Droplet Collision Research Articles

Critical charges for droplet collisions

Two micron-sized water droplets approaching each other do not always coalesce due to the cushioning effect of the air between them. When the droplets do not carry any electrical charges, one needs to consider the breakdown of hydrodynamics at very small scales to decide whether the droplets collide and coalesce or not. In contrast, two approaching droplets that are oppositely charged always coalesce if the charges are large enough. To find the charge for which the transition to charge-dominated collisions occurs, we computed the collision efficiency of charged, hydrodynamically interacting droplets settling in quiescent air, including the noncontinuum regime at small interfacial distances. For oppositely charged droplets, we find that the transition occurs when a saddle point of the relative droplet dynamics exits the region within which the continuum hydrodynamics breaks down. For cloud droplets with radii 16 and 20µm, we observe that the transition occurs at ∼103 elementary charges e. For charges smaller than this, we predict that the coalescence rate depends primarily upon the Knudsen number (Kn, the ratio of the mean-free-path of air to the mean droplet radius), whereas coalescence for much larger charges does not depend upon Kn. For droplets charged with the same polarity, we find the critical charge to be substantially larger (∼104e for the above radii) for reasons that we discuss. Published by the American Physical Society 2024

Mechanism of collision and drainage of liquid droplet around sphere placed within a hollow cylinder

It is attempted earnestly to elucidate the mechanism of collision and drainage of liquid mass around the spherical substrate suspended within the hollow cylinder using Gerris open-source code by employing Volume of Fluid (VOF) methodology. Various influencing parameters, namely, sphere-to-droplet diameter ratio (Ds/Do), Weber number(We), Ohnesorge number (Oh), and Bond number(Bo) are employed to observe the drainage mechanism through the constricted path. The pattern of the interfacial morphology of droplet collision and drainage mechanism is presented using numerical contours. It is important to mention herein that the droplet undergoes several important stages like collision, cap formation, engulfment, drainage, and pinch-off. The passage between the sphere and the cylinder is sufficiently wider at a lower value of Ds/Do due to which the liquid mass is drained out completely without any hindrance. The drainage process becomes considerably faster at a higher We compared to a lower We. In addition, the flow of liquid mass through the passage gets delayed at a greater Oh than a lower Oh assuming a given value of We and Ds/Do. The liquid drop requires less time to pass through the constricted path at lower Bo for a given value of Ds/Do and We. We have also attempted to quantify the drainage of liquid volume passes through the passage, which is denoted as (Q*=Q/Qo). One can notice the increasing pattern of Q/Qo with continuous progress of time stamp for all cases of Ds/Do for a fixed value of We.

Numerical investigation of non-Newtonian droplet collisions: Comparison of volume of fluid and the local front reconstruction method with experimental data

Droplet-droplet collisions of non-Newtonian fluids are often encountered in industrial applications such as spray drying, fluid catalytic cracking, coating and granulation. However, there has been limited focus on a comprehensive analysis of the dynamics of these non-Newtonian binary droplet collisions. In this work, the non-Newtonian binary droplet collisions of 500 ppm xanthan gum solutions are simulated using the Volume of Fluid method and the Local Front Reconstruction Method to determine the applicability of these methods for the simulations of binary non-Newtonian droplet collisions. After verification, the simulations are compared to experimental data from literature. The outcomes for off-center collisions in the simulations resemble the experimental observations, including the oscillation of the ligament. For head-on collisions, the initial interactions and collision dynamics can be predicted with both methods at low Weber numbers, while LFRM shows improved performance at higher Weber numbers. Further, the use of an effective viscosity for the simplified representation of the droplet collision has been proven unsuccessful due to the absence of a universal effective viscosity for all situations.

Are turbulence effects on droplet collision–coalescence a key to understanding observed rain formation in clouds?

