Drop Breakup Research Articles

Computational investigation of drop behavior and breakup in peristaltic flow

The behavior of liquid drops in the retropulsive jet produced by a peristaltic wave is investigated computationally. The computational geometry consists of a tube which is closed at one end, with the peristaltic wave that deforms the boundary moving toward it. A modified solver with the capability to couple mesh deformation and adaptive mesh refinement around moving drops was developed and validated with experimental data, and good agreement was found. A parametric study was then performed to determine the effect of interfacial tension, viscosity ratio, relative occlusion, and initial drop position on the drop's behavior and breakup characteristics. In particular, breakup regimes on graphs of capillary number vs viscosity ratio were determined for each initial drop position and relative occlusion. It was found that these breakup regimes were bounded above and below, and an optimal capillary number for breakup was determined. The volume of the parent drop after breakup decreased linearly with capillary number for low capillary numbers and was independent of the viscosity ratio. For higher capillary numbers, this volume generally increased with the viscosity ratio. It was also found that a drop with lower interfacial tension reached the apex plane sooner than a drop with higher interfacial tension, but once there, took longer to pass through this plane and longer to breakup. The viscosity ratio had negligible influence on the drop transit times for viscosity ratios less than one, while the breakup time generally increased with the viscosity ratio.

Towards a Standard Method for Estimating Fragmentation Rates in Emulsification Experiments

The fragmentation rate function connects the fundamental drop breakup process with the resulting drop size distribution and is central to understanding or modeling emulsification processes. There is a large interest in being able to reliably measure it from an emulsification experiment, both for generating data for validating theoretical fragmentation rate function suggestions and as a tool for studying emulsification processes. Consequently, several methods have been suggested for measuring fragmentation rates based on emulsion experiments. Typically, each study suggests a new method that is rarely used again. The lack of an agreement on a standard method has become a substantial challenge. This contribution critically and systematically analyses four influential suggestions of how to measure fragmentation rate in terms of validity, reliability, and sensitivity to method assumptions. The back-calculation method is identified as the most promising—high reliability and low sensitivity to assumption—whereas performing a non-linear regression on a parameterized model (as commonly suggested) is unsuitable due to its high sensitivity. The simplistic zero-order method is identified as an interesting supplemental tool that could be used for qualitative comparisons but not for quantification.

A numerical study of hollow water drop breakup during freezing

We present a numerical investigation of the breakup and freezing of a pendant hollow water drop beneath a cold curved surface. The drop contains a bubble surrounded by a shell of water that forms at an outer wetting angle of θo with the surface. The freezing begins on the cold curved surface and evolves in the direction of gravity. As it freezes, the water accumulates and forms a bulbous end at the bottom of the drop. Breakup can occur, inducing a daughter water drop. As a result, the freezing process of the remaining hollow drop attached to the surface takes less time, and the frozen drop shrinks. However, this breakup has no effect on the bubble. The various parameters under consideration include the Bond number Bo, the Stefan number St, the size of the bubble, and the angle θo. It is found that the breakup of the drop during freezing takes place for increasing Bo (from 0.1 to 3.0), increasing θo (from 60° to 120°), decreasing St (in the range of 0.01–0.64), or decreasing bubble size. On the other hand, the shape of the curved surface has little influence on the breakup of the drop. Phase diagrams of θo vs Bo and of St vs Bo are also presented to provide a more general picture of the breakup and freezing of the water drop.

