Collision Behavior of Heterogeneous Liquid Droplets

The vaporization of a freely moving drop in a uniform, high-temperature gas stream is investigated through direct numerical simulation. The incompressible Navier-Stokes equations with surface tension and phase change are solved in conjunction with the energy equations of each phase. The sharp liquid-gas interface is tracked using the geometric Volume-of-Fluid (VOF) method and an immersed Dirichlet boundary condition for temperature is imposed at the interface. The simulation approach is validated by simulating water and acetone drops at nearly zero Weber numbers, and the simulation results agree very well with the empirical relation for spherical drops. Parametric simulations were conducted to investigate the aerodynamic breakup of vaporizing drops at low to moderate Weber and Reynolds numbers. The range of Weber numbers considered has covered the vibrational and bag breakup regimes. Through the simulation results, we have characterized the impact of drop deformation and breakup on the drop vaporization rate. When the drop Weber number increases, the windward surface area increases more rapidly over time. As a result, the rate of drop volume reduction also increases. The correlation between the vaporization rate and the windward surface area is examined for different Weber and Reynolds numbers. Using the approximate correlation between the drop vaporization rate and the windward surface area and the TAB model for drop deformation, a new time-dependent drop vaporization model is proposed. The present model agrees well with the simulation results and shows a significant improvement over the conventional model for spherical drops.

A theoretical study of liquid column deformation discharged perpendicularly into a subsonic transverse gas flow is carried out. Liquid jet trajectory prior to breakup is determined from an analytical approach for momentum flux ratios lower than 100 and Weber numbers up to 100. Force balance on liquid element is analyzed in free stream direction assuming that surface tension and viscous forces are small compared to the aerodynamic force for the above range of momentum flux ratio and Weber number. Mass shedding from jet surface and liquid evaporation are neglected. A logarithmic correlation for penetration depth of liquid jet with circular cross-section is derived which takes into account the liquid to gas momentum flux ratio and drag coefficient. The changes in free stream properties e.g. the gas viscosity and velocity are incorporated in terms of the drag coefficient. The results are presented for various test conditions corresponding to their experimental counterpart in literature.

Hydrodynamics of collision interactions between a particle and gas‐liquid interface such as droplet/film is of keen interest in many engineering applications. The collision interaction between a suspended liquid (water) film of thickness 3.41 ± 0.04 mm and an impacting hydrophilic particle (glass ballotini) of different diameters (1.1–3.0 mm) in low particle impact Weber number ( ) range (1.4–33) is reported. Two distinct outcomes were observed—particle retention in the film at lower Weber number and complete penetration of the film toward higher Weber number cases. A collision parameter was defined based on energy balance approach to demarcate these two interaction regimes which agreed reasonably well with the experimental outcomes. It was shown that the liquid ligament forming in the complete penetration cases breaks up purely by “dripping/end pinch‐off” mechanism and not due to capillary wave instability. An analytical model based on energy balance approach was proposed to determine the liquid mass entrainment associated with the ligament which compared well with the experimental measurements. A good correlation between the %film mass entrained and the particle Bond number ( ) was obtained which indicated a dependency of Bo1.72. Computationally, a three‐dimensional CFD model was developed to simulate these interactions using different contact angle boundary conditions which in general showed reasonable agreement with experiment but also indicated deficiency of a constant contact angle value to depict the interaction physics in entirety. The computed force profiles from computational fluid dynamics (CFD) model suggest dominance of the pressure force over the viscous force almost by an order of magnitude in all the Weber number cases studied. © 2015 American Institute of Chemical Engineers AIChE J, 62: 295–314, 2016

Experimental research into the characteristics of child droplets formed due to collisions of liquid fragments in a gas

Binary collision of a burning droplet and a non-burning droplet of xylene: Outcome regimes and flame dynamics