Rain formation is a critical factor governing the lifecycle and radiative forcing of clouds and therefore it is a key element of weather and climate. Cloud microphysics-turbulence interactions occur across a wide range of scales and are challenging to represent in atmospheric models with limited resolution. Based on past experiments and idealized numerical simulations, it has been postulated that cloud turbulence accelerates rain formation by enhancing drop collision-coalescence. We provide substantial evidence for significant impacts of turbulence on the evolution of cloud droplet size distributions and rain formation by comparing high-resolution observations of cumulus congestus clouds with state-of-the-art large-eddy simulations coupled with a Lagrangian particle-based microphysics scheme. Turbulent coalescence must be included in the model to accurately represent the observed drop size distributions, especially for drizzle drop sizes at lower heights in the cloud. Turbulence causes earlier rain formation and greater rain accumulation compared to simulations with gravitational coalescence only. The observed rain size distribution tail just above cloud base follows a power law scaling that deviates from theoretical scalings considering either a purely gravitation collision kernel or a turbulent kernel neglecting droplet inertial effects, providing additional evidence for turbulent coalescence in clouds. In contrast, large aerosols acting as cloud condensation nuclei ("giant CCN") do not significantly impact rain formation owing to their long timescale to reach equilibrium wet size relative to the lifetime of rising cumulus thermals. Overall, turbulent drop coalescence exerts a dominant influence on rain initiation in warm cumulus clouds, with limited impacts of giant CCN.

Three-dimensional lattice Boltzmann model with self-tuning equationof state for multiphase flows.

In this work, the recent lattice Boltzmann (LB) model with self-tuning equationof state (EOS) [Huang et al., Phys. Rev. E 99, 023303 (2019)2470-004510.1103/PhysRevE.99.023303] is extended to three dimensions for the simulation of multiphase flows, which is based on the standard three-dimensional 27-velocity lattice and multiple-relaxation-time collision operator. To achieve the self-tuning EOS, the equilibrium moment is devised by introducing a built-in variable, and the collision matrix is improved by introducing some velocity-dependent nondiagonal elements. Meanwhile, the additional cubic terms of velocity in recovering the Newtonian viscous stress are eliminated to enhance the numerical accuracy. For modeling multiphase flows, an attractive pairwise interaction force is introduced to mimic the long-range molecular interaction, and a consistent scheme is proposed to compensate for the ɛ^{3}-order discrete lattice effect. Thermodynamic consistency in a strict sense is established for the multiphase LB model with self-tuning EOS, and the wetting condition is also treated in a thermodynamically consistent manner. As a result, the contact angle, surface tension, and interface thickness can be independently adjusted in the present theoretical framework. Numerical tests are first performed to validate the multiphase LB model with self-tuning EOS and the theoretical analyses of bulk and surface thermodynamics. The collision of equal-sized droplets is then simulated to demonstrate the applicability and effectiveness of the present LB model for multiphase flows.

Experimental insight into dynamics of water droplet impacting on solid surface and theoretical prediction for maximum spreading coefficient at low Weber number

The hydrodynamics of a droplet impacting solid surface at low Weber number has been studied comprehensively by using a high-speed camera and a theoretical approach based on the improved models of surface energy and viscous dissipation. The impact process is elucidated by analyzing quantitatively the interface evolution of droplet impact solid surface, and the effects of glycerol solution concentration, surfactant concentration, impact velocity, and wall contact angle on spreading width and rebounding height are extensively investigated, respectively. Four stages, namely, approaching, spreading, retracting and stabilizing stages are identified visually during a complete droplet collision. Increasing the concentration of glycerol solution can simultaneously reduce droplet spreading width and rebounding height. However, improving surfactant concentration or enhancing impact velocity can promote droplet spread but hinder its rebound. Decreasing wall contact angle is beneficial to droplet propagation, whereas disadvantageous to droplet rebound. Both surface energy and viscous dissipation are accurately considered based on a real geometric shape and an improved spreading time at the maximum spreading, and thus a novel theoretical formula for the maximum spreading coefficient of droplet impacting at low Weber number has been developed and proved to have a higher prediction accuracy than the previous models under present experimental conditions.

