Theoretical model for multiple breakup of fluid particles in turbulent flow field

Generalized phenomenological model, based on the theories of probability and isotropic turbulence, is developed for multiple breakup of fluid particles in turbulent flow field. The approach uses a series of successive binary breakup events occur at a time scale comparable to the colliding eddy turnover time. It was found that the use of energy density, instead of energy, will increase the predicted binary breakup rate which is usually underestimated by the existing models in the literature. Generalization of the binary breakup model for multiple fragmentations is performed by defining a “remaining energy function” for the colliding eddy which means the contribution of original eddy to the later breakup events. For ternary breakage, the model shows a reasonably good agreement with the experimental data. The quaternary fragmentation frequency, however, is of negligible importance at lower energy dissipation rates but its contribution to breakage fraction at higher energy dissipation rates becomes considerable. The results also show that ternary and quaternary breakups have a considerable 90% contribution to the overall fragmentation, while pentenary and further fragmentations are of lower importance at low energy dissipation rates. At higher levels of energy dissipation rate, fragmentations up to six daughter particles contribute to more than 95% of the overall fragmentations. © 2016 American Institute of Chemical Engineers AIChE J, 62: 4508–4525, 2016     

Single drop breakup in turbulent flow

The breakup process of a single drop in homogeneous isotropic turbulence was studied using direct numerical simulations. A diffuse interface free energy lattice Boltzmann method was applied. The detailed visualization of the breakup process confirmed breakup mechanisms previously outlined such as initial, independent, and cascade breakups. High‐resolution simulations allowed to visualize another drop breakup mechanism, burst breakup, which occurs when the mother drop has a large volume, and the flow is highly turbulent. The simulations indicate that the type of the breakup mechanism is a strong function of mother drop size and energy input. Large mother drops in highly turbulent flow fields are more likely to burst, producing a large number of drops of the size close to the Kolmogorov length scale. Small drops in moderate turbulence tend to break only once (initial breakup). The interfacial energy of a drop was tracked as a function of time during drop deformation and breakage. The maximum energy level of the deformed mother drop was compared to commonly used estimates of critical energy necessary to break a drop. Our results show that these reference levels of critical energy are usually underestimated. Moreover, in some cases even if the critical energy level was exceeded, the drop did not break because the time of the interaction between the drop and the eddies was not enough to finish the breakup. The numerical insight presented here can be used as a guideline for the selection of assumptions and simplifications behind breakup kernels.     

Sheet formation during drop deformation and breakup in polyethylene/polycarbonate systems sheared between parallel plates

A polycarbonate drop was sheared inside a polyethylene matrix in a transparent rotating parallel plate device at 220 °C and low shear rates. A flat sheet was formed during the initial shearing of the drop. The drop then developed into either a thin thread or a sheet with a thin cylindrical tip. Sheet formation was found to occur at a critical strain or time. A stress ratio (S_r) between the matrix breakup stress, made up of the matrix normal stress and viscous stress, and the drop restoring stress, made up of the drop normal stress and the interfacial stress, is used to characterize the sheet formation during the drop deformation and breakup process. It was found that the viscosity ratio (η_r), stress ratio (S_r) and Deborah number (De) of the system could be used to predict the drop deformation and breakup.     

A model for drop and bubble breakup frequency based on turbulence spectra

In this article, a new Eulerian model for breakup frequency of drops induced by inertial stress in homogeneous isotropic turbulence is developed for moderately viscous fluids, accounting for the finite response time of drops to deform. The dynamics of drop shape in a turbulent flow is described by a linear damped oscillator forced by the instantaneous turbulent fluctuations at the drop scale. The criterion for breakup is based on a maximum value of drop deformation, in contrast with the usual critical Weber criterion. The breakup frequency is then modeled as a function of the power spectrum of Weber number (or velocity square), based on the theory of oscillators forced by a random signal, which can be related to classical statistical quantities, such as dissipation rate and velocity variance. Moreover, the effect of viscosities of both phases is included in the breakup frequency model without resorting to any additional parameter. © 2018 American Institute of Chemical Engineers AIChE J, 65: 347–359, 2019     

Transformation of single drop breakup from binary to ternary and multiple in turbulent jet flows

By releasing liquid drops in turbulent jet flows,we investigated the transformation of single drop breakup from binary to ternary and multiple.Silicone oil and deionized water were the dispersed phase and con-tinuous phase,respectively.The probability of binary,ternary,and multiple breakup of oil drops in jet flows is a function of the jet Reynolds number.To address the underlying mechanisms of this transfor-mation of drop breakup,we performed two-dimensional particle image velocimetry(PIV)experiments of single-phase jet flows.With the combination of drop breakup phenomenon and two-dimensional PIV results in a single-phase flow field,these transformation conditions can be estimated:the capillary number ranges from 0.17 to 0.27,and the Weber number ranges from 55 to 111.     

