Drop Size Research Articles

A data-driven model of drop size prediction based on artificial neural networks using small-scale data sets

An artificial neural network (ANN) method is introduced to predict drop size in two kinds of pulsed columns with small-scale data sets. After training, the deviation between calculate and experimental results are 3.8% and 9.3%, respectively. Through ANN model, the influence of interfacial tension and pulsation intensity on the droplet diameter has been developed. Droplet size gradually increases with the increase of interfacial tension, and decreases with the increase of pulse intensity. It can be seen that the accuracy of ANN model in predicting droplet size outside the training set range is reach the same level as the accuracy of correlation obtained based on experiments within this range. For two kinds of columns, the drop size prediction deviations of ANN model are 9.6% and 18.5% and the deviations in correlations are 11% and 15%.

Demixing behavior of Pickering emulsions stabilized by Janus particles and uniform Pickering particles at different pH values

This work investigates the demixing behavior of Pickering emulsions consisting of water, n-hexadecane, and two different types of Pickering particles. The first type is uniform, and the second consists of one-side modified Janus particles influencing the emulsion behavior significantly. Both particle types are able to stabilize the emulsions, but lead to clear differences in the emulsion drop size and size distribution. This results in different creaming times varying between minutes and hours and different clearance processes of the water excess phase. Large pH effects were found in addition. At some conditions, non-adsorbed particles were observed that sediment over time in addition to the creaming of the emulsion.

Methodology for modeling spray cooling of a cylindrical tube heated in the film boiling regime

This study examines spray cooling of horizontal, circular tubes when the surface temperature exceeds the Leidenfrost point, and the individual drop impacts are in the film boiling regime. Although film boiling is not an optimal condition for heat transfer, it is encountered in transient cooling processes or when high temperatures persist along the tube. The goal of the study is to apply existing models for drop impact and heat transfer to surfaces more complex than flat plates and to determine the overall steady state heat removal rate as an essential parameter for heat exchanger design. The spray characteristics are prescribed by a local number flux and drop size, assuming a random distribution in space and a uniform velocity of all drops. The angle of individual drop impingement on the cylindrical tube is accounted for through the maximum spreading diameter of the drop on the surface and the normal component of impact velocity. Furthermore, drop-drop interaction on the heated surface is accounted for at high local number flux values through an effective coverage area coefficient.The results are expressed in the form of a local heat transfer coefficient. These results confirm that the most influential parameters regarding heat transfer are the liquid mass flow rate in the nozzle and the drop diameter; however, they also indicate that the non-normal impact of drops over portions of the cylindrical tube leads to a highly reduced number flux; hence heat transfer. This oblique impact angle arises for one from the local spray angle, but more drastically from the curved, cylindrical surface; the latter leading to a dramatic sharp decrease in heat transfer. This is important information when considering the use of multiple spray nozzles, either circumferentially or longitudinally along the tube, since it dictates the optimal spacing between neighbouring nozzles.

Bloodstain tails: Asymmetry aids reconstruction of oblique impact

In the field of forensic science, elongated bloodstains formed from oblique impact of droplets are sometimes used to reconstruct aspects of a bloodletting event. For low impact angles, these stains can include an asymmetric tail that bloodstain analysts can use qualitatively to establish directionality. Quantitative analysis of these bloodstain tails, and any insight that they can provide into the impact dynamics, is lacking due to experimental challenges. Previous studies of bloodstain shapes have predominantly focused on relatively large drip drops that fall vertically on flat and inclined surfaces; yet, for inclinations that produce low impact angles, gravitational effects can reshape and obscure tails, preventing insight into how tails develop on horizontal surfaces. Here, we carry out systematic experiments in which human blood droplets with diameters less than a millimeter impact a horizontal surface at impact angles ranging from 16° to 65°. High-speed imagery confirms that the tail is not part of a prompt splashing event, but rather forms at the last moments of spreading, maintaining its shape as it dries. For each stain, we link the tail length and elliptical geometry to the blood drop size and impact velocity vector that created it. Additionally, we report a power-law correlation of the dimensionless tail length with the angle and Weber and Reynolds numbers, and we describe how this correlation in conjunction with other existing correlations can improve reconstruction of the droplet size and impact velocity.

