Formation Of Satellite Droplets Research Articles

Mean Droplet Size and Local Velocity in Horizontal Isothermal Free Jets of Air and Water, respectively, Viscous Liquid in Quiescent Ambient Air

AbstractMeasurements using two‐dimensional Phase Doppler Anemometry as well as high speed cinematography in free jets at several nozzle exit pressures and mass flow rates, show that the Sauter mean droplet diameter decreases with increasing air and liquid‐phase mass flow ratio due to the increase of the air stream impact on the liquid phase. This leads to substantial liquid fragmentation, respectively primary droplet breakup, and hence, satellite droplet formation with small sizes. This trend is also significant in the case of a liquid viscosity higher than that of water. The increased liquid viscosity stabilizes the droplet formation and breakup by reducing the rate of surface perturbations and consequently droplet distortions, ultimately also leading, in total, to the formation of smaller droplets. The droplet velocity decreases with the nozzle downstream distance, basically due to the continual air entrainment and due to the collisions between the droplets. The droplet collisions may induce further liquid fragmentation and, hence, formation of a number of relatively smaller droplets respectively secondary breakup, or may induce agglomeration to comparatively larger liquid fragments that may rain out of the free jet.

Drop Formation by Thermal Fluctuations at an Ultralow Surface Tension

We present experimental evidence that drop breakup is caused by thermal noise in a system with a surface tension that is more than 10(6) times smaller than that of water. We observe that at very small scales classical hydrodynamics breaks down and the characteristic signatures of pinch-off due to thermal noise are observed. Surprisingly, the noise makes the drop size distribution more uniform, by suppressing the formation of satellite droplets of the smallest sizes. The crossover between deterministic hydrodynamic motion and stochastic thermally driven motion has repercussions for our understanding of small-scale hydrodynamics, important in many problems such as micro- or nanofluidics and interfacial singularities.

Nonlinear viscous liquid jets from a rotating orifice

A liquid jet follows a curved trajectory when the orifice from which the jet emerges is rotating. Surface-tension-driven instabilities cause the jet to lose coherence and break to form droplets. The sizes of the drops formed from such jets are in general not uniform, ranging from drops with diameters of the order of the jet diameter to droplets with diameters which are several orders of magnitude smaller. This presentation details a theoretical investigation of the effects of changing operating parameters on the break-up of curved liquid jets in stagnant air at room temperature and pressure. The Navier–Stokes equations are solved in this system with the usual viscous free-surface boundary conditions, using an asymptotic method based upon a slender-jet assumption, which is clearly appropriate from experimental observations of the jet. Nonlinear temporal simulations of the break-up of the liquid jets using slender theory are also presented. These simulations based upon both a steady-trajectory assumption, and the more general equations which allow for an unsteady trajectory, show all the break-up modes viewed in experiments. Satellite-droplet formation is also considered.

Satellite droplet formation by unstable binary drop collisions

The formation of satellite droplets by stretching separation in unstable binary collisions of equal-sized drops is investigated. Based on data from detailed experiments on the formation and breakup of ligaments in off-center collisions with appreciable impact parameter, the process of satellite droplet formation is modeled. The experiments are carried out using two streams of monodisperse drops of various liquids. Drop sizes and velocities, and dimensions of ligaments and sizes of satellites are formed after unstable off-center collisions are measured with an image-processing technique. The model represents the physics of the collisions by functions of nondimensional characteristic numbers. The functions are determined using the experimental data. The experiments are well reproduced by the model, which reveals the importance of both the drop size and the liquid viscosity for the formation of the satellites.

Adaptive collision meshing and satellite droplet formation in spray simulations

Improved numerical methods and physical models have been applied to droplet collision modeling. Numerically, an adaptive collision mesh method is developed to calculate collision rate. This method produces a collision mesh that is independent of the gas phase mesh and adaptively refined according to local parcel number density. An existing model describing the satellite droplet formation during the collision process is improved to reflect the experimental findings that the satellite droplets are much smaller than the parent droplets. The adaptive collision mesh and the improved satellite model have been used to simulate three impinging spray experiments. The model was able to qualitatively predict the occurrence of small satellite drops and bi-modal post-collision drop size distributions. The effect of the collision mesh and the satellite droplet model on a high-speed non-evaporating diesel spray is also assessed.