Hypergolic Ignition by Off-Center Binary Collision of Monoethanolamine-NaBH4 and Hydrogen Peroxide Droplets

Hypergolic ignition of H2O2 and MEA-NaBH4 by off-center collision of their droplets was experimentally studied, focusing on the characteristics and mechanism of droplet mixing, droplet heating and evaporation, and gas-phase ignition. The whole collision ignition process was divided into five stages, which were compared, respectively, with that of head-on collision. Under the condition of a slightly off-center collision (for cases where B < 0.35), H2O2 droplets penetrate MEA-NaBH4 droplets after the collision and coalesce with it, but the internal H2O2 drop inside the MEA-NaBH4 droplet does not form a stable sphere. Instead, it rotates and expands inside the mixed droplet. With B increasing to 0.59, the droplets no longer coalesce after collision but separate away, forming satellite droplets. In such cases, multi-ignition mode is observed. When B increases to a certain extent, specifically, 0.85, a grazing collision is observed such that no mass transfer exists during the interaction of droplets, which leads to ignition failure. A theoretical model quantifying droplet swelling rate was established to calculate the volume change of the droplet. It was found that the swelling can be attributed to the flash boiling of superheated internal H2O2 fluid. Meanwhile, the ignition delay time was found to linearly decrease with B at various Wes until the extent where the chemical reaction takes over control, leading to an almost constant time delay defined as RDT. Additionally, the regime of ignition modes corresponding to different droplet mixing features is summarized in the We-B parametric space.

Impacts of Stochastic Coalescence Variability on Warm Rain Initiation Using Lagrangian Microphysics in Box and Large-Eddy Simulations

Abstract Various coalescence methods for Lagrangian microphysics schemes are tested in box and large-eddy simulation (LES) models, including the stochastic all-or-nothing (AON) superdroplet method (SDM) and a deterministic version of SDM (dSDM) that applies a fractional approach similar to the average impact method. In LES, variabilities driven by microphysics and by flow realizations are separated using the “piggybacking” technique. Rain initiation averaged over many realizations of the box model is delayed, and rain variability increases as the number of superdrops per collision volume NSD is decreased using SDM. In contrast, rain initiation time using SDM in LES is insensitive to NSD for 32 ≤ NSD ≤ 512. This is explained through the interaction between LES grid boxes, each acting as a separate collision volume. Variability across the ensemble of LES collision volumes using SDM results in rain quickly initiating in some of the LES grid cells at low NSD and leading to a similar overall timing of rain initiation from the cloud compared to simulations with high NSD. There is a ∼20% decrease in the total rain mass and mean rain flux as NSD is increased from 32 to 256, with little additional change as NSD is increased from 256 to 512. The fractional coalescence approach in dSDM leads to reduced microphysical variability and a 15–18-min delay in rain initiation compared to SDM. An additional LES ensemble with microphysical variability feeding back to the dynamics shows that flow variability dominates the impact of microphysical variability on rain properties. Thus, flow variability must be constrained to isolate impacts of microphysical variability. Significance Statement An emerging tool in cloud microphysics modeling represents drops by computational particles called “superdroplets” that evolve in the modeled flow. Recent studies have documented that different superdroplet models produce widely varying predictions of rain. Understanding these differences is an important step in the wider adoption of these models by the community. Here, we examine different methods for representing droplet collision-coalescence in a superdroplet model and sensitivity to the number of superdroplets employed. The timing of rain initiation is insensitive to the superdroplet number in 3D cloud simulations, but rain is substantially delayed using a coalescence method that limits random variability in droplet collisions. We also show that flow variability must be constrained to isolate impacts of microphysical variability on rain properties.

Quantitative liquid storage by billiards‐like droplet collision on surfaces with patterned wettability

AbstractThere has been significant interest in researching droplet transport behavior on composite wetting surfaces. However, current research is primarily focused on modifying individual droplets and lacks an in‐depth investigation into high‐precision droplet storage. This study introduces a “billiard ball” droplet transport and storage platform (TSP) with differentiated areas. Within this platform, the volume of droplets stored in the area reaches a consistent threshold through droplet “scrambling,” inspired by the water‐gathering behavior of spiders. The TSP involves connecting two regions of different sizes using a three‐dimensional stepped wedge angle structure. However, this connection is not seamless, leaving a 2‐mm gap between the regions. This gap is intentionally designed to enable continuous droplet transfer while preventing any static migration. Through systematic experimental and simulation analysis, we investigated the influence of superhydrophilic pattern structures and parameters on quantitative droplet storage. We established a functional relationship between the pattern area and the stored volume, and analyzed the intrinsic mechanism of droplet collision separation. This enabled us to achieve on‐demand quantitative droplet storage and autonomize the storage process. The “billiard ball” droplet transport–storage platform proposed in this study holds promising applications in the fields of biomedical and organic chemistry.