Effect of inertia on capillary-driven breakup of drops surrounded by another fluid

We study the capillary-driven breakup of a slender drop suspended in a quiescent viscous fluid using direct numerical simulation. We focus on a parametric space comprising viscosity ratio and Ohnesorge number. While the large Ohnesorge number approximation of the problem has received experimental and theoretical attention over the years, the influence of inertia—at small Ohnesorge number—on the behavior of the slender drop is not well studied. We first validate our simulation results with previous experimental results at large viscosity ratios. We then consider the drop suspended in a quiescent fluid and systematically study the capillary-driven breakup of the drop at different Ohnesorge numbers and viscosity ratios. Our simulations reveal that the slender drop breaks up under all conditions, but the instability is transitional for some viscosity ratios. By considering both inertial and viscous effects in the ambient surrounding fluid, we show how the structure of the flow field is modified upon the introduction of inertia and how the viscosity of the surrounding fluid aids in vorticity diffusion. Finally, we extend the stability diagram for drops, which classifies them into asymptotically unstable and asymptotically stable states in a parametric space comprising viscosity ratio and Ohnesorge number. We finely probe the stability diagram and present a stability curve in the parametric space of viscosity ratio and Ohnesorge number.

Deformation of drops by outer eddies in turbulence

Drop deformation in fluid flows is investigated as an exchange between the kinetic energy of the fluid and the surface energy of the drop. We show analytically that this energetic exchange is controlled only by the stretching (or compression) of the drop surface by the rate-of-strain tensor. This mechanism is analogous to the stretching of the vorticity field in turbulence. By leveraging the non-local nature of turbulence dynamics, we introduce a new decomposition that isolates the energetic exchange arising from local drop-induced surface effects from the non-local action of turbulent fluctuations. We perform direct numerical simulations of single inertial drops in isotropic turbulence and show that an important contribution to the increments of the surface energy arises from the non-local stretching of the fluid–fluid interface by eddies far from the drop surface (outer eddies). We report that this mechanism is dominant and independent of surface dynamics in a range of Weber numbers in which drop breakup occurs. These findings shed new light on drop deformation and breakup in turbulent flows, and opens the possibility for the improvement and simplification of breakup models.

The Role of Stochastic Time-Variations in Turbulent Stresses When Predicting Drop Breakup—A Review of Modelling Approaches

Many industrially relevant emulsification devices are of the high-energy type, where drop deformation and subsequent breakup, take place due to intense turbulent fluid–drop interactions. This includes high-pressure homogenizers as well as rotor-stator mixers (also known as high-shear mixers) of various designs. The stress acting on a drop in a turbulent flow field varies over time, occasionally reaching values far exceeding its time-averaged value, but only during limited stretches of time, after which it decreases down to low values again. This it is one factor separating turbulent from laminar emulsification. This contribution reviews attempts to take this intermittently time-varying stress into account in models predicting the characteristic drop diameter resulting from emulsification experiments, focusing on industrially applicable emulsification devices. Two main frameworks are discussed: the Kolmogorov–Hinze framework and the oscillatory resonance framework. Modelling suggestions are critically discussed and compared, with the intention to answer how critical it is to correctly capture this time-varying stress in emulsification modelling. The review is concluded by a list of suggestions for future investigations.

Dynamics of a viscous drop under an oscillatory uniaxial extensional Stokes flow

We quantify the transient deformation and breakup of a neutrally-buoyant drop with viscosity λμ∗ immersed in another Newtonian fluid with viscosity μ∗ undergoing oscillatory uniaxial extension at zero Reynolds number. The interfacial tension acting between drop phase and medium phase is γ∗. The drop is initially a sphere of radius a∗. Since the external flow oscillates harmonically with a frequency ω∗, the strength of the imposed flow is characterized by an instantaneous capillary number, Ca=Ca0cos(Det), where Ca0=μ∗ε̇a∗/γ∗ and De=ω∗μ∗a∗/γ∗ is the dimensionless frequency, or Deborah number. Here, ε̇ is the rate of extension in the imposed flow. We utilize boundary-integral computations to calculate the evolution of drop interface as a function of Ca0 and De, focusing primarily on the case where the drop and surrounding fluid have equal viscosities. The computations suggest two families of behavior for the drop deformation. First, below a critical Deborah number (which we determine to be in the interval 0.375<De<1.0), the drop breaks up in a finite time at a critical capillary number that is a function of De. At sufficiently small De the critical capillary number increases linearly with De and the breakup mode is that of “center-pinching”. On increasing De the break-up mode switches to “end-pinching”, and on further increasing De it appears that the critical capillary number diverges at a critical Deborah number between 0.375 and 1.0. This divergence signals the transition to the second family of behavior where the drop attains a long-time periodic state, or alternance, regardless of Ca0. However, at large Ca0 the drop dynamics exhibits a two time-scale behavior: the drop deforms instantaneously at a fast capillary relaxation time-scale τ∗=μ∗a∗/γ∗, whereas the maximum deformation attained during a cycle of the imposed flow grows at the slow time-scale τ∗Ca0=ε̇(μ∗a∗/γ∗)2. As such, the state of alternance is approached exceedingly slowly at large Ca0. Lastly, we perform calculations for different viscosity ratios and find the drop dynamics to be in qualitative agreement with above observations.

