Droplet Spreading Dynamics Research Articles

AI predicts water droplet spreading dynamics and icing patterns on cold surfaces

The techniques could lead to improvements in aircraft anti-icing, spray-freeze drying, and influenza vaccine storage.

Universal Aspects of Droplet Spreading Dynamics in Newtonian and Non-Newtonian Fluids.

Droplet impacts are common in many applications such as coating, spraying, or printing; understanding how droplets spread after impact is thus of utmost importance. Such impacts may occur with different velocities on a variety of substrates. The fluids may also be non-Newtonian and thus possess different rheological properties. How the different properties such as surface roughness and wettability, droplet viscosity, and rheology as well as interfacial properties affect the spreading dynamics of the droplets and the eventual drop size after impact are unresolved questions. Most recent work focuses on the maximum spreading diameter after impact and uses scaling laws to predict this. In this paper, we show that a proper rescaling of the spreading dynamics with the maximum radius attained by the drop and the impact velocity leads to a unique single and thus universal curve for the variation of diameter versus time. The validity of this universal functional shape is validated for different liquids with different rheological properties as well as substrates with different wettabilities. This universal function agrees with a recent model that proposes a closed set of differential equations for the spreading dynamics of droplets.

Rapid droplet spreading on a hot substrate

Due to its high efficiency, droplet spray cooling is widely used in various industrial and scientific applications. The spreading of droplets can greatly affect heat transfer, and temperature can also affect the dynamics of droplet spreading. In this study, both experiment and numerical simulations are used to investigate the effects of temperature on droplet spreading on a hot substrate from the nanoscale dynamics of moving contact lines to macroscale thermo-capillary flows. It is found that with increasing substrate temperature, during fast droplet spreading, satellite droplets transit from first-stage pinch-off to second-stage pinch-off and then to no pinch-off. These phenomena can be attributed to the effects of temperature at different scales. In the nanoscale region of moving contact lines, temperature and corresponding viscosity can alter the dynamic wetting angle of the moving contact lines. At the microscale interface region, temperature can change the viscosity near droplet interfaces, leading to variation in the viscous force. At the macroscale droplet region, the temperature of a droplet can change its surface tension, leading to thermo-capillary flow along the droplet interface. The pinch-off dynamics of droplet spreading on hot substrate can be analyzed according to the propagation of interfacial capillary waves at different temperatures and the resultant neck dynamics. These findings provide insight into droplet-spreading regimes on hot substrates under different temperatures.

Droplet spreading dynamics on hydrophobic textured surfaces: A lattice Boltzmann study

A three-dimensional (3D) lattice Boltzmann method based on the Allen-Cahn equation (A-C LBM) is employed to study the spreading dynamics of impacting droplets on the hydrophobic flat and textured surfaces. At first, the simulation of the equilibrium state of a droplet and also the impacting droplet spreading on a flat surface are considered at various wetting conditions to examine the accuracy and efficiency of the present numerical technique. The obtained results for these cases show excellent agreement with available theoretical, numerical, and experimental data in the literature that confirms the validity of the A-C LBM employed for simulation of such complex interfacial dynamics. Upon validation, the implemented A-C LBM is applied for investigation of the droplet impingement on the hydrophobic textured surface and the results are compared with those obtained by considering the flat surface. The present study shows that using microscale textures on a hydrophobic surface dramatically reduces the contact area between the impacting droplet and the solid wall due to the momentum redirection phenomenon. Indeed, the hydrophobic surface used with in-plane circular ridges causes the spreading lamella to eject out-of-plane with a liquid bowl shape. This mechanism converts a part of the horizontal momentum of the spreading to the vertical momentum that prevents droplets to have intense interaction. For an impacting droplet at a high Weber number, it is concluded that the geometrical parameters of the ridge dictate the morphology of the spreading on the hydrophobic surface. However, the droplet dynamics at a low Weber number depend on both the texture size and the surface wettability, so that the physical mechanisms of the droplet spreading and lamella ejection dramatically change by variation of these parameters. The obtained results show that when the adhesion force of the substrate is dominant (lower contact angles), the wetting property of the surface plays an effective role than the texture geometry in the formation of the liquid bowl at low Weber numbers. Also, the present study demonstrates the capability of the A-C LBM for the prediction of the studied multiphase flow structures and characteristics with extremely complex interface phenomena.

