Droplet Width Research Articles

Characteristic evolution and energy variation during the generation of water droplet

Understanding water droplet characteristic is an important prerequisite for improving wet dust removal efficiency. Using the high-speed camera system, the process of water droplet generation under the different Ca2+ concentrations and injecting velocities was studied. The width and length of water droplet increased, whereas the ratio of droplet width and length decreased with generation time. The water droplet generation time decreased with injecting velocity increasing, whereas kept almost unchanged with Ca2+ concentration. The equivalent diameter of droplet decreased with injecting velocity, whereas presented first a slight decrease and then a slight increase with Ca2+ concentration. This result suggested that the injecting velocity effect was stronger than the Ca2+ effect on the water droplet generation time and size. Furthermore, the effective injecting force and capillary force were mainly forces to influence the droplet generation in force analysis. RF (ratio of capillary force and effective pressure force) was first used to evaluate the synergistic effect of capillary force and effective injecting force. The greater RF, the water droplet generation time was longer and water droplet diameter was larger. Furthermore, the relationship between surface energy per unit (E/S) of water droplet and RF was a negative correlation. Those results can provide valuable suggestions to the development theory of dust removal.

Analysis of wettability and contact angle of sodium bicarbonate impregnated wooden surfaces

Scots pine and spruce wood samples were vacuum impregnated with 3, 5, and 9% sodium bicarbonate solution. Contact angle measurements were made by dropping 0.05 mL of pure water and 3% saltwater solution onto the material’s surface. The surface roughness of each sample was measured, and that of Scots pine control samples was higher than that of spruce samples, but the surface roughness values of spruce wood were higher in the samples impregnated with sodium bicarbonate. When pure water or saltwater solution was dropped onto the samples, it was observed that as the waiting times increased, the contact angle value decreased, the droplet height decreased, and the droplet width increased. It was found that the contact angles were higher in the control samples of both tree species than in the samples of 5% and 7%. The contact angles of 9% impregnation solution, pure water, and salt water were higher than the control samples. As the solution ratio increased on the surfaces impregnated with sodium bicarbonate, the contact angle also increased, and the wettability behavior decreased accordingly. Sodium bicarbonate solution is effectively used in the impregnation process for pine and fir woods, making the materials more resistant to water under outdoor conditions. This solution significantly reduces the risk of deformation of wood by increasing the contact angle and reducing its water absorption properties.

Exploring impact, spreading, and bonding dynamics in molten metal deposition for novel drop-on-demand printing

This study delves into the dynamics of molten metal deposition (MMD)-based drop-on-demand (DoD) printing, focusing on the interaction between aluminum droplets and substrates. Nozzle-to-substrate distances below 20 mm prevent droplet pinch-off, while distances exceeding 40 mm result in no droplet-substrate adhesion. Operating within the substrate temperature range of 350–550 °C is crucial, avoiding delamination, and shrinkage pits at lower temperatures, and substrate deformation and heightened oxidation at higher temperatures. Droplet adhesion is impeded at nozzle temperatures below 700 °C. Impact-driven and inviscid, DoD-MMD exhibits spreading outpacing overall solidification, particularly at higher temperatures. Surface tension forces dominate, influencing droplet spreading and leading to underdamped interfacial oscillations. Weak droplet-substrate adherence, facilitated by Van der Waals forces, allows easy droplet detachment, beneficial for successive drop-on-drop deposition. Unique to DoD-MMD, ridges along the droplet periphery act as solidification paths, influenced by thermal contraction and surface tension. The spherical pancake shape of the droplet, characterized by a solidification angle >90°, is elucidated through Weber and Freezing numbers. The final deposited droplet width to initial diameter ratio increases with the droplet temperature and deposition height. In contrast to other metal DoD studies, the spreading factor decreases with a rise in substrate temperature, attributed to intensified oxidation at higher substrate temperatures.