Drop breakup and entrainment in the updraft

This study aims to investigate the characteristics of gas–liquid countercurrent contact processes. In spray towers or other applications, several drops containing pollutants are entrained by the updraft flue gas, which can easily cause environmental pollution. Traditionally, this drop entrainment phenomenon is alleviated by increasing the diameter of the drops. However, the breakup of a large drop would also cause drop entrainment to become serious, a process referred to as secondary atomization. Herein, we propose the boundary of three drop modes in the updraft: drop falling mode, reverse entrainment mode, and breakup entrainment mode. The critical Weber number (We) is the key dimensionless number marking the beginning of the drop breakup. The ratio of the drag force to gravity and We are proposed as criteria for the drop entrainment.     

An experimental investigation on the breakup of surfactant-laden non-Newtonian jets

The combined effect of polymers and soluble surfactants on the dynamics of jet breakup, and especially on satellite drop formation, was experimentally investigated. Xanthan gum and Carbopol^® 934 NF were dissolved in water with Sodium Dodecyl Sulfate as the surfactant. Controlled disturbances were imposed at the laminar jet interface using a piezoelectric vibrating nozzle with breakup dynamics recorded using a high-speed camera. Drop and ligament diameters were measured from the digital images. The focus of the work was investigating how bulk and interfacial properties of the prepared fluids influenced ligament and drop evolution. It was found that if the proper concentration of surfactant (close to the critical micelle concentration, CMC) was selected, and if the flow time scales were large enough, Marangoni interfacial stresses may lead to an increase in satellite drop size as previously reported for breakup simulations of shear-thinning jets covered with insoluble surfactant. It was also experimentally confirmed that the introduction of surfactant contributes to a delay in jet breakup.     

Erosion and breakup of polymer drops under simple shear in high viscosity ratio systems

The deformation and breakup of a single polycarbonate (PC) drop in a polyethylene (PE) matrix were studied at high temperatures under simple shear flow using a specially designed transparent Couette device. Two main breakup modes were observed: (a) erosion from the surface of the drop in the form of thin ribbons and streams of droplets and (b) drop elogation and drop breakup along the axis perpendicular to the velocity direction. This is the first time drop breakup mechanism (a), “erosion,” has been visualized in polymer systems. The breakup occurs even when the viscosity ratio (η_r) is greater than 3.5. although it has been reported that breakup is impossible at these high viscosity ratios in Newtonian systems. The breakup of a polymer drop in a polymer matrix cannot be described by Capillary number and viscosity ratio only; it is also controlled by shear rate, temperature, elasticity and other polymer blending parameters. A pseudo first order decay model was used to describe the erosion phenomenon and it fits the experimental data well.     

Modelling of high viscosity oil drop breakage process in intermittent turbulence

A multifractal model of the fine-scale structure of turbulence is applied to describe breakage of viscous drops of immiscible liquid immersed in a fully developed turbulent flow. A population of drops whose diameter falls within the inertial subrange of turbulence is considered here. The population balance equation is used to predict the drop size distributions. Calculations are performed for binary and multiple breakage. Several daughter distribution functions are applied and the results of their application are compared with experimental data. Experimental investigations of drop breakup were carried out in a flat bottom stirred tank having the diameter of and equipped with Rushton type agitator and four baffles. Silicone oils with viscosity of 10, 100, 500 and 1000 m Pa s were dispersed in the aqueous continuous phase. Measurements were performed using high resolution digital camera. Experimental results as well as numerical simulations show that after the initial period of multiple breakage, the strongly asymmetric type of binary breakage dominates.     

Dispersed phase holdup and drop size distribution in pulsed plate columns

Dispersed phase holdup was measured in a pulsed plate column for the kerosene-water system under binary conditions and under solute transfer from dispersed to continuous and continuous to dispersed phases. The experimental data were satisfactorily modelled through a recirculation regime model. The drop size distribution, measured by a photographic technique, exhibited a multinodal character at low agitation rates and high dispersed phase flow rate. Sauter mean drop diameter was found to depend on the agitation rate, the dispersed phase flow rate, the mass transfer direction and the plate free area. Correlations for d₃₂ and the interfacial area were presented using Kolmogoroff's isotropic turbulence model.     