We report experimental results characterizing the dynamics of a liquid jet impinging normally on hydrophilic, hydrophobic, and superhydrophobic surfaces spanning the Weber number (based on the jet velocity and diameter) range from 100 to 1900. The superhydrophobic surfaces are fabricated with both hydrophobically coated silicon and polydimethylsiloxane that exhibit alternating microribs and cavities. For all surfaces a transition from a thin radially moving liquid sheet occurs. This takes the form of the classical hydraulic jump for the hydrophilic surfaces but is markedly different for the hydrophobic and superhydrophobic surfaces, where the transition is significantly influenced by surface tension and a break-up into droplets is observed at high Weber number. For the superhydrophobic surfaces, the transition exhibits an elliptical shape with the major axis being aligned parallel to the ribs, concomitant with the frictional resistance being smaller in the parallel direction than in the transverse direction. However, the total projected area of the ellipse exhibits a nearly linear dependence on the jet Weber number, and was nominally invariant with varying hydrophobicity and relative size of the ribs and cavities. For the hydrophobic and superhydrophobic scenarios, the local Weber number based on the local radial velocity and local depth of the radially moving liquid sheet is observed to be of order unity at the transition location. The results also reveal that for increasing relative size of the cavities, the ratio of the ellipse axis (major-to-minor) increases.

We study the head-on collision between two weakly deformable droplets, each of radius a (in the range 10–150 μm), moving towards one another with characteristic impact speeds ±U′c. The liquid comprising the drop has density ρd and viscosity μd. The collision takes place in an incompressible continuum gas with ambient density ρg [Lt ] ρd, ambient pressure p′∞ and viscosity μg [Lt ] μd The gas–liquid interface is surfactant free with interfacial tension σ. The Weber number based on the drop density, Wed ≡ ρdU′2ca/σ [Lt ] 1 and the capillary number based on the gas viscosity, Cagg ≡ μgU′cσ [Lt ] 1. The Reynolds number characterizing flow inside the drops satisfies Red ≡ aU′cρd/μd [Gt ] We1/2d and the Stokes number characterizing the drop inertia, St ≡ 2Wed(9Cag)−1 ≡ 2(ρdU′caμ−1g)/9 is O(1) or larger.We first analyse a simple model for the rebound process which is valid when St [Gt ] 1 and viscous dissipation in both the gas and in the drop can be neglected. We assume that the film separating the drops only serves to keep the interfaces from touching by supplying a constant excess pressure 2σ/a. A singular perturbation analysis reveals that when ln(We−1/4d) [Gt ] 1, rebound occurs on a time scale t′b = &23frac;1/2πaWe1/2dln1/2 (We−1/4d)U′−1c. Numerical results for Weber numbers in the range O(10−6) − O(10−1) compare very well to existing experimental and simulation results, indicating that the approximate treatment of the bounce process is applicable for Wed < 0:3.In the second part of the paper we formulate a general theory that not only models the flow inside the drop but also takes into account the evolution of the gap width separating the drops. The drop deformation in the near-contact inner region is determined by solving the lubrication equations and matching to an outer solution. The resulting equations are solved numerically using a direct, semi-implicit, matrix inversion technique for capillary numbers in the range 10−8 to 10−4 and Stokes numbers from 2 to 200. Trajectories are mapped out in terms of Cag and the parameter χ = (Wed/Cag)1/2 so that St ≡ 2/9χ2. For small Stokes numbers, the drops behave as nearly rigid spheres and come to rest without any significant rebound. For O(1) Stokes numbers, the surfaces deform noticeably and a dimple forms when the gap thickness is approximately O(aCa1/2). The dimple extent increases, reaches a maximum and then decreases to zero. Meanwhile, the centroids of the two drops come to rest momentarily and then the drops rebound, executing oscillatory motions before finally coming to rest. As the Stokes number increases with Cag held fixed, more energy is stored as deformation energy and the maximum radial extent of the dimple increases accordingly. For St [Gt ] 1, no oscillations in the centroid positions are observed, but the temporal evolution of the minimum gap thickness exhibits two minima. One minimum occurs during the dimple evolution process and corresponds to the minimum attained by the dimple rim. The second minimum occurs along the axis of symmetry when the dimple relaxes, a tail forms and then retracts. A detailed analysis of the interface shapes, pressure profiles and the force acting on the drops allows us to obtain a complete picture of the collision and rebound process.