Effect of inevitable ions on kerosene droplet formation and evolution

AbstractBACKGROUNDUnderstanding the effect of ions on collector generation characteristics is crucial for adjusting the oil/water interface and enhancing mineral flotation.METHODSWe conducted a study of the kerosene droplet generation process in the presence of NaCl, MgCl2, and AlCl3 using a high‐speed motion acquisition system.RESULTS AND CONCLUSIONSThe results showed that the generation process of kerosene droplets could be divided into two stages, droplet expansion and column contraction, according to variations of the droplet width. With the increasing capillary inner diameter, the generation time of the kerosene droplet increased, while the w/h value (column width/column height) of the kerosene column decreased. When the w/h value decreased to 0, the droplet column ruptured, and the droplet separated from the capillary. As the ion valence increased, the equivalent diameter (d) of the kerosene droplet increased due to the ionic hydration and followed the order dAl3+ > dMg2+ > dNa+. Furthermore, as the ion concentration increased, the equivalent diameter increased with the same capillary inner diameter, and the w/h value decreased. A model of the kerosene column height and capillary inner diameter (R) was established to predict the characteristics of the generated kerosene droplet. © 2023 Society of Chemical Industry (SCI).

Modeling vorticity stretching of viscoelastic droplets during shearing flow

In the present work, we focus on the large deformation of a viscoelastic droplet suspended in a Newtonian matrix. We use the constrained volume model as a basic theoretical framework for the description of droplet shape evolution, and we account for the viscoelasticity of the droplet phase using the single-mode Giesekus model. The velocity gradient term describing flow inside the droplet is modified by the viscoelastic stresses, and the resulting model—we herein call the non-Newtonian constrained volume model—is calibrated by matching its predictions to those of the model of Yu et al. [J. Rheol. 48, 417–438 (2004)] at small deformation and slow flow conditions. The non-Newtonian constrained volume model is then examined under conditions of large deformation and/or fast flow, and its predictions are compared against experimental results. The new model shows the growth of the droplet's width in the vorticity direction at conditions of large capillary number, moderate-to-large viscosity ratio, and small elastocapillary number.

Droplet impact dynamics on single-pillar superhydrophobic surfaces

While ridged, spherical, or cone superhydrophobic surfaces have been extensively utilized to explore the droplet impact dynamics and the possibility of reducing contact time, superhydrophobic surfaces with a single small pillar have received less attention. Here, we report the rebound and splashing phenomena of impact droplets on various single-pillar superhydrophobic surfaces with the pillars having smaller or equal sizes compared to the droplets. Our results indicate that the single-pillar superhydrophobic surfaces inhibit the droplet splashing compared to the flat ones, and the rebound droplets on the former sequentially exhibit three morphologies of top, bottom, and breakup rebounds with the increasing of Weber number, while those on the latter only show the (bottom) rebound. The pillar significantly enlarges the droplet spreading factor but hardly changes the droplet width. Both the relations between the maximum spreading and width factors and the Weber number on all surfaces approximately follow a classical 1/4-power law. Reduction in the contact time is observed for the rebound droplets on the single-pillar superhydrophobic surfaces, dependent on the rebound morphology. Specially, the breakup rebound nearly shortens the contact time by more than 50% with a larger pillar-to-droplet diameter ratio yielding a greater reduction. We provide scaling analyses to demonstrate that this remarkable reduction is ascribed to the decrease in the volume of each sub-droplet after breakup. Our experimental investigation and theoretical analysis provide insight into the droplet impact dynamics on single-pillar superhydrophobic surfaces.

Computational Fluid Dynamic Study on Oil-Water Two Phase Flow in A Vertical Pipe for Australian Crude Oil

A 3D steady state numerical model for the oil-water dispersed flow has been discovered to study the impacts of shear stress on the dispersed phase behaviour in a pipe with vertical situation. CFD tool by ANSYS software is used to investigate the wall shear stress and water droplet pressure. The flow range for the continuous process was explained through the resolution of the Navier-Stokes conservation equations with k–? turbulence model are summed in Reynolds. A recent experimental method analysis was simulated. The geometry is 3.2 m long and 38 mm in diameter tube. Oil droplet width has been presumed to be dependent on flow Reynolds number and it has demonstrated numerically for this case of study. When the mixture velocity Um of1.5 m/s, the droplet diameter Dd was found 4 mm. Shear stress was developed by current work for a different number of velocities (1.5,2,2.5 m/s) at oil fraction (cut off) is 0.2,the simulation results show that, the greatest shear stress value was at the uppermost point of pipe and it was 69 Pa.