Characterization of liquid‐liquid dispersions with variable viscosity by coupled computational fluid dynamics and population balances

Sustaining stable liquid‐liquid dispersion with the desired drop size still relies on experimental correlations, which do not reflect our understanding of the underlying physics and have a limited prediction capability. The complex behavior of liquid‐liquid dispersions inside a stirred tank, which is equipped with a Rushton turbine, was characterized by a combination of computational fluid dynamics and population balance equations (PBE). PBE took into account both the drop coalescence and breakup. With the increasing drop viscosity, the resistance to drop breakage also increases, which was introduced by the local criteria for drop breakup in the form of the local critical Webber number (We_c). The dependency of We_c on the drop viscosity was derived from the experimental data available in the literature. Predictions of Sauter mean diameter agree well with the experimentally measured values allowing prediction of mean drop size as a function of variable viscosity, interfacial tension, and stirring speed. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2403–2414, 2015     

Effect of compatibilization on the deformation and breakup of drops in step-wise increasing shear flow

Drop deformation and breakup were investigated in the presence of a block copolymer in step-wise simple shear flow using a home-made Couette cell connected to an Anton Paar MCR500 rheometer. Polyisobutylene (PIB) was used as the matrix, while five different molecular weights of polydimethylsiloxane (PDMS) were selected to provide drops with a relatively wide range of viscosity ratio. A block copolymer made of PDMS-PIB was used for interfacial modification of the drop-matrix system. The copolymer concentration was 2 wt% based on the drop phase. The experiments consisted in analyzing the drop shape and measuring the variation of the length to diameter ratio, L/D, both in steady state and in transient regimes till breakup. This allowed revising of the classical Grace curve that reports the variation of the critical capillary number for breakup as a function of viscosity ratio and providing also a new one for blends compatibilized with an interfacial active agent with a given molecular weight.     

Drop size correlation and population balance model for an agitated-pulsed solvent extraction column

Agitated-pulsed column (APC) is a newly designed extraction column with excellent mass transfer performance. In this work, Sauter mean drop diameter d₃₂ and drop size distribution was investigated under different operation conditions in a 25 mm diameter APC. The results show that with an increase in pulsation intensity and agitation speed the drop size distribution is narrowed and d₃₂ is decreased significantly. With increasing dispersed-phase velocity, d₃₂ increased and drop size distribution become narrow, while there was no noticeable change with continuous velocity. The cumulative size distribution was found to be predicted well using the Inverse Gaussian function. A new correlation was proposed to predict the experimental d₃₂ data of the APC column used in this study. Furthermore, population balance model was applied to predict the drop size distribution with refitted parameters in the breakage, coalescence kernels functions.     

Stability of multiple emulsions under shear stress

Multiple liquid emulsions of the water in oil in water (W₁/O/W₂) type are used in a variety of consumer or technical applications, for instance in the encapsulation of certain active ingredients. The encapsulation process and release mechanisms of the inner phase of the carrier drops are important in order to properly process and formulate such liquid-liquid systems. In this work the stability and breakage of multiple W₁/O/W₂ emulsions under mechanical shear stress are investigated for emulsions with different surfactants and surfactant concentrations of the internal emulsion. Stressing the emulsions in a mechanical stirring process is compared to the membrane emulsification process. The membrane emulsification process results in higher encapsulation efficiencies than the stirring process. The emulsion droplets were subjected to shear stress below and above the critical capillary number for drop breakup. The results show that stable inner emulsions with sufficient surfactant concentrations increase the overall encapsulation efficiency for multiple emulsions subjected to shear stress, although the effect is not prominent. The depletion of the carrier oil droplets could be achieved for Ca numbers below the critical limit, reducing the encapsulation efficiency below 10 %. This shows that even a low shear stress can result in content release from the internal droplet phase. The experimental emulsion release study is supported by a numerical simulation of drop deformation and break-up under shear stress.     

Experimental measurement of bubble breakup in a jet bubbling reactor

The bubble breakups in a jet bubbling reactor are captured using a high-speed camera and the velocity field is measured by particle image velocimetry. Two typical breakup patterns, jet breakup and jet-vortex breakup are observed. The breakup time interval of the jet-vortex breakup is two orders of magnitude higher than the jet breakup. The probability of the jet-vortex breakup and the jet breakup accounting in the total breakup events increases and decreases with the jet velocity and the mother bubble size, respectively. The bubble breakup region increases with the jet velocity. The bubble breakup frequency increases with the turbulent dissipation rate and the mother bubble size. The average number of daughter bubbles increases with the Weber number. An L-shaped daughter bubble size distribution is observed. Empirical correlations are established for the bubble breakup frequency, the average number of daughter bubbles and daughter bubble size distribution, and fitted well with the experimental results.     