Axial spreading of droplet impact on ridged superhydrophobic surfaces

HypothesisDue to the complex hydrodynamics of droplet impact on ridged superhydrophobic surfaces, quantitative droplet spreading characteristics are unrevealed, limiting the practical applications of ridged superhydrophobic surfaces. During droplet impacting, the size ratio (the ratio of the ridge diameter to the droplet diameter) is an important factor that affects droplet spreading dynamics. ExperimentsWe fabricated ridged superhydrophobic surfaces with size ratios ranging from zero to one, and conduct water droplet impact experiments on these surfaces at varied Weber numbers. Aided by the numerical simulations and theoretical analysis, we illustrate the droplet spreading dynamics and reveal the law on the maximum axial spreading coefficient. FindsThe results show that the droplet spreading and retraction dynamics on ridged superhydrophobic surfaces are significantly asymmetric in the axial and spanwise directions. Focusing on the maximum axial spreading coefficient, we find it decreases first and then increases with increasing size ratios, indicating the existence of the critical size ratio. The maximum axial spreading coefficient can be reduced by 25-40% at the critical size ratio compared with that on flat surfaces. To predict the maximum axial spreading coefficient, two theoretical models are proposed respectively for size ratios smaller and larger than the critical size ratio.

A Phenomenon Study on Spreading and Evaporating Process of Droplet on DBD Actuator for Wind Turbine Anti-icing

This paper reports on the phenomenon of the unique spreading and evaporation process of water droplets on the surface of a dielectric barrier discharge (DBD) actuator. High-speed photography was used to capture the droplet spreading dynamics, and the temperature field evolution was characterized by infrared imaging. On the DBD actuator, the maximum spreading diameters of the droplets are shown to be increased by ∼95%, and the contact angles decrease from 58º to 13º, indicating that the DBD plasma significantly increases the hydrophilicity of the actuator surfaces. It is also revealed that the evaporation time induced by the DBD plasma is 6.54 times faster than that of an electric heater. It is argued that coupled effects of the hydrophilicity caused by plasma and the heat flux in the streamers bridging the electrodes and the droplets should be the crucial points of plasma evaporation physics of impinging water droplets, which are especially meaningful in anti-icing applications.

Prediction of the droplet spreading dynamics on a solid substrate at irregular sampling intervals: Nonlinear Auto-Regressive eXogenous Artificial Neural Network approach (NARX-ANN)

This paper introduces a Nonlinear Auto-Regressive eXogenous Artificial Neural Network (NARX-ANN) model for prediction of spreading dynamics. 1220 experimental data of spreading dynamics of different droplets on various substrates have been collected from literature for model development. The model input parameters are Weber number, Ohnesorge number, and the tangent of equilibrium contact angle. An auxiliary input has been also added to take into account the irregular time sampling. D-optimal design of experiments has been utilized to determine the best parameters for the NARX model. It was found that the prediction capability of NARX model was better in comparison with KC and AGM models. The statistical parameters of the best developed NARX model including mean square error MSE=3.257×10-4, average absolute relative deviation (AARD) = 4.240%, and coefficient of determination (R2)=0.993 demonstrate the excellent prediction capability of the proposed model.

Maximum Spreading of Urea Water Solution during Drop Impingement

AbstractDroplet impingement of urea water solution (UWS) is a common source for liquid film and solid deposits formed in the tailpipe of diesel engines. In order to better understand and predict wetting phenomena on the tailpipe wall, this study focuses on droplet spreading dynamics of urea water solution. Impingement of single droplets is investigated under defined conditions by high‐speed imaging using shadowgraphy technique. The experimental studies are complemented by numerical simulations with a phase‐field method. Computational results are in good agreement with experimental data for the advancing phase of spreading and the maximum and terminal spreading radius, whereas for the receding phase notable differences occur. For the maximum spreading radius, an empirical correlation derived for glycerol‐water‐ethanol mixtures is found to be valid for millimeter‐sized UWS droplets as well. A numerical simulation for a much smaller droplet however indicates that this correlation is not valid for the tiny droplets of UWS sprays in technical applications.