Gap in drop collision rate between diffusive and inertial regimes explains the stability of fogs and non-precipitating clouds

Rain drops form in clouds by collision of submillimetric droplets falling under gravity: larger drops fall faster than smaller ones and collect them on their path. The puzzling stability of fogs and non-precipitating warm clouds with respect to this avalanche mechanism has been a longstanding problem. How can droplets of diameter around 10 $\mathrm {\mu }$ m have a low collision probability, inhibiting the cascade towards larger and larger drops? Here we review the dynamical mechanisms that have been proposed in the literature and quantitatively investigate the frequency of drop collisions induced by Brownian diffusion, electrostatics and gravity, using an open-source Monte Carlo code taking all of them into account. Inertia dominates over aerodynamic forces for large drops, when the Stokes number is larger than $1$ . Thermal diffusion dominates over aerodynamic forces for small drops, when the Péclet number is smaller than $1$ . We show that there exists a range of size (typically 3–30 $\mathrm {\mu }$ m for water drops in air) where neither inertia nor Brownian diffusion are significant, leading to a gap in the collision rate. The effect is particularly important, due to the lubrication film forming between the drops immediately before collision, and secondarily to the long-range aerodynamic interaction. Two different mechanisms regularise the divergence of the lubrication force at vanishing separation: the transition to a non-continuum regime in the lubrication film, when the separation is comparable to the mean free path of air, and the induction of a flow inside the drops due to shear at their surfaces. In the gap between inertia-dominated and diffusion-dominated regimes, dipole–dipole electrostatic interactions becomes the major effect controlling the efficiency of drop collisions.

Wettability, droplet impact and anti-icing performance of micro-nano hierarchical structure on Ti6Al4V surface via integrating of chemical modification and laser-induced plasma micromachining

Superhydrophobic functional surfaces are widely used in medical treatment, pipeline transportation, and ship corrosion protection and have great potential in the field of anti-icing. Ultrafast laser-induced plasma micromachining (LIPMM) combined with a chemical modification of a fluoroalkyl low surface-energy substance (Novec) was used to fabricate superhydrophobic surfaces with periodic layered micro-nano arrays on Ti6Al4V. The wettability, droplet collision behavior and wear resistance of surfaces with different physical and chemical properties were analyzed. In terms of static anti-icing, based on the classical nucleation theory, the icing-delay performance of different surfaces was analyzed. Ice adhesion strength and frosting properties were also studied. It was found that the micro-nano structure surface fabricated by LIPMM had strong hydrophobicity (contact angle of 164°, roll-off angle of 1.0°), high icing delay time (3072 s, 4 μL of water droplet on the surface at −10 °C), low ice adhesion strength (38.2 kPa), and better durability. Additionally, the droplets bounced off this surface after colliding at different angles (0°, 5°, 10°, and 20°). This study provides a feasible solution for fabricating anti-icing surfaces on Ti6A14V.

Physical and Numerical Experimentation of Water Droplet Collision on a Wall: A Comparison between PLIC and HRIC Schemes for the VOF Transport Equation with High-Speed Imaging

Liquid films are often found in engineering applications with thicknesses ranging from micrometer scales to large scales with a wide range of applications. To optimize such systems, researchers have dedicated themselves to the development of new techniques. To further contribute to this development, the objective of this work is to present the results of the collision of water droplets on a wall by means of experimentation and numerical simulations. For physical experimentation, an injector is used to generate a chain of water droplets that collide with the opposite wall, forming a liquid film. Images of the droplets were obtained using two high-speed recording cameras. The results for different droplet sizes and impact angles are presented and the relationship between the momentum parameter and non-dimensional pool size was established. Modeling such processes is a common challenge in engineering, with different techniques having their advantages and limitations. The simulations in this work were run using the volume of fluid method, which consists of solving a transport equation for the volume fraction of each considered fluid. A correlation was found between the surface tension to momentum transport ratio, Scd, and the non-dimensional pool size for different droplet sizes and impact angles. Regions where partial depositions were most likely to occur were found via physical experiments.