The formation and breakup of molten oxide jets under periodic excitation

The experiments on the capillary breakup of slag jets at high temperatures are presented in this article. The impact of external excitations on the disintegration process was investigated in a furnace with optical access filmed at frame rates up to 10,000 fps. A synthetic calcia‐alumina slag was used to form jets at different temperatures (1570–1660°C) and jet velocities (0.6–1.4 ms^?1). The impact of external vibration on the breakup was evident: for low jet velocities, the jet length decreased, the droplet size increased, satellite droplet formation was hindered, and a distinct “pumping mechanism” was observed. For jets with higher velocity, the jet length decreased by 30%, the droplet generation frequency increased from 20 to 250 droplets per second, the drop sizes were uniform, and satellite formation was also suppressed. In this case, the ideal case in which the volume of one wave instability forms one droplet was achieved. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3350–3361, 2014     

On the steady‐state drop size distribution in stirred vessels. Part I: Effect of dispersed phase viscosity

Previous studies on emulsification have used the maximum drop size (d_max) or Sauter mean diameter ( ) to investigate the effect of viscosity on the drop size distribution (DSD), however, these parameters fall short for highly polydispersed emulsions. In this investigation (Part I), the steady‐state DSD of dilute emulsions is studied using of silicon oils with viscosities varying across six orders of magnitude at different stirring speeds. Different emulsification regimes were identified; our modeling and analysis is centered on the intermediate viscosity range where interfacial cohesive stresses can be considered negligible and drop size increases with viscosity. The bimodal frequency distributions by volume were well described using two log‐normal density functions. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3293–3302, 2018     

In situ visualization of drop deformation,erosion, and breakup in high viscosity ratio polymeric systems under high shearing stress conditions

In this paper, deformation and breakup under simple shear of single molten polymer drops in a polymer matrix were investigated. Flow visualization was carried out in a Couette‐Flow apparatus under relatively high shear rates and temperatures up to 230°C. Drop/Matrix combinations were composed of polystyrene drops of 0.5–0.6 mm in diameter in polyethylene matrix, and ethylene–propylene copolymer drops of approximately the same size in polypropylene matrix. The deformation and breakup processes were studied under steady state and time‐dependent shearing conditions. Either for steady state or time‐dependant shearing conditions, drop elasticity generated at relatively high shear rates helped the drops to align perpendicular to the flow direction, i.e., parallel to vorticity axis. Also, the most striking non‐Newtonian effects for the high viscosity ratio systems were the surface erosion and the drop splitting mechanisms. The particles eroded off the main droplet surface were very fine, in the range of 10–50 μm, and led to a significant reduction in main drop size before its final breakup. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 100: 2582–2591, 2006     

On the influence of particle shape and process conditions in the pressure drop and hydrodynamics in a wall-effect fixed bed

A low tube-to-particle diameter ratio (d_t/d_e,p) fixed bed, packed with spherical and nonspherical catalyst supports, was used to investigate pressure drop at varying temperature (298–673?K) and inlet pressure (245–294?kPa). The d_t/d_e,p ranged from 3 to 6, namely, a large wall-effect fixed bed, with an average void fraction between 0.38 and 0.61. These conditions pertain to multitubular fixed-bed reactors used for exothermic reactions. The pressure drop was notably influenced by the particle size and morphology as well as temperature. The use of particles with d_t/d_e,p?0.55) appeared suitable for pressure drop control. The fluid velocity profiles were calculated by applying the Navier–Stokes–Darcy–Forchheimer equation computing the respective permeability parameters with refitted state-of-the-art pressure drop correlations. The fluid flow exhibited different velocity zones across the fixed bed, the highest velocity zone being located near the reactor wall. The axial velocity component was influenced by the catalyst morphology, as well as temperature and inlet pressure.     

A unified theoretical model for breakup of bubbles and droplets in turbulent flows

Pressure has a significant effect on bubble breakup, and bubbles and droplets have very different breakup behaviors. This work aimed to propose a unified breakup model for both bubbles and droplets including the effect of pressure. A mechanism analysis was made on the internal flow through the bubble/droplet neck in the breakup process, and a mathematical model was obtained based on the Young–Laplace and Bernoulli equations. The internal flow behavior strongly depended on the pressure or gas density, and based on this mechanism, a unified breakup model was proposed for both bubbles and droplets. For the first time, this unified breakup model gave good predictions of both the effect of pressure or gas density on the bubble breakup rate and the different daughter size distributions of bubbles and droplets. The effect of the mother bubble/droplet diameter, turbulent energy dissipation rate and surface tension on the breakup rate, and daughter bubble/droplet size distribution was discussed. This bubble breakup model can be further used in a population balance model (PBM) to study the effect of pressure on the bubble size distribution and in a computational fluid dynamics‐population balance model (CFD‐PBM) coupled model to study the hydrodynamic behaviors of a bubble column at elevated pressures. © 2014 American Institute of Chemical Engineers AIChE J, 61: 1391–1403, 2015