Spreading Dynamics of Droplet Impact on a Wedge-Patterned Biphilic Surface

The influence of apex angle and tilting angle on droplet spreading dynamics after impinging on wedge-patterned biphilic surface has been experimentally investigated. Once the droplet contacts the wedge-patterned biphilic surface, it spreads radially on the surface, with a tendency toward a more hydrophilic area. After reaching the maximum spreading diameter, the droplet contracts back. From the experimental results, the normalized diameter β ( β = D / D 0 ) was found to be related with the Weber number ( W e = ρ D V 2 / γ ) as β max ∼ W e 1 / 5 . during the first spreading process. Below 67.4°, a larger apex angle can help a droplet to spread on the surface more quickly. The maximum spreading diameter has a tendency to increase with the Weber number, and then decrease after the Weber number, beyond 2.7. Approximately, the critical Weber number is about 5, when the droplet lifts off the surface. Considering the effect of apex angle, the maximum normalized spreading diameter has a rough expression as β ∼ α τ

On the role of liquid viscosity in affecting droplet spreading on a smooth solid surface

The role of liquid viscosity on droplet spreading behavior upon impacting on a smooth stainless steel surface has been experimentally investigated. Results show the droplet spreading dynamics with increasing viscosity (characterized by the Ohnesorge number, Oh) exhibits complex dependence on the impact inertia (characterized by Weber number, We). Specifically, for a small impact inertia (We<30), the droplet oscillates in the vertical direction around the maximum height Ha. The non-dimensional maximum diameter βmax first increases and then decreases with increasing Oh, and this non-monotonic phenomenon has not been reported previously. For an intermediate impact inertia (60<We<240), the droplet has no oscillation after it spreads to βmax, and it has the form of a rim-bounded lamella. Although βmax shows a monotonic decrease with increasing Oh, some unsmooth disturbance around the rim occurs only at intermediate Oh. For a higher impact inertia (We>240), droplet splashing emerges and then vanishes with increasing Oh, although βmax still decreases monotonically. All the observed phenomena imply that liquid viscosity may have a dual role in affecting the droplet spreading, which previous models of βmax do not take into account.

A Computational Model for the Analysis of Spreading of Viscoelastic Droplets over Flat Surfaces

The spreading of viscous and viscoelastic fluids on flat and curved surfaces is an important problem in many industrial and biomedical processes. In this work the spreading of a linear viscoelastic fluid with changing rheological properties over flat surfaces is investigated via a macroscopic model. The computational model is based on a macroscopic mathematical description of the gravitational, capillary, viscous, and elastic forces. The dynamics of droplet spreading are determined in sessile and pendant configurations for different droplet extrusion or formation times for a hyaluronic acid solution undergoing gelation. The computational model is employed to describe the spreading of hydrogel droplets for different extrusion times, droplet volumes, and surface/droplet configurations. The effect of extrusion time is shown to be significant in the rate and extent of spreading.

Experimental investigation on the Leidenfrost phenomenon of droplet impact on heated silicon carbide surfaces

Due to its superiority in suppressing hydrogen generation under severe accident conditions, silicon carbide (SiC) has been regarded as one of the promising candidates among the diverse accident tolerant fuel (ATF) claddings. Droplet impact experiments are conducted on preheated CVD-SiC surfaces with different roughness and the polished sintered-SiC and stainless-steel surface. The effects of surface roughness, contact angle and thermal properties on the impact behavior and cooling efficiency are discussed. The experiments are carried out in the range of 10 < We < 120 and Tsurf < 460 °C. The observed droplet impact phenomena on all the surfaces are categorized into five regimes, i.e. deposition, rebound with secondary atomization, breakup with secondary atomization, rebound and breakup. Deposition corresponds to nucleate boiling. Rebound and breakup are the hydrodynamic phenomena of film boiling. The rest two correspond to transition boiling. Droplet breakup can be induced thermally or mechanically in the transition boiling. Surface roughness can enhance droplet breakup both in the film and transition boiling. The small contact angle also promotes breakup. The thermal property of surfaces has little effect on the critical Weber number for droplet breakup, but affect the Leidenfrost point temperature (LPT) and CHF temperature significantly. The rupture of liquid film induced by roughness reduces the stagnant pressure beneath the droplet and lower the LPT. The droplet spreading dynamics are analyzed quantitatively, and developed an empirical model for droplet maximum spreading factor. It is found that the LPT model based on homogeneous nucleation mechanism coincides well with present experimental results.

