at lower temperatures (<7 K) seem to be off. We attribute this discrepancy to the masking effect of the exceedingly large droplets from the fragmentation peak in previous measurements of droplet sizes. Within the temperature range of our investigation, although the expansion condition changes from subcritical to supercritical, there is no abrupt change in either the velocity distribution or the size distribution of the condensation peak, and the most salient effect is in the increasing intensity of the fragmentation peak. The absolute doping efficiency, as expressed by the ratio of ion-doped droplets over the total number of ions from the ESI source, is on the order of 10-4, while only hundreds of doped ions have been detected. Further improvements in the ESI source are key to extending the technology for future experiments. On the other hand, the separation of the two groups of droplets in velocity is beneficial for size selection of only the smaller droplets for future experiments of electron diffraction.

Modelling of sessile water droplet shape evolution during freezing with consideration of supercooling effect

The freezing process of a supercooled water droplet on a cold plate is studied theoretically and experimentally. A novel model that considers both the supercooling effect on the physical properties and the gravity effect on the droplet shape is developed to simulate the droplet freezing behaviors. The model introduces a dynamic contact angle coupled with a slipping velocity to describe the tip singularity formation. Experiments are conducted on 10, 20 and 30μL supercooled water droplets and the droplet freezing behaviors including the freezing front movements and droplet profile evolutions are observed and analyzed using the image recognition technology. The freezing rates and times and the droplet profiles calculated by the model agree well with the experimental observations. The model can better predict the freezing characteristics especially the freezing rate and time than the traditional model that ignores the supercooling effect, with the deviation in freezing time decreasing from over 40% to about 10% for droplets with different volumes at different temperatures and a larger supercooling degree causing a more obvious difference between the new and traditional models. The calculation results suggest that the final droplet profile is less dependent on the supercooling degree because it is less affected by the freezing rate. As the cold plate temperature goes down, the freezing rate increases and the freezing time decreases.

Surface properties of sodium, potassium, and their binary alloys in the liquid state

The results from investigating the surface characteristics of liquid sodium, potassium, and four potassium–sodium alloys are considered. The Auger spectra and profiles of metal droplets with atomically pure surfaces in the solid and liquid state are studied under the same experimental conditions. It is shown that potassium is a surfactant with respect to sodium at the temperature of an experiment in the investigated range of volume concentrations. It is noted that the obtained values of surface tension are 15% higher than the reference values.

Disjoining Pressure in Partial Wetting on the Nanoscale.

Partial wetting on the nanoscale may result in the formation of sessile liquid nanodroplets on flat substrates. In this case, the molecular forces generate a strong interaction between nanodroplet interfaces. This interaction is expressed in the mean-field approximation by the disjoining pressure and determines an important deviation from the spherical cap shape of the nanodroplets. This deviation is observed on the atomic force microscopy images of sessile nanodroplets of oleic acid on glass. The disjoining pressure was manipulated by hydroxylation of the glass surface. This surface modification generated a strong negative disjoining pressure due to structural forces arising from the orientation of oleic acid molecules with their polar heads toward the substrate. As a result, the shape of oleic acid nanodroplets showed large deviations from the spherical cap shape, with the liquid-vapor interface tilting angle with respect to the plane substrate having a maximum (herein considered to be the contact angle) a certain distance from the substrate, followed by its decrease to zero at the droplet edge. The integration of the augmented Young-Laplace equation, where the dependence of the negative structural disjoining pressure on the interface separation distance was assumed to be an exponential decay, yielded height profiles of droplets in good agreement with the experiment.

Influence of the fluid structure on the binding potential: Comparing liquid drop profiles from density functional theory with results from mesoscopic theory.

For a film of liquid on a solid surface, the binding potential g(h) gives the free energy as a function of the film thickness h and also the closely related (structural) disjoining pressure Π=-∂g/∂h. The wetting behaviour of the liquid is encoded in the binding potential and the equilibrium film thickness corresponds to the value at the minimum of g(h). Here, the method we developed in the work of Hughes et al. [J. Chem. Phys. 142, 074702 (2015)], and applied with a simple discrete lattice-gas model, is used with continuum density functional theory (DFT) to calculate the binding potential for a Lennard-Jones fluid and other simple liquids. The DFT used is based on fundamental measure theory and so incorporates the influence of the layered packing of molecules at the surface and the corresponding oscillatory density profile. The binding potential is frequently input in mesoscale models from which liquid drop shapes and even dynamics can be calculated. Here we show that the equilibrium droplet profiles calculated using the mesoscale theory are in good agreement with the profiles calculated directly from the microscopic DFT. For liquids composed of particles where the range of the attraction is much less than the diameter of the particles, we find that at low temperatures g(h) decays in an oscillatory fashion with increasing h, leading to highly structured terraced liquid droplets.

Morphological Transformation of Surface Femtodroplets upon Dissolution.

Constructing controllable liquid patterns with high resolution and accuracy is of great importance in droplet depositions for a range of applications. Simple surface chemical micropatterns have been popularly used to regulate the shape of liquid droplets and the final structure of deposited materials. In this work, we study the morphological evolution of a dissolving femtoliter droplet pinned on multiple microdomains. On the basis of minimization of interfacial energy, the numerical simulations predict various symmetric droplet profiles in equilibrium at different liquid volumes. However, our experimental results show both symmetric and asymmetric shapes of droplets due to contact line pinning and symmetry breaking during droplet dissolution. Upon slow volume reduction, the deposited microdroplet arrays on one single type of simple surface prepatterns spontaneously morphed into a series of complex regular 3D shapes. The findings in this work offer insights into design and prepararion of the rich and complex morphology of liquid patterns via simple surface premicropatterns.

Using micro-ct to investigate nanofluid droplet sorption in dry powder beds

Liquid droplet sorption in dry porous media is an important process for a wide range of scientific and engineering applications. However, visualizing droplet sorption is difficult due to the opacity of the porous media used in most of the applications. In this study, micro-CT technology is used to characterize the sorption profiles of nanofluid droplets in PMMA powder beds. Scan results reveal that the region of the powder bed wetted by the nanofluid has substantially higher pixel index values than the dry powder, thus enabling visualization of the sorption profile. The wetted regions themselves consistently have semi-spheroid shapes with craters on the top surface. The craters may be induced by powder repacking rather than droplet inertia ejecting well-settled powder particles. The sorption of multiple droplets maintains the features of a single droplet granule but increases the lateral spreading more than the penetration in the vertical direction. The inhomogeneous distribution of the pixel index value suggests accumulation of the nanofluid near the wetting front due to inhomogeneous porosity in the wetted region of the powder bed. It is considered that droplet sorption and capillary force may cause the powder particles to repack to generate a low porosity in the center of the wetted region. Nanoparticle distribution in the powder bed after complete evaporation of the nanofluid was also visualized. In conclusion, nanoparticle-enhanced micro-CT imaging has demonstrated the feasibility to visualize three-dimensional sorption profiles of a fluid in dry porous powder beds and thus provided an efficient means to study the sorption process in an opaque porous medium. We also envision that micro-CT can be utilized to characterize nanoparticle distribution in porous media in applications where nanomaterials are introduced for additional functionality of the final products.