The effect of bubble acceleration on the liquid film thickness in micro tubes

When water droplets impact solid surfaces at high velocity, they often develop radial protrusions, known as fingering instabilities, that subsequently break up during spreading and retraction, a process termed splashing. Here, we investigate the fingering dynamics of shear-thinning viscoelastic droplets impacting superhydrophobic surfaces. At low polymer concentrations, liquid elasticity promotes the emergence of elongated fingers while simultaneously stabilizing them against breakup, thereby suppressing splashing. In contrast, an increasing polymer concentration enhances viscous damping, reducing the number of fingers and ultimately suppressing the fingering instability. Our results indicate that the onset of fingering is governed by the interplay of inertia, surface tension, and viscous stresses, while the number of fingers scales robustly with the Weber number. This highlights the dominance of inertia-capillary dynamics in our range of Weber numbers once the instability is triggered. Remarkably, all impact outcomes resulted in complete rebound, in contrast to a previous observation for viscoelastic droplets. Finally, we employ a theoretical framework to predict the temporal evolution of the mean ligament length across polymer concentrations, providing quantitative insight into how elasticity modifies drop retraction dynamics.

Mesler entrainment is the formation of a very large number of very small bubbles by a relatively low velocity drop impacting a liquid surface. The role of the Weber number in Mesler entrainment has received significant attention. However, the effect of the capillary number, which quantifies the relative importance of viscous and surface tension forces, has not been explored. This is due primarily to the fact that virtually all Mesler entrainment research has used a single liquid, water, as the working fluid. This, combined with certain experimental restrictions, makes difficult an independent variation of the Weber and capillary numbers. To address this problem, Mesler entrainment was investigated using two silicone oils, having kinematic viscosities of 0.65 cSt and 10.0 cSt, respectively, revealing the effect of the capillary number on Mesler entrainment, a result which has not been obtained heretofore. The silicone oils give extremely repeatable results when compared to water. © 2012 American Institute of Chemical Engineers AIChE J, 2012

We experimentally investigate the binary droplet impact dynamics on flat and square-micropillared hydrophobic polydimethylsiloxane (PDMS) substrates. The primary droplet is initially impacted on the substrate and allowed to achieve static conditions, which may be characterized by the Cassie-Baxter or Wenzel state, depending on the droplet impact velocity and pitch of micropillars. Following this, a secondary droplet is introduced, which impacts on the primary droplet as a vertical head-on collision. We examine how surface wettability (by varying the solid fraction of substrates from 1-0.069) and Weber number (1.41-11.21) influence the dynamic interaction of droplets and their resulting fate. High-speed visualization is utilized to capture the transient evolution of binary droplet impact. Different interaction regimes are observed, namely, no lift-off, lift-off, partial lift-off, direct coalescence, and conglutination with droplet breakup. When the vertical head-on collision of droplets occurs, at a given Weber number, the lift-off probability on micropillared substrates increases in comparison to that of no lift-off on flat substrates, which further transits to partial lift-off/direct coalescence/conglutination based on variations in solid fraction and Weber number. An energy-based analysis is presented to model the maximum spreading ratio of secondary droplets and maximum axial height attained during the receding phase of binary droplets, which agrees with present measurements. Our results show that, in the Cassie-Baxter state, the maximum height does not depend on solid fraction. Instead, it is governed by the Weber number and increases with Weber number. Finally, to replace the complex form of the energy equation, simplified empirical correlations are proposed for the maximum spreading ratio of secondary droplets and the maximum axial height. Insights from this study can be used to modify surface morphology for desired droplet impact, benefiting applications such as spray cooling, self-cleaning, and energy harvesting.