Accelerated spreading of inviscid droplets prompted by the yielding of strongly elastic interfacial films

The complexity associated with droplets spreading on surfaces has attracted significant interest for several decades. Sustained activity results from the many natural and manufactured systems that are reliant on droplet-substrate interactions and spreading. Interfacial shear rheology and its influence on the dynamics of droplet spreading has to date received little attention. In the current study, saponin β-aescin was used as an interfacial shear rheology modifier, partitioning at the air-water interface to form a strongly elastic interface (G’/G” ∼ 6) within 1 min aging. The droplet spreading dynamics of Newtonian (water, 5 wt% ethanol, 0.0015 wt% N-dodecyl β-D-glucopyranoside) and non-Newtonian (xanthan gum) fluids were shown to proceed with a time-dependent power-law dependence of ∼0.50 and ∼0.10 (Tanner’s law) in the inertial and viscous regimes of spreading, respectively. However, water droplets stabilized by saponin β-aescin were shown to accelerate droplet spreading in the inertial regime with a depreciating time-dependent power-law of 1.05 and 0.61, eventually exhibiting a power-law dependence of ∼ 0.10 in the viscous regime of spreading. The accelerated rate of spreading is attributed to the potential energy as the interfacial film yields as well as relaxation of the crumpled interfacial film during spreading. Even though the strongly elastic film ruptures to promote droplet spreading, interfacial elasticity is retained enhancing the dampening of droplet oscillations following detachment from the dispensing capillary.

Nonwettable Hierarchical Structure Effect on Droplet Impact and Spreading Dynamics.

In this study, the nano/micro hierarchical structure effect of a nonwettable surface on droplet impact was investigated by high-speed visualization. A dual-scale structure of a superhydrophobic surface was designed for manipulating a wide range of capillary pressures (103-106 Pa), and it was supposed to trigger a hierarchical effect on the droplet dynamics. Distilled water droplets of various sizes and initial velocity were subjected to the prepared samples, and the impact behavior, the spreading diameter, and contacted time, were quantitatively measured. The apparent maximum spreading and contact time of the low Weber number ( We#) condition was less dependent on the microscaled design factor of the multiscale-fabricated surface. However, in the high We# condition, the wavy formation shape and the fragmented criteria of the droplet impact were affected by the configuration of the surface morphology. The hierarchical effect from the dual-scale structure on droplet spreading dynamics has been discussed through a balance between capillary pressure induced by the structure and the dynamic pressure of droplet impact.

Measurement of nanoscale molten polymer droplet spreading using atomic force microscopy.

We present a technique for measuring molten polymer spreading dynamics with nanometer scale spatial resolution at elevated temperatures using atomic force microscopy (AFM). The experimental setup is used to measure the spreading dynamics of polystyrene droplets with 2 μm diameters at 115-175 °C on sapphire, silicon oxide, and mica. Custom image processing algorithms determine the droplet height, radius, volume, and contact angle of each AFM image over time to calculate the droplet spreading dynamics. The contact angle evolution follows a power law with time with experimentally determined values of -0.29 ± 0.01, -0.08 ± 0.02, and -0.21 ± 0.01 for sapphire, silicon oxide, and mica, respectively. The non-zero steady state contact angles result in a slower evolution of contact angle with time consistent with theories combining molecular kinetic and hydrodynamic models. Monitoring the cantilever phase provides additional information about the local mechanics of the droplet surface. We observe local crystallinity on the molten droplet surface, where crystalline structures appear to nucleate at the contact line and migrate toward the top of the droplet. Increasing the temperature from 115 °C to 175 °C reduced surface crystallinity from 35% to 12%, consistent with increasingly energetically favorable amorphous phase as the temperature approaches the melting temperature. This platform provides a way to measure spreading dynamics of extremely small volumes of heterogeneously complex fluids not possible through other means.

Numerical investigation of droplet spreading and heat transfer on hot substrates

Droplet spray cooling has wide applications in electronic cooling, steam generators, evaporators and condensers etc due to its high efficiency. The cooling effect depends on the droplet spreading dynamics greatly. In our study the transient two-dimensional axisymmetric model for droplet cooling is developed with a level set method, where the dynamics of the moving contact line is described with the Molecular Kinetic Theory (MKT). After validation with experimental data, the effect of impact velocity, surface tension, initial droplet radius, equilibrium contact angle and liquid viscosity on droplet spreading is investigated. It is found that the dynamics of the moving contact line can be described accurately with MKT, and the predicted droplet spreading radius agrees quite well with the experimental data, while the Constant Contact Angle (CCA) model overpredicts the droplet spreading rate. The maximum heat flux occurs at the point when the droplet spreading transits from capillary-inertial spreading to capillary-viscous spreading. The droplet spreading rate will increase with the increasing impact velocity, surface tension and initial radius, or decreasing equilibrium contact angle and liquid viscosity. Due to the effect of thermo-capillary force, the cold substrate can promote the droplet spreading, and the hot substrate can retard the droplet spreading. These findings may be of great significance for effective droplet spreading cooling.