Numerical simulations of jet pinching-off and drop formation using an energetic variational phase-field method

We study the retraction and pinch-off of a liquid filament and the formation of drops by using an energetic variational phase field model, which describes the motion of mixtures of two incompressible fluids. An efficient and accurate numerical scheme is presented and implemented for the coupled nonlinear systems of Navier–Stokes type linear momentum equations and volume preserving Allen–Cahn type phase equations. Detailed numerical simulations for a Newtonian fluid filament falling into another ambient Newtonian fluid are carried out. The dynamical scaling behavior and the pinch-off behavior, as well as the formation of the consequent satellite droplets are investigated.

Deformation and breakup of a stretching liquid bridge covered with an insoluble surfactant monolayer

The breakup of surfactant-laden drops and jets is of technological interest and fundamental scientific importance. Surfactants are routinely used to control the breakup of drops and jets in applications ranging from inkjet printing to crop spraying. Accurate computation of breakup of surfactant-laden drops and jets is often the key to the development of new applications and to providing a rational fundamental understanding of both existing and emerging applications. While highly accurate algorithms for studying the breakup of surfactant-free drops and jets are well documented and much is now known about the dynamics in such situations, little is known by contrast about the closely related problem of interface rupture when surfactant effects cannot be neglected. The deformation and breakup of a stretching liquid bridge of an incompressible Newtonian fluid whose surface is covered with an insoluble surfactant monolayer are analyzed here experimentally and computationally. In the experiments, high-speed visualization is used to capture the transient deformation of a bridge. The dynamic shapes of bridges (captive between two rods of 3.15 mm diameter) are captured and analyzed with a time resolution of 1 ms. The bridge lengths are 3.15 mm initially and about 4–7 mm at breakup, which occurs after stretching for about 0.1–0.2 s, depending on the volume and viscosity of the liquid and the surface density of spread monolayers. The dynamics of a surfactant-covered bridge is governed by the Navier-Stokes and convection-diffusion equations. First, these equations are solved with a three-dimensional, but axisymmetric, or two-dimensional (2D), finite element algorithm using elliptic mesh generation. Second, the governing set of 2D equations is reduced to a set of one-dimensional (1D) equations by means of the slender-jet approximation and the resulting set of 1D equations is solved with a 1D finite element algorithm. The presence of surfactant results not only in the lowering of surface tension and the capillary pressure, but also in surface tension gradients and Marangoni stresses, both of which affect the transient dynamics leading to breakup. In particular, the role of Marangoni stresses in delaying bridge breakup and on formation of satellite droplets is investigated as a function of the initial surface density and surface activity of the surfactant, and surface Peclet number that measures the importance of convection relative to diffusion. The predictions of the 2D algorithm are confirmed to be faithful to the physics by demonstrating that the computed results accord well with the experiments and existing scaling theories. In the pinch-off region, the surfactant is swept out of a thinning neck by strong convection. The calculations thus reveal that the scaling behavior in the presence of surfactant parallels that observed in the absence of surfactant, in accordance with recent reports by others. The 2D computations and the experiments are used in tandem to identify regions in the space of governing parameters where the 1D equations can be used with confidence.

Simulations of binary drop collisions with a multiple-relaxation-time lattice-Boltzmann model

In this paper, we report simulations of drop-drop collisions using a multi-relaxation-time multiphase flow lattice Boltzmann model. Employing a multi-relaxation-time (MRT) model in lieu of the Bhatnagar-Gross-Krook (BGK) model used in the standard lattice-Boltzmann equation enables realization of stable computations of drop collisions at relatively lower fluid viscosities without increasing the lattice resolution to prohibitive levels. Head-on and off-center computations of collisions are carried out using axisymmetric and three-dimensional (3D) versions of the MRT model, respectively. Time-resolved results showing the interactions of the interfaces of drops for different characteristic nondimensional parameters are presented. Computations show that at low Weber numbers, We, coalescence with relatively smaller deformation occurs, sometimes entrapping a stable microbubble. At higher We, head-on collisions lead to reflexive separation with or without the formation of satellite droplets. The size of the satellite droplets appears to increase with increase in the We. The Ohnesorge number, Oh, seems to modulate the transient characteristics and the outcome of collisions. It is found that the greater the Oh, the smaller is the size of the satellite droplets formed. For off-center collisions at a given We, at lower values of the impact parameter permanent coalescence is observed, while higher values result in separation by stretching action. These findings are in satisfactory agreement with experimental observations.