Categorization of iso-pentane flashing spray based on morphology, thermodynamical and mechanical effects

Accidental release of superheated liquids is typically accompanied with hazardous flashing jets. Indeed, flashing jets undergo fragmentation into massive fine droplets, thus forming ideal circumstances for fires and explosion. To gain a deeper understanding of depressurized release, we studied the dynamics of iso-pentane at superheats of 40–80 °C and injection pressures of 0.6–3.0 MPa. The internal flow pattern and external spray morphology are visualized at quasi-steady stage using a high-speed camera. Results show that the flashing patterns can be classified into non-flashing, transitional flashing, and flare flashing arising from the interaction between thermodynamic and mechanical effects. The contribution of thermodynamic effect decreases as mechanical effect intensifies, due to the suppression of bubble nucleation and burst. We propose the index k, based on JaRp = k(WevOh)−1/7, to identify different flashing regions, i.e., k below 211 for non-flashing, k between 212 and 425 for transitional flashing, and k above 425 for flare flashing. Besides, the microscopic characteristics involving droplet velocity and diameter distribution are investigated and a new correlation for drop size is proposed, which is dependent on factors such as nozzle aspect ratio, mechanical force, and thermodynamic force. These findings should help to define policies to decrease the risk associate with flashing jets.

Correction: Klauser et al. Line Tension and Drop Size Dependence of Contact Angle at the Nanoscale. Nanomaterials 2022, 12, 369

There was an unclear passage in the original publication [...]

Experimental Studies on Two-Phase Flow with a Novel Slotted Plate Internal in an Air Pulsed Column

ABSTRACT A novel air pulsed column plate internal featuring plates having concentric circular slots of fixed width (3 mm) is conceptualized, tested, and compared against standard sieve plate internal for counter-current two-phase flow. This new plate design (slotted plates) offers significant intensification in terms of specific interfacial area by as much as ~ 50% vis-à-vis standard sieve plates. The studies are carried out in a 3 inch diameter air pulsed column with tap water as the continuous phase and 30% (v/v) tributyl phosphate in dodecane as the dispersed phase. A high-speed imaging system is used to quantify the state of dispersion and obtain drop size distribution along with Sauter mean drop diameter. The effects of pulsing velocity, dispersed phase velocity and continuous phase velocity on dispersed phase holdup, drop size and consequentially specific interfacial area have been systematically studied for both internals. In all cases, slotted plates are characterized by generation of smaller drops and a higher holdup leading to significant improvement in specific interfacial area. Previously reported correlations for estimating dispersed phase holdup and Sauter mean diameter in pulsed sieve plate columns are found to be inadequate for slotted plate internals. Therefore, new correlations for prediction of holdup and drop diameter have been proposed for the new plate design.

Fine characterization of the capillary instability of free viscoelastic jets

The experimental approach presented in this article investigates low-velocity small-diameter cylindrical viscoelastic jets. It consists in producing and analyzing sets of jet portion images taken at different positions along the jet axis, i.e., from the nozzle producing the jet down to the spray region. A very significant part of the work was dedicated to develop analyzing tools: a proper orthogonal decomposition to identify the onset of the capillary instability, a procedure to determine the mean jet breakup length and a multi-scale tool to describe the jet local shape and its evolution along the jet axis. Used in a similar previous study, the multi-scale analysis has been extended in the present work. These tools are shown to be well suited to the experimental study conducted here, and in particular to meet the need for statistical analysis that free jets impose. They are applied to study the capillary instability of free jets of dilute polyethylene oxide solutions produced from a micrometer nozzle. The parameters of the study are the molar mass of the polymer and the velocity of the jet. Results on the detection of the capillary instability onset, the jet evolution dynamics towards the Bead On A String (BOAS) pattern, the local extensional relaxation time and the terminal elongational viscosity of the solutions, the bead coalescence mechanism and its influence on the size of the spray drops are obtained. Analysis of these results reveals that the polymers undergo two episodes of mechanical degradation during the process: the first one at injection, the second one during the elasto-capillary regime of the jet breakup. Moreover, the scenario in the literature suggesting a sufficiently relaxed axial tension of the flow for the capillary instability to occur is found to be not always valid. It is also shown that the average size of the drops correlates with the intensity of the bead coalescence mechanism that takes place on the BOAS. These results demonstrate the richness of the adopted approach and in particular of the multi-scale analysis to study the development of a fluid interfacial instability.