Secondary crushing of droplets of water-oil emulsions

When fuel oil is supplied to an accurate chamber, its spraying process takes place due to injectors and sprinkler devices. This process is called primary droplet crushing. It is often not enough to burn fuel efficiently. Since the size of fuel droplets in the combustion chamber often reaches several millimeters, which increases underburning and leads to uneven burnout. In such cases, it is advisable to use secondary crushing of water-oil fuel droplets. Secondary crushing of droplets reduces the average size of droplets in the fuel spray torch by several times. At the first stage of secondary crushing of droplets, their collisions with each other in the jet are realized, after which the formed droplets are subjected to collisions with the walls of thermal equipment. At the next stage, pyrolysis of such droplets occurs at the periphery of the jet, which leads to the formation of solid particles and subsequent collisions of droplets of water-oil fuels with them. At the final stage, the formed secondary fragments are subjected to intense heating in the combustion chamber, which allows for micro-explosive grinding. The present study is aimed at studying the characteristics of secondary crushing of water-oil fuel droplets with the addition of specialized additives. The results of the conducted studies have shown that the use of an additive based on a special combination of positively and negatively charged ions reduces the size of fuel droplets by 25%. It has been found that when using such an additive, the ratio of the free surface areas of droplets increases several times with a combination of all secondary grinding modes.

Influence of collision conditions between aerosol flows of liquid droplets and solid particles typical for wet vortex dust collectors

Various industrial devices and systems make use of collisions of droplets with solid particles in aerosol flows. The characteristics of these collisions are usually predicted adopting the same approaches as for binary collisions of a liquid droplet with a solid particle. However, the conditions of such binary collisions are different from those in the spray composition. There are very few experimental findings for sprays. The purpose of this research was to experimentally determine the characteristics of interaction of droplets with particles of slurry fuel components in sprays. High-speed three-dimensional video recording made it possible to identify conditions when liquid droplets break up, and droplets and particles agglomerate to form slurry droplets. Droplet-particle interaction regimes were identified. Collective effects in a cascade of droplet-particle interactions were recognized. The frequency of collision regime occurrence was determined, considering the recorded collective effects in sprays. The characteristics of droplet-particle collisions in sprays were compared with those of binary interactions. Conditions were determined when the findings on binary collisions can be adapted to different systems with multi-phase sprays. The findings obtained promote research and development in the field of secondary atomization of composite fuel droplets.

Numerical study of head-on collisions between two glass microsphere droplets

The collision of molten glass microsphere droplets represents a fundamental phenomenon in spheronization, yet a comprehensive understanding of this process remains elusive. A numerical simulation is conducted to investigate the head-on collision dynamics of two molten glass microsphere droplets at varying Weber numbers, by integrating the level set and volume of fluid methods. Three distinct collision regimes are identified: merging, separation into satellite-free droplets, and separation leading to the formation of satellite droplets. Furthermore, the critical Weber numbers delineating the different regimes are presented. Examination of axial and radial variations in the droplets reveals the existence of five distinct states spanning the three collision regimes. The distribution of external vortices around the droplets directly influences the outcomes of droplet collisions. High-pressure regions and high-pressure liquid bridges within droplets serve as key factors in determining the merging or separation of the droplets. Region of high pressure at the end of the liquid bridge acts as a critical indicator for distinguishing between collision separations with and without satellite droplet generation. Observations of velocity and pressure distributions in separations that produce satellite droplets are consistent with the end pinch-off mechanism. This study holds significant implications for controlling high sphericity during the spheronization of glass microsphere droplets.

Study on the influence of collision conditions on the surface morphology of compound droplets

In this study, a three-dimensional compound droplet collision numerical model is established by using volume of fluid. The morphological evolution of compound hollow droplets affected by high-speed solid droplet was studied in detail. Parameterized analysis is conducted on the velocity VS, center distance ϕ, and diameter ζ of high-speed small droplets. Through the analysis of the compound droplets flow field, it is found that the broken mode of compound droplets is caused by the increase in Pn (dimensionless pressure) and θ (velocity angle). The results show that the surface Pn of compound droplets is positively correlated with the velocity VS of high-speed small droplets, while there is a more complex relationship with the dimensionless center distance ϕ and dimensionless diameter ζ. When the values of ϕ and ζ are appropriate, Pn can reach its maximum value. The broken mode of compound droplets can be divided into three categories: shear deformation, shear crushing, and violent crushing.