Numerical simulation of binary liquid droplet collision

A numerical investigation of binary droplet collision has been conducted. The complete process of the collision of two liquid droplets is dynamically simulated by solving the incompressible Navier-Stokes equations coupled with the convective equation of the level set function that captures the interface between the liquid and the gas phases. The simulations cover four major regimes of binary collision: bouncing, coalescence, reflexive separation, and stretching separation. For water droplets in air, the numerical results are compared with the experiments by and Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] on collision consequences. For hydrocarbon (C14H30) droplets in nitrogen gas, the simulated results are compared in detail with the time-resolved photographic images of the collision processes obtained by Qian and Law [J. Fluid Mech. 331, 59 (1997)] in every collision regime. The present numerical results suggest that the mechanism of a bouncing collision is governed by the macroscopic dynamics. However, the fact that the present macroscopic numerical model is unable to capture the collision regime of coalescence after minor deformation supports the speculation that its mechanism is related to the microscopic dynamics. Furthermore, the transition from bouncing to coalescence collisions has been predicted and agrees well with the analytical model. The mechanism of satellite droplet formation for head-on collision and stretching separation collision is also studied based on the detailed time-resolved dynamic simulation results. It is then confirmed that end pinching is the main cause of satellite formation in head-on collisions whereas the capillary-wave instability becomes dominant in large impact parameter cases. In the case of an intermediate impact parameter, the effects of twisting and stretching due to the angular momentum and the inertia of the colliding droplets are significant for the satellite formation.

Lattice Boltzmann model for axisymmetric multiphase flows

A lattice Boltzmann model is presented for axisymmetric multiphase flows. Source terms are added to a two-dimensional standard lattice Boltzmann equation for multiphase flows such that the emergent dynamics can be transformed into the axisymmetric cylindrical coordinate system. The source terms are temporally and spatially dependent and represent the axisymmetric contribution of the order parameter of fluid phases and inertial, viscous, and surface tension forces. A model which is effectively explicit and second order is obtained. This is achieved by taking into account the discrete lattice effects in the Chapman-Enskog multiscale analysis, so that the macroscopic axisymmetric mass and momentum equations for multiphase flows are recovered self-consistently. The model is extended to incorporate reduced compressibility effects. Axisymmetric equilibrium drop formation and oscillations, breakup and formation of satellite droplets from viscous liquid cylindrical jets through Rayleigh capillary instability, and drop collisions are presented. Comparisons of the computed results with available data show satisfactory agreement.

Modeling of droplet collision-induced breakup process

The present article proposes a new droplet collision model considering droplet collision-induced breakup process with the formation of satellite droplets. The new model consists of several equations to investigate the post-collision characteristics of colliding droplets and satellite droplets. These equations are derived from the conservations of droplet mass, momentum, and energy between before and after collision, and make it possible to predict the number of satellite droplets, and the droplet size and velocity in the analytical way. To validate the new collision model, numerical calculations are performed and their results are compared with experimental data published earlier for binary collision of water droplets. It is found from the results that the new model shows good agreement with experimental data for the number of satellite droplets. It can be also shown that the predicted mean diameter by the new model decrease with increasing the Weber number because of the collision-induced breakup, whereas the O’Rourke model fails to predict the size reduction via the binary droplet collision.

Droplet collision processes in an inter-spray impingement system

The main objectives of the present article are in developing and evaluating a new model for the droplet collision, and in discussing the physical feature for the mutual impinging sprays. The new model is originally devised to be capable of predicting the droplet collision-induced breakup accompanied with the formation of satellite droplets. From the well-established conservation equations, the several formulae are newly proposed by consideration of some important regimes such as bounce, coalescence, and stretching and reflexive separation. This formulation makes it possible to predict the number of satellite droplets, and the droplet sizes and velocities. The extensive experiments are conducted for the inter-spray impingement systems under the various conditions to investigate the influence of impinging angle and impingement distance upon the spray characteristics. The droplet sizes and velocities are measured by the phase Doppler particle analyzer system and the distribution of liquid volume fraction is also measured by the self-manufactured patternator. In addition, numerical predictions by the new model and the O’Rourke model are compared with experimental data for the various parameters. It is found that the SMD (Sauter mean diameter) measured in the downstream region after inter-spray impingement are 40% smaller than those for the case of single nozzle. The new model shows vigorous breakup during collision, which is no longer seen in the O’Rourke model.