Allogeneic Serum Eye Drops: A Randomized Clinical Trial to Evaluate the Clinical Effectiveness of Two Drop Sizes.

Allogeneic serum from blood donors is starting to be used to treat patients with dry eye disease (DED). However, the optimal dose is not known. We therefore aimed to evaluate the clinical efficaciousness and user-friendliness of micro-sized versus conventional-sized allogeneic serum eye drops (SEDs). In a randomized trial, patients with DED first receive micro-sized SEDs (7µl/unit) for 1month, followed by a 1-month washout, before receiving conventional-sized SEDs (50µl/unit) for 1month; or vice versa. The primary endpoint was the Ocular Surface Disease Index (OSDI) score. Secondary endpoints were tear break-up time (TBT), tear production (TP), and presence of corneal punctate lesions (CP). The user-friendliness of both application systems was also compared. A linear mixed model for cross-over design was applied to compare both treatments. Forty-nine patients completed the trial. The mean OSDI score significantly improved from 52 ± 3 to 41 ± 3 for micro-sized SEDs, and from 54 ± 3 to 45 ± 3 for conventional-sized SEDs. Non-inferiority (margin = 6) of micro-sized SEDs was established. We demonstrate a significant improvement for TBT in case of conventional-sized SEDs and for CP in both treatment groups. TP trended towards an improvement in both treatment groups. The user-friendliness of the conventional drop system was significantly higher. For the first time, non-inferiority of micro-sized allogeneic SEDs was established. The beneficial effect of both SED volumes was similar as measured by the OSDI score. Although user-friendliness of the micro drop system was significantly lower, it is an attractive alternative as it saves valuable donor serum. ClinicalTrials.gov (NCT03539159).

Sub-cloud rain evaporation in the North Atlantic winter trade winds derived by pairing isotopic data with a bin-resolved microphysical model

Abstract. Sub-cloud rain evaporation in the trade wind region significantly influences the boundary layer mass and energy budgets. Parameterizing it is, however, difficult due to the sparsity of well-resolved rain observations and the challenges of sampling short-lived marine cumulus clouds. In this study, sub-cloud rain evaporation is analyzed using a steady-state, one-dimensional model that simulates changes in drop sizes, relative humidity, and rain isotopic composition. The model is initialized with relative humidity, raindrop size distributions, and water vapor isotope ratios (e.g., δDv, δ18Ov) sampled by the NOAA P3 aircraft during the Atlantic Tradewind Ocean–Atmosphere Mesoscale Interaction Campaign (ATOMIC), which was part of the larger EUREC4A (ElUcidating the RolE of Clouds–Circulation Coupling in ClimAte) field program. The modeled surface precipitation isotope ratios closely match the observations from EUREC4A ground-based and ship-based platforms, lending credibility to our model. The model suggests that 63 % of the rain mass evaporates in the sub-cloud layer across 22 P3 cases. The vertical distribution of the evaporated rain flux is top heavy for a narrow (σ) raindrop size distribution (RSD) centered over a small geometric mean diameter (Dg) at the cloud base. A top-heavy profile has a higher rain-evaporated fraction (REF) and larger changes in the rain deuterium excess (d=δD-8×δ18O) between the cloud base and the surface than a bottom-heavy profile, which results from a wider RSD with larger Dg. The modeled REF and change in d are also more strongly influenced by cloud base Dg and σ rather than the concentration of raindrops. The model results are accurate as long as the variations in the relative humidity conditions are accounted for. Relative humidity alone, however, is a poor indicator of sub-cloud rain evaporation. Overall, our analysis indicates the intricate dependence of sub-cloud rain evaporation on both thermodynamic and microphysical processes in the trade wind region.