Fall and break-up of viscous miscible drops in a Hele-Shaw cell

We study the fall of pancake-shaped drops in a Hele-Shaw cell filled with a more viscous ambient fluid in the case where the drop and ambient fluid are miscible. We propose a theoretical expression for the falling velocity of the drops which takes into account elongated drops with width smaller than the gap of the cell. We also provide experimental evidence for the break-up of miscible drops, which can be caused by internal fluid motion within the drop, or by an instability in the shape of the drop.

Theoretical deformation modeling and drop size prediction in the multimode breakup regime

A theoretical model has been proposed to incorporate internal flow mechanics to better predict the deformation and the resulting breakup of a liquid drop in a continuous uniform air jet in the multimode breakup regime. A Weber-number-dependent breakup criterion predicts the deformation of the drop at the time of the breakup, which occurs at the time the internal pressure at the drop equator exceeds internal pressure at the pole. This breakup criterion is used to determine an improved coefficient used in the Taylor Analogy Breakup (TAB) model. The TAB model is also extended to include the effects of turbulence within the drop. Hill vortices form within the drop as a result of viscous forces and flow around the drop. It is proposed that these vortices contribute to the deformation that eventually leads to the outer ring and smaller drop within the ring that is classic to multimode breakup. Instability analysis is used to model the breakup of the outer ring and predict the resultant droplet sizes. The model-predicted breakup times and ring breakup droplet diameter are compared with experimental results collected using digital in-line holography.

An efficient phase-field method for turbulent multiphase flows

With the aim of efficiently simulating three-dimensional multiphase turbulent flows with a phase-field method, we propose a new discretization scheme for the biharmonic term (the 4th-order derivative term) of the Cahn-Hilliard equation. This novel scheme can significantly reduce the computational cost while retaining the same accuracy as the original procedure. Our phase-field method is built on top of a direct numerical simulation solver, named AFiD (www.afid.eu) and open-sourced by our research group. It relies on a pencil distributed parallel strategy and a FFT-based Poisson solver. To deal with large density ratios between the two phases, a pressure split method [1] has been applied to the Poisson solver. To further reduce computational costs, we implement a multiple-resolution algorithm which decouples the discretizations for the Navier-Stokes equations and the scalar equation: while a stretched wall-resolving grid is used for the Navier-Stokes equations, for the Cahn-Hilliard equation we use a fine uniform mesh. The present method shows excellent computational performance for large-scale computation: on meshes up to 8 billion nodes and 3072 CPU cores, a multiphase flow needs only slightly less than 1.5 times the CPU time of the single-phase flow solver on the same grid. The present method is validated by comparing the results to previous studies for the cases of drop deformation in shear flow, including the convergence test with mesh refinement, and breakup of a rising buoyant bubble with density ratio up to 1000. Finally, we simulate the breakup of a big drop and the coalescence of O(103) drops in turbulent Rayleigh-Bénard convection at a Rayleigh number of 108, observing good agreement with theoretical results.