Droplet collision with hydrophobic and superhydrophobic surfaces: Experimental studies and numerical modeling

The characteristics of the collision of water droplets with textured hydrophobic and superhydrophobic surfaces obtained using two techniques were studied experimentally. The surface processing techniques are based on laser modification of the surface layer and changes in its chemical composition. Weber numbers in the experiments were varied in the range of 10–200. Regimes of water droplet-surface collision, the critical conditions for the transition between regimes, as well as integral characteristics of the formed liquid fragments were identified. The main characteristics of the process under study, such as the droplet spreading diameter, the height of its rebound from the surface, the number of secondary fragments during its break up were obtained experimentally. A model with a two-dimensional axisymmetric formulation was used to predict the characteristics of water droplet-textured surface collision based on the phase field method. The results of experimental studies and numerical modeling are in satisfactory agreement (differences of no more than 3–5 %). The conditions, when it is necessary to consider the values of static and dynamic contact angles during the modeling process, were determined.

Mathematical modeling of droplet collisions in sprays under microgravity conditions

Two-phase flows under microgravity conditions play a crucial role in Space technology and science. Studying the behavior of dispersed droplets suspended in a gas flow and their influence on the characteristics of the carrier flow is the main task of computational modeling of turbulent two-phase flows. To understand the features and predict the behavior of such flows, along with experimental studies, it is necessary to develop mathematical models, which adequately describe all the basic physical and chemical processes in a gas-droplet environment at different scales.In this paper we obtain solutions for the problem of two droplets collision, using solutions for cumulative jets, and propose droplet collision outcome criterion. This research will focus on the process of two interacting droplets coalescence into one and coalescence with subsequent separation into two or more droplets. A semi-analytical method has been developed for application of the solution of the cumulative jet problem to the problem of droplet collision. A differential equation has been obtained that describes the following possible outcomes of droplet collision: coalescence and coalescence with subsequent separation. A criterion for determining the outcome of on-head droplet collision has been obtained. In accordance with the developed criterion, the number and size of formed droplets are obtained. The effect of collision on moving droplet evaporation in a heated atmosphere was regarded.

New insights into head-on bouncing of unequal-size droplets on a wetting surface

The impact of a liquid droplet with another droplet or onto a solid surface are important basic processes that occur in many applications such as agricultural sprays and inkjet printing, and in nature such as pathogens transport by raindrops. We investigated the head-on collision of unequal-size droplets of the same liquid on wetting surfaces using the direct numerical simulations technique at different size ratios. The unsteady Navier–Stokes equations are solved and the liquid–gas interface is tracked using the geometric volume-of-fluid method. The numerical model is validated by comparing simulation results of two extreme cases of droplets bouncing with the experimental data from previous studies and the agreement is quite accurate. The validated model is employed to simulate droplets bouncing at several size ratios at different Weber numbers and Ohnesorge number. Two distinct regimes are identified, namely, the inertial regime, where the restitution coefficient is a constant value close to 0.3, the viscous regime, where the restitution coefficient declines. To understand the bouncing behaviour, the velocity field is analysed and an energy budget calculation is performed. The distribution of the sessile droplet energy is found to be important and the sessile droplet surface energy is calculated by its deformation characteristics such as crater depth. Finally, a scaling analysis is performed to rationalize the insensitivity of the coefficient of restitution in the inertial regime, and its decline in the viscous regime, at large size ratios.

Droplet collision of hypergolic propellants

AbstractIn the present mini‐review, droplet impacting on a liquid pool, jet impingement, and binary droplet collision of nonreacting liquids are first summarized in terms of basic phenomena and the corresponding nondimensional parameters. Then, two representative hypergolic bipropellant systems, a hypergolic fuel of N,N,N′,N′‐tetramethylethylenediamine (TMEDA) and an oxidizer of white fuming nitric acid (WFNA) and a monoethanolamine‐based fuel (MEA‐NaBH4) and a high‐density hydrogen peroxide (H2O2), are discussed in detail to unveil the rich underlying physics such as liquid‐phase reaction, heat transfer, phase change, and gas‐phase reaction. This review focuses on quantifying and interpreting the parametric dependence of the gas‐phase ignition induced by droplet collision of liquid hypergolic propellants. The advances in droplet collision of hypergolic propellants are important for modeling the real hypergolic impinging‐jet (spray) combustion and for the design optimization of orbit‐maneuver rocket engines.