MIGRACIÓN DE GOTAS POR EFECTO TERMOCAPILAR: DEPENDENCIA CUADRÁTICA DE LA TENSIÓN SUPERFICIAL CON LA TEMPERATURA

We study the migration of droplets on a solid surface which is under a uniform temperature gradient. The present article focus on partial wetting fluids which surface tension depends on the squared temperature. These type of liquids, called self-rewetting, show a complex dynamics and here we will compare with those liquids of linear dependence in the temperature. Unlike to the latter ones, the droplet width increases with the time.

A three-dimensional model for analyzing the anisotropic wetting behavior of striped surfaces

Anisotropic wetting shows potential application in advanced microfluidics and biosensors. This study proposes a three-dimensional (3-D) methodology using a finite element method to investigate the anisotropic wettability of striped surfaces. The variations of free energy (FE), free energy barrier (FEB), contact angle (CA), contact angle hysteresis (CAH), droplet shape and the three-phase contact line shape of an anisotropic droplet during the spreading process are explored. It is found that the droplet length and three-phase contact line length fluctuate by the increase of the droplet width and three-phase contact line width during the spreading process of droplet. In addition, a relatively small stripe width with higher free energy is necessary to achieve a large equilibrium CA and a small CAH or easily reach the equilibrium CA. The present methodology can be potentially used for designing architected surfaces with anisotropic wetting properties in microfluidic devices, lab-on-a-chip systems, and self-cleaning surfaces.

Effect of initial droplet shape on the tangential force required for spreading and sliding along a solid surface

Despite the extensive study of wetting in literature, there are still many unresolved issues regarding forced wetting. One of them refers to the effect of the initial droplet shape on the force required for spreading and sliding along a solid surface; an effect that has not ever been explicitly reported. Previous experimental works, in general, assume initially axisymmetric droplet shapes. In this study, experiments are performed with an innovative device, Kerberos, capable of subjecting sessile droplets at different tilting angles to varying centrifugal forces in order to explore the spreading/sliding behavior of droplets of different volumes and different initial shapes (including non-axisymmetric). A broad validation of the technique is achieved by the repeatability and consistency of measurements. Results for initially axisymmetric and non-axisymmetric droplets concerning contact angles, droplet length, droplet shape and velocity are presented and discussed. Furthermore, detailed results for the critical tangential accelerations required for the inception of spreading and sliding are presented showing the different sensitivity of these parameters on the droplet initial shape. Experimental results are employed to test the applicability of the well-known Furmidge equation for the retention force in the case of initially non-axisymmetric droplets. On this account, the initial length of droplets is found to be a more appropriate length scale in the Furmidge equation than the initial droplet width.

Experimental and Numerical Investigation of an Overheated Aluminum Droplet Wetting a Zinc-Coated Steel Surface

Wetting steel surfaces with liquid aluminum without the use of flux can be enabled by the presence of a zinc-coating. The mechanisms behind this effect are not yet fully understood. Research results on single aluminum droplets falling on commercial galvanized steel substrates revealed the good wetting capability of zinc coatings independently from the coating type. The final wetting angle and length are apparently linked to the time where zinc is liquefied during its contact with the overheated aluminum melt. This led to the assumption that the interaction is basically a fluid dynamic effect of liquid aluminum getting locally alloyed by zinc. A numerical model was developed to describe the transient behavior of droplet movement and mixing with the liquefied zinc layer to understand the spreading dynamics. The simulations reveal a displacement of the molten zinc after the impact of the droplet, which ultimately leads to an accumulation of zinc in the outer weld toe after solidification. The simulation approach neglects the effect of evaporating zinc, resulting in a slight overestimation of the final droplet width. However, in terms of spreading initiation during the first milliseconds, the simulation is in good correlation with experimental observations and demonstrates the reason for the good wetting in the presence of zinc coatings.