Breakup model of oscillating drops in turbulent flow field

Following the drop oscillation breakup mechanism, a theoretical model for drop breakup probability is proposed based on the three-dimensional Maxwell velocity distribution. The model considers both the interfacial energy increase constraint and viscous energy increase constraint. The model shows that for low-viscous drops, the breakup probability is determined by the Weber number (WeL), and for intermediate or high viscous drops, the breakup probability is determined by the combined influence of the Weber number (WeL) and the Ohnesorge number (Oh). By combining the theoretical model of drop breakup time constructed in our previous work, the breakup frequency model is obtained based on the statistical description framework. The accuracy and generality of the model were then validated using the direct experimental data. Moreover, effects of the drop diameter, turbulent energy dissipation rate, and interfacial tension on the predicted drop breakup frequency were analyzed in detail.

Investigation of the dispersing characteristics of antral contraction wave flow in a simplified model of the distal stomach

The dispersing characteristics of antral contraction wave (ACW) flow in the antrum are investigated by reproducing the flow generated by an ACW and determining its effect on liquid drops. The goal is to gain information about the flow field and mechanical stresses, which are responsible for the food disintegration. Toward this end, a model antrum prototype was constructed, consisting of a cylinder that was closed at one end to represent the antrum and closed pylorus. A moving hollow piston with a parabolic inner contour was used to model an ACW. A computational model was developed that reflects this prototype. Experiments and simulations were first performed for fluids with different rheological properties, two relative occlusions (0.60 and 0.75), and several ACW speeds (1.0–7.5 mm/s). The simulations were validated with velocity measurements, and the characteristics of the retropulsive jet were quantified at different Reynolds numbers (0.5–105.3). Experiments were then performed in which liquid drops of different viscosity were placed in a highly viscous fluid with low interfacial tension, similar to conditions in a stomach. It was found that the viscosity ratio (0.001–0.1) influences the retraction dynamics of a drop's tail after stresses are relaxed. The flow and stress information from the simulations was used to analyze fluid transport in the antrum and to quantify drop breakup conditions. It was found that a drop broke up if both a critical capillary number of 0.51 was exceeded and the drop passed within a critical dimensionless distance of 0.3 to the wave apex.

Effects of dynamic deformation of pendant water drops on the electric field between hollow porcelain insulator sheds under extreme rainfall

Hollow porcelain insulators in substations are frequently confronted with rain flashovers under extreme rainfall. This study aims to investigate the spatial and temporal variation of electric fields between hollow porcelain insulator sheds affected by dynamic deformation of pendant water drops and effects of the dimensionless number of fluids, the Weber number (We) and the electric Bond number (BoE), on it for influencing factors' analysis. Flow-electric field coupling simulations were carried out to compute the magnitude and the position of AC electric fields between the sheds. The results show that the maximum electric field at a point in time (Etmax) increases significantly after the breakup of the pendant water drop, and its position alters accordingly. For low We and BoE, the global maximum electric field (Egmax) increases with increasing We and BoE, respectively. It is much closer to the adjacent sheds and occurs later than Etmax at the breakup of the pendant water drop (Ebmax). By contrast, Egmax decreases in different degrees at high We and BoE, respectively. There is little difference between Egmax and Ebmax in the position and the occurring time. The influence mechanism on the maximum electric field and discharges and the relationship between discharges induced by the pendant water drop and rain flashover are discussed.

Effect of surfactants on jet break-up in drop-on-demand inkjet printing

Jet formation and break-up in inkjet printing has been studied and understood mainly for pure liquids. Questions remain as to the role of surfactants on the inkjet printing process at the microsecond timescale. Here, numerical and experimental results demonstrating the effects of surfactants on jet break-up and drop formation at the scales relevant to drop-on-demand inkjet printing are presented. The rapid expansion of the free surface during the fast jetting process results in a depletion of surfactants along the air–liquid interface, resulting in surface tension gradients. During ejection, surfactants are concentrated toward the head of the droplet, while the trailing ligament is found to be almost devoid of surfactants. As a consequence, the initial evolution and pinch-off of the jet from the nozzle are found to be very similar to that of pure water, even though the equilibrium surface tension of the surfactant solution is lower by a factor of two. However, particularly for strong surfactants, Marangoni forces arising from surface tension gradients between the head drop and the ligament are found to delay and can even prevent the break-up of the main drop from the ligament thereby inhibiting the formation of satellite drops.