미세노즐을 통한 액적형성에 관한 수치적 연구

The drop ejection process from a micro nozzle is investigated by numerically solving the conservation equations for mass and momentum. The liquid-gas interface IS tracked by a level set method which is extended for two-fluid flows With irregular solid boundaries. Based on the numerical results, the liquid jet breaking and droplet formation behavior is found to depend strongly on the pulse type of forcing pressure and the contact angle at the gas-liquid-solid interline. The negative pressure forcing can be used to control the formation of satellite droplets. Also, various nozzle shapes are tested to Investigate their effect on droplet formation.br/

Impact dynamics of drops on thin films of viscoelastic wormlike micelle solutions

The impact dynamics of water drops on thin films of viscoelastic wormlike micelle solutions is experimentally studied using a high-speed digital video camera at frame rates up to 4000 frame/s. The composition and thickness of the thin film is modified to investigate the effect of fluid rheology on the evolution of crown growth, the formation of satellite droplets and the formation of the Worthington jet. The experiments are performed using a series of wormlike micelle solutions composed of a surfactant, cetyltrimethylammonium bromide (CTAB), and a salt, sodium salicylate (NaSal), in deionized water. The linear viscoelastic shear rheology of the wormlike micelle solutions is well described by a Maxwell model with a single relaxation time while the steady shear rheology is found to shear thin quite heavily. In transient homogeneous uniaxial extension, the wormlike micelle solutions demonstrate significant strain hardening. The size and velocity of the impacting drop is varied to study the relative importance of Weber, Ohnesorge, and Deborah numbers on the impact dynamics. The addition of elasticity to the thin film fluid is found to suppress the crown growth and the formation of satellite drops with the largest effects observed at small film thicknesses. A new form of the splashing threshold is postulated which accounts for the effects of viscoelasticity and collapses the satellite droplet data onto a single master curve dependent only on dimensionless film thickness and the underlying surface roughness. Additionally, a plateau is observed in the growth of the maximum height of the Worthington jet height with increasing impact velocity. It is postulated that the complex behavior of the Worthington jet growth is the result of a dissipative mechanism stemming from the scission of wormlike micelles.

On the evolution of particle size average and size distribution in suspension polymerization processes

AbstractThe dispersion of methyl methacrylate (MMA) and its suspension polymerization were used as models to elaborate the evolution of particle size average and size distribution in the course of suspension polymerization. The underlying mechanisms for the occurrence of the dynamic and static steady states in the population of drops were defined and their effects on the evolution of drop/particle size average and size distributions were examined. The characteristic intervals of suspension polymerizations (transition, steady‐state, growth, and identification) were elaborated. The formation of satellite droplets and their evolution in the course of polymerization were also discussed.

Drop Ejection from an Oscillating Rod

The dynamics of a liquid drop which is supported on a solid rod that is forced to undergo large-amplitude, time-periodic oscillations along its axis is studied using a computational approach based on the Galerkin/finite element method and an adaptive mesh generation technique which enables discretization of overturning interfaces and analysis of drop breakup. When the forcing amplitude is small, the drop deformations are small and the drop remains intact as it undergoes shape oscillations. Larger forcing amplitudes result in the formation of a liquid thread, or neck, which connects two fluid masses: the fluid adjacent to the rod and a nearly globular fluid mass. If the drop deforms such that its length is sufficiently large, the thread ruptures and the globular fluid mass—a so-called primary drop—is ejected from the fluid remaining on the rod. The critical forcing amplitude Ac necessary to attain this length and hence drop breakup, the interface shape at breakup, and the volume of the ejected primary drop are determined computationally as functions of the Reynolds number, forcing frequency, and drop size. Over a wide range of values of the forcing amplitude above Ac, ejection occurs as the drop recedes from its maximum length during its second period of oscillation. These results show that Ac increases as Reynolds number and/or drop size decreases. The maximum length the drop reaches prior to ejection and the position and velocity of the rod for times approaching breakup are shown to profoundly affect the dynamics of drop breakup and the resulting interface shapes. These results show that the forcing amplitude and/or frequency can be chosen so as to prevent the formation of long liquid necks, which typically favor the formation of satellite droplets after breakup. Because drop ejection does not rely on external forces other than those due to rod motion, this method of drop formation holds promise for microgravity applications as well as terrestrial drop-on-demand technologies in which gravitational force is negligible compared to surface tension force.