Optimizing continuous emulsification with 3D printing

Multiphase processes are important in a wide range of industries including foods, pharmaceuticals, and consumer packaged goods. Improvement of these operations is challenging because of the complex hydrodynamics of the processing unit. We approached intensification of emulsification operations using continuous processing and hydrodynamic optimization with computer aided design and three dimensional printing (3dP) of fixed bed (FB) unit operations. We built and tested the emulsification capability of 3dPFB to establish key relationships among digital design variables, such as surface to volume ratio of the 3dPFB, 3.3≤s×10−4≤9.0m−1, and process performance metrics, such as drop size distribution (23.1±5.7<DSD<125.7±33.2μm). We showed that the emulsification performance can be designed a priori and demonstrated gradient 3dPFB design and complex emulsification to further establish the digital basis of design-property relationships and capabilities of 3dPFB in multiphase unit operations.

Multiscale simulation of nanodrop over surfaces with varying hydrophilicity

Macroscale solvers primarily depend on empirical constitutive relations, which curbs their applicability and reliability. On the other hand, though the microscale solver is much more accurate, it cannot be used for engineering scale domains because of the high computational cost. As an alternative, in the present study, a new adiabatic two-phase multiscale solver has been developed by coupling Finite volume and molecular dynamics solvers with the help of the domain decomposition method. Due to the finiteness of the molecular subdomain, molecules near the boundary miss forces from the missing molecules. An effort has been made to develop a new boundary force model which mimics the effect of those missing molecules. The spreading of a drop has been simulated over surfaces with varying hydrophilicity using the solver and compared with the result of full molecular dynamics simulation. Further, the computational time has been compared with the full molecular dynamics simulation for different drop sizes to show the usefulness of the developed model. Drop translation over biphilic surfaces has also been simulated with the new solver.

Role of hydrophobic sand particle granularity on water droplet post-impact dynamics

This paper investigates, experimentally and theoretically, the effects of sand particle size and hydrophobicity of a water drop impacting horizontal and inclined surfaces within a context of post-wildfire mudflow precursors. Although previous research established that wildfires often turn hillslope surficial soil hydrophobic, little research shows how wildfire-altered soil surfaces affect raindrops' impact behavior. Specific findings point to a significant effect of sand type on the drop impact dynamics. After spreading, the drop gathers back more on finer than coarser hydrophobic sands due to the substrate air-entrapped grooves, as in the Cassie-Baxter model, leading to drop retraction, rebound, splash, and fragmentation into droplets. The results indicate that if the hillslope dominant median grain size is fine, alteration to hydrophobicity would multifold enhance drop downhill mobility. In contrast, coarse sand surfaces exhibit minimal effects on drop mobility after hydrophobization. In addition, the paper proposes a modified Tang et al. model for the maximum spread factor as a function of the median grain size and hydrophobicity. This research offers essential findings from the perspective of the previous limiting understanding that only drop infiltration prevents erosion in hydrophilic slopes.

Further development and testing of a rainfall test rig

Changes made recently by The Ministry of Health New Zealand, to the internal noise design requirements for Preschools, has required that the design of the roof reduces rainfall noise to Ministry of Education, Design Quality Learning Spaces Acoustics (DQLS) Version 3.0, for rainfall noise. Previously Canterbury Acoustic Testing Services (CATS) had developed a rainfall noise test rig, in accordance with ISO 10140-1: 2016 [3] and ISO 10140-5:2010/Amd 1:2014 and carried out testing on a series of warm roof/ceiling constructions. Preschools tend to use cold roof systems where the thermal insulation sits on the ceiling, rather than in a warm roof, where the insulation is part of the roof structure. So there has been no tested performance data for rainfall noise acoustic design purpose, using a cold roof construction. As part of the testing program, there was a need to recommission the rig, to verify rain drop size and rainfall rate. A testing program was established, to include the base roof structure (roofing iron only) to a full buildup of roof and ceiling, to get a better understanding of how each component in the system contributes to the control of the rainfall noise.