Statistical analysis of E-jet print parameter effects on Ag-nanoparticle ink droplet size

In this paper, we have studied the print parameter effects on electrohydrodynamic inkjet (E-jet) resolution using statistical analysis. In order to make the E-jet manufacturing process feasible, the effect of printing parameters on the ejected droplet size must be modelled and optimized. To this end, there exist two approaches: parameter effects can be modelled using theoretical calculations or they can be generated directly from empirical data using statistical analysis. The first option has been explored by multiple research groups, whereas the latter has received less interest. In this article, the effect of printing parameters on the width of AC-pulsed E-jet deposited Ag-nanoparticle ink droplets are investigated using design of experiments (DoE) approach and statistical analysis. As a result, a statistical model for deposited droplet width is generated using four print parameters (print height, bias voltage, peak voltage and frequency) as predictors. The model can predict 94.24% of the measured width variation with a standard deviation of 1.05 µm.

Formation and stability of string phase in polyamide 6/polystyrene blends in confined flow: Effects of nanoparticles and blend ratio

Influences of silica nanoparticles on the microstructural evolution of polyamide 6 (PA6)/polystyrene (PS) blends with varying blend ratios were investigated in confined shear flow. Hydrophilic silica nanoparticles were found to promote the formation of PA6 strings with excellent shape stability during shearing. It was ascribed to the promoted coalescence of PA6 droplets induced both by the significantly increased droplet viscoelasticity and confinement, and the reduced interfacial tension by adding silica nanoparticles. Additionally, the width and aspect ratio of droplets obtained by experiments were compared with the predictions of Maffettone–Minale, Minale, Shapira‐Haber, MMSH, and modified M models. Good agreements were found in the droplet width in blends with low nanoparticle concentrations, whereas the experimental aspect ratio showed a negative deviation to model predictions, which was attributed to the enhanced droplet viscoelasticity and the omitted droplet orientation angle in these models. © 2015 American Institute of Chemical Engineers AIChE J, 62: 564–573, 2016

Two dimensional Leidenfrost droplets in a Hele-Shaw cell

We experimentally and theoretically investigate the behavior of Leidenfrost droplets inserted in a Hele-Shaw cell. As a result of the confinement from the two surfaces, the droplet has the shape of a flattened disc and is thermally isolated from the surface by the two evaporating vapor layers. An analysis of the evaporation rate using simple scaling arguments is in agreement with the experimental results. Using the lubrication approximation we numerically determine the shape of the droplets as a function of its radius. We furthermore find that the droplet width tends to zero at its center when the radius reaches a critical value. This prediction is corroborated experimentally by the direct observation of the sudden transition from a flattened disc into an expending torus. Below this critical size, the droplets are also displaying capillary azimuthal oscillating modes reminiscent of a hydrodynamic instability.

Advancing and receding wetting behavior of a droplet on a narrow rectangular plane

The contact angle (CA) measurements are generally performed on a large planar surface of a specific substrate with the width larger than the droplet size. In this study, the contact angle hysteresis on a narrow rectangular plane with a width smaller than the droplet size is experimentally studied through the inflation–deflation process by the needle–syringe method. The inflation process by stepwise addition of the liquid to the droplet leads to the contact line advancing outwardly along the major axis with advancing angle (θa). Although the droplet width is constrained by the edge of the plane, the CA along the minor axis (θw) increases and its value is greater than θa (θw > θa). Deflation process by stepwise withdrawal of liquid from the droplet results in the contact line retracting inwardly along the major axis as the CA reduces to receding angle (θr). In the meantime, the CA along the minor axis decreases as well. Both advancing and receding angles acquired from the narrow rectangular plane are confirmed with those obtained form the typical large surface of acrylic glass. On the basis of free energy minimization and liquid-induced defects model, Surface Evolver simulations are performed to reproduce the behavior of droplet on the narrow rectangular plane during the inflation–deflation process. The results of experiment and simulation agree with each other very well.