Viscous Force Retards Initial Droplet Spreading

A droplet could spread on a solid substrate within several milliseconds, and be divided into two stages: a fast inertial stage and a subsequent slow viscous stage. The effects of inertia and viscosity on spreading are presented with Ohnesorge number. A small Ohnesorge number corresponds to an initial inertial spreading. In this study, spreading experiments were carried out with a time resolution of 1 μs. Results disclose that the viscous force could retard droplet spreading at the beginning of liquid/solid surface contact, even with an Ohnesorge number smaller than 0.1. According to simulation results, the viscous retardation could be ascribed to the real high local shear rate along the contact line at the spreading front. These results provide a new insight on droplet spreading dynamics and proposes, where exists a third viscous-inertial stage during the initial droplets spreading process.

Dynamics of Microscale Liquid Propagation in Micropillar Arrays.

Understanding the dynamics of microscale liquid propagation in micropillar arrays can lead to significant enhancement in macroscopic propagation modeling. Such a phenomenon is fairly complicated, and a fundamental understanding is lacking. The aim here is to estimate three main parameters in liquid propagation, capillary pressure, average liquid height, and contact angle on the pillar side, through modeling and experimental validation. We show that the capillary pressure is not constant during liquid propagation, and the average capillary pressure is evaluated using its maximum and minimum values. The average liquid height influences the permeability of such a structure, which is challenging to determine as a result of the complicated three-dimensional (3D) meniscus shape. A simple physical model is provided in this paper to predict the average liquid height with less than 7% error. The contact angle on the micropillar side, which has considerable impact on the capillary pressure and the average liquid height, has been debated for a long time. We propose a model to predict this contact angle and validate it against experimental values in the literature. Our findings also indicate that the microscopic motion of the liquid front is significantly affected by the ratio of the pillar height to edge-to-edge spacing, and a correlation is provided for quantification. The proposed models are able to predict the droplet spreading dynamics and estimate spreading distance and time reasonably.

Films, layers, and droplets: The effect of near-wall fluid structure on spreading dynamics.

We present a study of the spreading of liquid droplets on a solid substrate at very small scales. We focus on the regime where effective wetting energy (binding potential) and surface tension effects significantly influence steady and spreading droplets. In particular, we focus on strong packing and layering effects in the liquid near the substrate due to underlying density oscillations in the fluid caused by attractive substrate-liquid interactions. We show that such phenomena can be described by a thin-film (or long-wave or lubrication) model including an oscillatory Derjaguin (or disjoining or conjoining) pressure and explore the effects it has on steady droplet shapes and the spreading dynamics of droplets on both an adsorption (or precursor) layer and completely dry substrates. At the molecular scale, commonly used two-term binding potentials with a single preferred minimum controlling the adsorption layer height are inadequate to capture the rich behavior caused by the near-wall layered molecular packing. The adsorption layer is often submonolayer in thickness, i.e., the dynamics along the layer consists of single-particle hopping, leading to a diffusive dynamics, rather than the collective hydrodynamic motion implicit in standard thin-film models. We therefore modify the model in such a way that for thicker films the standard hydrodynamic theory is realized, but for very thin layers a diffusion equation is recovered.

Spreading dynamics of droplet on an inclined surface

A three-dimensional unsteady theoretical model of droplet spreading process on an inclined surface is developed and numerically analyzed to investigate the droplet spreading dynamics via the lattice Boltzmann simulation. The contact line motion and morphology evolution for the droplet spreading on an inclined surface, which are, respectively, represented by the advancing/receding spreading factor and droplet wetted length, are evaluated and analyzed. The effects of surface wettability and inclination on the droplet spreading behaviors are examined. The results indicate that, dominated by gravity and capillarity, the droplet experiences a complex asymmetric deformation and sliding motion after the droplet comes into contact with the inclined surfaces. The droplet firstly deforms near the solid surface and mainly exhibits a radial expansion flow in the start-up stage. An evident sliding-down motion along the inclination is observed in the middle stage. And the surface-tension-driven retraction occurs during the retract stage. Increases in inclination angle and equilibrium contact angle lead to a faster droplet motion and a smaller wetted area. In addition, increases in equilibrium contact angle lead to a shorter duration time of the middle stage and an earlier entry into the retract stage.