A complete knowledge of the effect of droplet viscosity on droplet-droplet collision outcomes is essential for industrial processes such as spray drying. When droplets with dispersed solids are dried, the apparent viscosity of the dispersed phase increases by many orders of magnitude, which drastically changes the outcome of a droplet-droplet collision. However, the effect of viscosity on the droplet collision regime boundaries demarcating coalescence and reflexive and stretching separation is still not entirely understood and a general model for collision outcome boundaries is not available. In this work, the effect of viscosity on the droplet-droplet collision outcome is studied using direct numerical simulations employing the volume of fluid method. The role of viscous energy dissipation is analysed in collisions of droplets with different sizes and different physical properties. From the simulations results, a general phenomenological model depending on the capillary number (Ca, accounting for viscosity), the impact parameter (B), the Weber number (We), and the size ratio (Δ) is proposed.

This study investigates whether adding ridges to a superhydrophobic cylindrical surface can reduce contact times compared to those of ridged flat or cylindrical surfaces, inspired by the shortened contact time achieved by adding ridges to flat surfaces. The study focuses on studying azimuthal ridges on the cylinder through experimentation, emphasizing the impact dynamics and contact time characteristics under varying We (Weber number) and D* (dimensionless droplet diameter). Within the ultralow Weber number range (ULWR), low Weber number range (LWR), and medium Weber number range (MWR), the contact time is longer than on ridged flat surfaces. In the high Weber number range (HWR), the opposite is observed: increased inertial forces lead to the rupture of the liquid film above the ridges due to Rayleigh-Plateau instability. As a result, the primary droplet splits into two sections with curvature effects promoting its recoiling and rebounding. This study introduces a criterion, defined as C = We/D*, and finds that when C exceeds 2.42, not only is the contact time shorter than on ridged flat or cylindrical surfaces, but it also further decreases with an increase in We or a decrease in D*. The contact time characteristics observed in the HWR offer potential applications in areas such as anti-icing.

The present article focuses on the numerical simulation of two-dimensional (2D) binary droplet collision outcomes in an incompressible continuum gas. The Weber numbers applied to predict the various collision outcomes are within the range of those reported in the previous experiments. The droplet collision dynamics are numerically predicted by solving, separately in both phases, the unsteady 2D Navier–Stokes equations using the control volume approach on non-staggered grids. The complex topological changes of droplet interfaces are described by the level set method (LSM), which simultaneously, provides an efficient and robust way to deal automatically with breaking and merging of interfaces without any numerical constraints. The obtained results demonstrated the essential role played by the surface tension in droplet collision dynamics as a stabilising or destabilising force leading to rebound, coalescence or fragmentation collision outcomes. The mechanism of droplet disintegration at relatively high Weber number and the formation of satellite droplets are also discussed.

We investigate the interfacial dynamics involved in the impact of a droplet on a liquid-liquid system, which involves the impingement of an immiscible core liquid drop from a vertical separation onto an interfacial shell liquid layer floating on a host liquid bath. The dynamics have been studied for a wide range of impact Weber numbers and two different interfacial shell liquids of varying volumes. The core drop, upon impact, dragged the interfacial liquid into the host liquid, forming an interfacial liquid column with an air cavity inside the host liquid bath. The dynamics is resolved into cavity expansion and rapid contraction, followed by thinning of the interfacial liquid. The interplay of viscous dissipation, interfacial pull, and core drop inertia influenced the necking dynamics. The viscous dissipation increases with the thickness of the interfacial layer, which depends on the volume and lateral spread over the water. The necking dynamics transitioned from inertia-dominated deep seal closure at higher spread, lower interfacial film volumes, and higher Weber numbers into inertia-capillary-dominated deep seal closure with an increase in film volumes, decrease in the spread of the interfacial fluid, or decrease in Weber number and finally into a no-seal closure at high volumes, low spread, and low Weber numbers.