Nonlinear Deformation of a Ferrofluid Droplet in a Uniform Magnetic Field

This paper reports experimental and numerical results of the deformation of a ferrofluid droplet on a superhydrophobic surface under the effect of a uniform magnetic field. A water-based ferrofluid droplet surrounded by immiscible mineral oil was stretched by a magnetic field parallel to the substrate surface. The results show that an increasing flux density increases the droplet width and decreases the droplet height. A numerical model was established to study the equilibrium shape of the ferrofluid droplet. The governing equations for physical fields, including the magnetic field, are solved by the finite volume method. The interface between the two immiscible liquids was tracked by the level-set method. Nonlinear magnetization was implemented in the model. Comparison between experimental and numerical results shows that the numerical model can predict well the nonlinear deformation of a ferrofluid droplet in a uniform magnetic field.

Shapes of dispersed phase in confined PIB/PDMS blends with different compositions during shear flow

The morphology of immiscible fluid mixtures under confined environment usually displays different scenarios compared with those presented in bulk systems. In this work, the influence of confinement and component ratio on the droplet morphology of immiscible polyisobutylene (PIB)/polydimethylsiloxane (PDMS) blends in confined steady shear flow was investigated. While increasing the degree of confinement, the morphology of dispersed phase experienced a transition from the bulk behavior toward the confined behavior. Increasing the concentration of PIB phases in confined blends resulted in more coarsened structure under low shear rate and generated pearl necklace or string-like structures under a higher shear rate. The maximum aspect ratio of PIB droplets increased while increasing PIB concentration. The width and the aspect ratio of PIB droplets obtained experimentally were compared to the predictions of a single droplet MM model for bulk flow and an M model considering confinement. The experimental droplet width agreed well with the predictions of these two models only in the small droplet zone, large deviations appeared for the degree of confinement up to 0.36 and higher, whereas constant droplet width was found. The M model decreased the deviation between the experimental aspect ratio and the prediction of MM model in the high Ca zone. Good agreement between the prediction of M model and experiment results was found when the orientation angles of the droplets were corrected by using the M model.

Morphology and phase behavior of ethanol nanodrops condensed on chemically patterned surfaces

Equilibrium wetting of ethanol onto chemically patterned nanostripes has been investigated using environmental atomic force microscopy (AFM) in noncontact mode. The chemical patterns are composed of COOH-terminated "wetting" regions and CH3-terminated "nonwetting" regions. A specially designed environmental AFM chamber allowed for accurate measurements of droplet height as a function of the temperature offset between the substrate and a macroscopic ethanol reservoir. At saturation, the height dependence scales with droplet width according to w1/2, in excellent agreement with the augmented Young equation (AYE) modeled with dispersive, nonretarded surface potentials. At small under- and oversaturations, the AYE model accurately fits the data if an effective DeltaT is used as a fitting parameter. There is a systematic difference between the measured DeltaT and the values extracted from the fits to the data. In addition to static measurements, we present time-resolved measurements of the droplet height which enable the study of condensation-evaporation dynamics of nanometer-scale drops.

Collective field theory of the fractional quantum Hall edge state and the Calogero-Sutherland model

Using the hydrodynamic collective field approximation for the v = 1 m fractional quantum Hall droplet dynamics we find that the low-energy excitations are described by c = 1 conformal field theory of a compact boson of radius √ m. Using the conformal field theory method we show that the one-particle density matrix of the edge state interpolates between the chiral Luttinger liquid behavior 〈ψ †(r)ψ(0)〉 ∼ r −m and the Calogero-Sutherland model behavior 〈ψ †(r)ψ(0)〉 ∼ r − ( m+1 m ) 2 as the droplet width is varied continuously. The result suggests complementary relation between the two-dimensional quantum Hall droplet and the one-dimensional Calogero-Sutherland model.

The sliding of sessile and pendent droplets the critical condition

The critical condition for the sliding of sessile and pendent droplets down a solid substrate has been investigated. For sessile droplets it was found that sin α c scaled with V − 2 3 and that for pendent droplets sin α c scaled with V − where α c is the critical substrate angle and V is the droplet volume. Good agreement between experimental and theoretical values (Dussan Equation) was obtained for sessile droplets. For pendent droplets, however, such agreement was only possible by assuming that the droplet width was independent of the droplet volume.