Role of viscosity in turbulent drop break-up

We investigate drop break-up morphology, occurrence, time and size distribution, through large ensembles of high-fidelity direct-numerical simulations of drops in homogeneous isotropic turbulence, spanning a wide range of parameters in terms of the Weber number $We$ , viscosity ratio between the drop and the carrier flow $\mu _r=\mu _d/\mu _l$ , where d is the drop diameter, and Reynolds ( $Re$ ) number. For $\mu _r \leq 20$ , we find a nearly constant critical $We$ , while it increases with $\mu _r$ (and $Re$ ) when $\mu _r &gt; 20$ , and the transition can be described in terms of a drop Reynolds number. The break-up time is delayed when $\mu _r$ increases and is a function of distance to criticality. The first break-up child-size distributions for $\mu _r \leq 20$ transition from M to U shape when the distance to criticality is increased. At high $\mu _r$ , the shape of the distribution is modified. The first break-up child-size distribution gives only limited information on the fragmentation dynamics, as the subsequent break-up sequence is controlled by the drop geometry and viscosity. At high $We$ , a $d^{-3/2}$ size distribution is observed for $\mu _r \leq 20$ , which can be explained by capillary-driven processes, while for $\mu _r &gt; 20$ , almost all drops formed by the fragmentation process are at the smallest scale, controlled by the diameter of the very extended filament, which exhibits a snake-like shape prior to break-up.

A Statistical Framework for Evaluating Rain Microphysics in Model Simulations and Disdrometer Observations

AbstractStatistical analyses of a large disdrometer data set and a diverse set of model simulations for convection using the Regional Atmospheric Modeling System were conducted, with the mutual goal of providing insights into precipitation formation and microphysical processes. We demonstrate that a two‐moment bulk microphysical model successfully captures the dominant observed modes of variability in rainfall related to rainfall intensity and raindrop size distributions. The model reproduced the general distribution of observed precipitation groups (PGs) derived from Principal Component Analysis. The multi‐variable analysis also uncovered some shortcomings in the model as well as limitations of the disdrometer data. The model solutions were constrained in their predicted drop size distributions (DSDs) due to the fixed DSD parameters assumed in a two‐moment microphysics scheme. A case study from the Mid‐latitude Continental Clouds and Convection Experiment field project demonstrated how model results can be used to contextualize the disdrometer observations which are limited in sample size, spatial coherence, and detection of small drops and low drop concentrations. The case study also showed that the spatial patterns of the statistically derived PGs revealed by the model are consistent with the hypothesized microphysical processes that determine surface rain DSDs. This work demonstrates how leveraging the strengths of observations and models together can improve our understanding and representation of rain microphysical processes.

Dynamics of two unequal micron-sized viscous emulsion drops flowing in a two-dimensional constricted microcapillary channel: A numerical study

Emulsions containing unequal-sized droplets are ubiquitous. Compared to the equal-sized emulsion droplet coalescence process in porous media, unequal-sized emulsion droplets show distinctly different dynamics and features when flowing through the capillary channel. In this paper, we numerically studied the flow of two unequal small micron-size emulsion drops flowing in a two-dimensional (2D) half-sine pulse shape constricted tube. The finite element method solves the momentum, continuity, and level set equations. The oil–water interface is tracked using the level set method. Effects of drop size, capillary number (interfacial tension), viscosity ratio, and geometrical shape constriction effects on the droplets' flow behavior across the throat, its flow velocities, and average viscous pressure across the tube were investigated. It is found when there is a significant difference in diameters of the two un-equalized droplets, they will flow separately through the throat, whereas when the two un-equalized droplets’ size is close to each other, they coalescence with each other after passing through the constriction. Higher interfacial tension leads unequal-sized droplets to coalescence more readily while droplets pass without coalescence at low interfacial tension cases. The highest pressure drop is recorded at the critical point where the two unequal-sized droplets begin to merge in the constriction throat. Increasing droplet viscosity reduces the chances of coalescence and increases the average viscous pressure drop hence leading to mobility reduction. In the case of geometrical constrictions, circular-shaped contracted tubes offer the least resistance to fluid flow and are more appropriate for enhanced oil recovery processes. We hope our numerical findings will provide more information to facilitate the enhanced oil recovery process.