Subcritical asymmetric Rayleigh breakup of a charged drop induced by finite amplitude perturbations in a quadrupole trap.

The breakup pathway of Rayleigh fission of a charged drop is unequivocally demonstrated by continuous, high-speed imaging of a drop levitated in an AC quadrupole trap. The experimental observations consistently exhibited asymmetric, subcritical Rayleigh breakup with an upward (i.e., opposite to the direction of gravity) ejection of a jet from the levitated drop. These experiments supported by numerical calculations show that the gravity induced downward shift of the equilibrium position of the drop in the trap causes significant, large amplitude shape oscillations superimposed over the center-of-mass oscillations. The shape oscillations result in sufficient deformations to act as triggers for the onset of instability below the Rayleigh limit (a subcritical instability). The concurrently occurring, center-of-mass oscillations, which are out of phase with the applied voltage, are shown to lead to an asymmetric breakup such that the Rayleigh fission occurs upwards via the ejection of a jet at the pole of the deformed drop. As an important application, it follows by inference that the nanodrop generation in electrospray devices will occur, more as a rule rather than as an exception, via asymmetric, subcritical Rayleigh fission events of microdrops due to inherent directionality provided by the external electric fields.

Synergistic Effect of the Fuel Microemulsion Characteristics on Drop Interaction with a Hot Wall

The utilization of fuel microemulsions helps in reducing harmful emissions, enhancing combustion efficiency, and preserving conventional fuels. This study is focused on the effect of the properties and phase behavior of water-in-diesel and water-in-biodiesel microemulsions that can be used as an alternative fuel on the droplet impingement dynamics of such fluids on a heated wall in the film boiling regime. The microemulsions represent complex fluids consisting of diesel fuel–rapeseed oil blends and distilled water with different mixture volume ratios. The emulsification is carried out using a mixture of a surfactant [isononylphenol poly(ethylene glycol) ether, PEG-6] and a co-surfactant (2-ethylhexanol) with a volume ratio of 9/1. The study considers the efficiency of the fuel samples in terms of the temperature-dependent viscosity and aggregate thermal stability as well as the quantitative characteristics of the spreading drop breakup, namely, mean diameter and number of ejected droplets. The fuel efficiency factor is derived to reveal the optimal samples. We test the phase behavior of the water–diesel fuel/rapeseed oil–PEG-6/2-ethylhexanol system in a wide temperature range. Comprehensive viscosity tests are carried out within the temperature ranges of stability to check the viscosity values of the developed microemulsions against the viscosity of the conventional diesel fuels.

Statistical characteristics of raindrop size distribution over the Western Ghats of India: wet versus dry spells of the Indian summer monsoon

Abstract. The nature of raindrop size distribution (DSD) is analyzed for wet and dry spells of the Indian summer monsoon (ISM) in the Western Ghats (WG) region using Joss–Waldvogel disdrometer (JWD) measurements during the ISM period (June–September) in 2012–2015. The observed DSDs are fitted with a gamma distribution. Observations show a higher number of smaller drops in dry spells and more midsize and large drops in wet spells. The DSD spectra show distinct diurnal variation during wet and dry spells. The dry spells exhibit a strong diurnal cycle with two peaks, while the diurnal cycle is not very prominent in the wet spells. Results reveal the microphysical characteristics of warm rain during both wet and dry periods. However, the underlying dynamical parameters, such as moisture availability and vertical wind, cause the differences in DSD characteristics. The higher moisture and strong vertical winds can provide sufficient time for the raindrops to grow bigger in wet spells, whereas higher temperature may lead to evaporation and drop breakup processes in dry spells. In addition, the differences in DSD spectra with different rain rates are also observed. The DSD spectra are further analyzed by separating them into stratiform and convective rain types. Finally, an empirical relationship between the slope parameter λ and the shape parameter μ is derived by fitting the quadratic polynomial during wet and dry spells as well as for stratiform and convective types of rain. The μ–λ relations obtained in this work are slightly different compared to previous studies. These differences could be related to different rain microphysics such as collision–coalescence and breakup.