The formation of satellite droplets by unstable binary drop collisions

Experimental investigations on the process of satellite droplet formation by unstable binary drop collisions are presented. The experiments are carried out using two monodisperse streams of drops of equal size. A systematic variation of the parameters influencing the collisions leads to an extended version of the stability nomogram which involves the numbers of satellite droplets formed by stretching separation after off-center collisions. The time scales for the formation of liquid filaments and their breakup into the satellites are measured and, in the case that a single satellite is formed, the satellite size is measured by means of a phase-Doppler anemometer. Furthermore, a theoretical model for the breakup of cylindrical liquid filaments in head-on and off-center collisions is presented. The model is based on a linear stability analysis of the filament formed after the collision. The critical wavelength associated with the largest deformation energy is calculated and identified with the disturbance which eventually breaks the filament and determines the number of satellites formed. Comparisons with experiments by Ashgriz and Poo [J. Fluid Mech. 221, 183 (1990)] for the head-on and near-head-on cases yield agreement of the numbers of satellites formed.

Adsorption Behavior of Nonionic Surfactants Studied by Drop Volume Technique

This study shows that the drop volume technique can be used to determine the adsorption behavior and interfacial adsorption kinetics of surfactants at fluid interfaces. Using this tensiometric method, one can determine not only the interfacial tension of the pure phases, but also the critical concentration for the formation of micelles (CMC) in a surfactant system, the quasi-static (equilibrium) interfacial tension, the diffusion coefficient as a function of surfactant concentration, and the maximum adsorption density at the interface. The determination of the dynamic interfacial tension allows to indirectly characterize the kinetics of surfactant adsorption. The time dependence of the interfacial coverage resulting from this adsorption process is well described by two approximation solutions (for short and long adsorption times), with the result that the diffusion coefficients calculated as a function of surfactant concentration using these two methods show good agreement. The droplet formation and dripping process of a surfactant solution in a capillary was found to be quite different depending on whether the process occurred in gaseous or fluid surroundings. In particular, the formation of satellite droplets was different for the two different media, in terms of both the volume and shape of the satellite droplets.

Dynamics of Growth and Breakup of Viscous Pendant Drops into Air

This paper presents a numerical study of the dynamics of a viscous liquid drop that is being formed directly at the tip of a vertical tube into ambient air. A model is developed to predict the evolution of the drop shape and its breakup based on RIPPLE, which is a solution algorithm for computing transient, two-dimensional, incompressible fluid flow with surface tension on free surfaces of general topology (D. B. Kothe and R. C. Mjolsness,AIAA J.30, 2694 (1992)). The full Navier–Stokes system is solved by using finite-difference formulation on a Eulerian mesh. The mesh is fixed in space, with the flow and surface moving through it to ensure accurate calculations of complex free surface flows and topology, including surface breakup and coalescence. The novel feature of the numerical algorithm is the use of a Eulerian volume-tracking approach which allows the calculations to pass the breaking point during formation of a drop continuously without interruption or numerical modification and, therefore, to explore the features of generation of satellite droplets. The effects of physical and geometric parameters on the nonlinear dynamics of drop growth and breakup are investigated. The focus here is on drop breakup and subsequent formation of satellite droplets. The effects of finite inertial, capillary, viscous, and gravitational forces are all accounted for to classify different formation dynamics and to elucidate features of satellite droplet generation. The numerical predictions are compared with experimental measurements for water drops, and the results show good agreement.

Droplet size control in liquid jet breakup

A Boundary Element Method (BEM) has been developed to investigate the nonlinear evolution of the surface of liquid jets injected from circular orifices under unsteady inflow conditions. For fixed wavelength perturbations, the model predicts the formation of main and satellite droplets. The size of the droplets is affected by changes in the perturbation wavelength, perturbation magnitude and Weber number. Satellite droplet velocities are less than main droplet velocities due to the sequential shedding of droplets from the orifice. Using this information, one can determine the likelihood of droplet recombinations downstream of the initial pinching event.