Jetting Dynamics of Viscous Droplets on Superhydrophobic Surfaces.

We investigated the dynamics of liquid jets engendered by the impact of droplets on a fractal superhydrophobic surface. Depending on the impact conditions, jets emanate from the free liquid surface with several different shapes and velocities, sometimes accompanied by droplet ejection. Experimental outcomes exhibit two different regimes: the singular jet and columnar jet. We found that droplet impacts at a lower impact velocity and low viscosity result in singular jets, attaining a maximum velocity nearly 20-fold higher than the impact velocity. The high-speed video frames reveal that the formation and subsequent collapse of the cylindrical air cavities within the droplet favor the formation of these high-speed singular jets. In contrast, the capillary wave focusing engenders columnar jets at a moderate to high impact velocity. With an increase in viscosity, singular jets are suppressed at lower impact velocities, whereas columnar jets are seen regularly. The columnar jets ascend and grow over time, feeding a bulbous mass, and subsequently the bulb separates itself from the parent jet due to capillary pinch-off phenomena. The quantitative analysis shows that columnar jets' top jet drop size varies nonmonotonically and is influenced by preceding jetting dynamics. At moderate viscosity, the drop size varies with jet velocity, following a power-law scaling. At very high viscosities, both singular and columnar jetting events are inhibited. The results are relevant to several recent technologies, including microdispensing, thermal management, and disease transmission.

Numerical simulation of multi-functional droplet production in microfluidics

In this work, we have investigated numerically the formation of stable Janus droplets in microfluidics flow focusing device. We have examined the effect of continuous phase capillary number (Ca) as it influences the drop size and the stability of a Janus drop for a fixed dispersed phase flow rate. The effect of flow rate ratio of disperse phases has also been examined to understand the relative distribution of the material in a single Janus droplet. Numerical simulations have been performed using the commercial software Ansys Fluent 19.2 with the Volume of Fluid (VOF) method to solve discrete versions of governing equations. We have extended our method to study the formation and stability of a ternary droplet. For this, a third inlet is incorporated at the middle of the initial channel geometry and fluid combination. In the case of ternary drop, we find that different phases re-arrange themselves after drop formation before reaching the final stable configuration.

Population balance modelling of an electrocoalescer

The mechanism of dehydration of a water-in-oil emulsion is complex and involves the growth of an emulsion of polydispersed water droplets in oil, under an electric field, and their gravitational settling and phase separation. In this work, a simple configuration is chosen to understand the mechanism of this complex process. A population balance-based model is developed to predict the performance of an electrocoalescer. The model explicitly accounts for the coalescence of water drops by the action of dipolar forces and gravity settling. A distributed parameter plug flow and a tank-in-series model are developed to account for the gravity settling. The dynamics of electrocoalescence are captured by analyzing the drop size distribution and mean diameter along with the height of the coalescer and time. A simplified model - considering that monodispersity prevails throughout the process is also developed, and the separation curves are compared with the polydispersed system. The effect of operational parameters, such as the strength of the electric field, water cut, viscosity of oil, the height of the coalescer, and polydispersity in the initial drop size distribution, is investigated. The main insight from this work is that there are essentially three stages of electrocoalescence, a slow initial incubation stage where droplets grow to around 1 mm in size without much settling, followed by a rapid settling of these droplets to set in the fast coalescence stage where most water is removed to result in a lean emulsion, followed by a slow simultaneous electrocoalescence and separation stage of this lean emulsion to result in a final separation. A scaled masterplot for the performance of an electrocoalescer, encompassing the effect of the process parameters is obtained. The model also suggests that electrocoalescence essentially leads to a polydisperse system and a population balance approach is critical to its analysis.