Modeling study on drop breakup time in turbulent dispersions

Drop breakup time describes the time scale of the drop breakup process. In this work, a mathematical model for drop breakup time is constructed by the dimensional analysis method. The adjustable parameters in the model are determined and further validated by comparing with the experimental data in the literature. Results show that the model accurately predicts the drop breakup time when Weber number (WeL) is low. Further, we analyzed the effect of drop diameter, WeL, interfacial tension, and drop viscosity on the breakup time. It is noted that the breakup time increases with the increase of drop diameter and viscosity, while decreases with the increase of WeL and interfacial tension. The internal flow mechanism was proposed to illustrate the influence of the interfacial tension on the breakup time. The breakup time model can be further used in the construction of breakup kernels in a population balance model.

Automated object tracking, event detection, and recognition for high‐speed video of drop formation phenomena

AbstractOptical imaging technologies have the potential to provide detailed information which can inform process design decisions via modeling of critical phenomena or provide innovative process sensors for use in online monitoring and control strategies. In this work, novel algorithms are developed for automated object tracking, event detection, and classification in high‐speed imaging sequences of drop breakup and coalescence. Using generalization of the physical patterns, a combined strategy extracts quantitative information about the spatiotemporal trajectory and events of every fluid‐object, mapping its lineage and relations to other objects without the need for a training dataset. This high‐level reference frame makes the extracted information easily accessible for evaluation of quantities over sets of objects or events of interest. Included results demonstrate the capability of the software for handling complex multievent scenarios at acceptable execution times, processing 2.7 GB image data (22,000 images/30 videos) in 110–115 s in MATLAB on a standard desktop computer.

ANALYTICAL STUDY OF THE MECHANISM OF DROPLET DEFORMATION AND BREAKUP IN SHEAR FLOWS

The problem of drop deformation and breakup in shear flow represents academic and practical interest and has attracted close attention over the intervening decades. Drop breakup is important for a wide range of engineering and biomedical applications including production and processing of emulsions, aerosols, etc. Although drop breakup operations are widely used in various industries, however, till quite presently there is no unequivocal treatment of the physical mechanism, which causes the fragmentation of dispersions in shear flows. In this paper the principles of constructing a mathematical model, which predicts the evolution of initially spherical droplet in shear flows of viscous liquid over a wide range of flow regimes as well physical parameters of both liquid phases, are considered. A mathematical model is presented that describes the deformation of a single drop suspended in another immiscible liquid under the combined action of three forces, namely, hydrodynamic force, capillary force and dissipative viscous force. The influence of each of these forces on the process of droplet deformation is discussed in the paper.&#x0D; The focus of the study is to more deeply analyze the dynamics of droplet deformation in shear flows and the transitional effects associated with current droplet shapes. Particular attention is paid to the analysis of critical conditions for the onset of irreversible deformation of droplets, which leads to their destruction. The deformed droplet is assumed to be in the form of prolate ellipsoid of revolution. The drop deformation is regarded as motion of the centers mass of the half-drops, symmetrical with respect to the drop center.&#x0D; The results of numerical calculations for droplet deformation in shear flows in comparison with experimental data of other authors are presented. A simple criterion for destruction of droplets in shear flows has been obtained. The results of the analysis confirm the reliability of the model and the competency of the assumption made. The model is able to predict the nature of droplet deformation and the conditions for their destruction in shear flows with known operating parameters with a greater degree of accuracy than the existing empirical relationships.