BUOYANCY-DRIVEN MOTION OF DROPS AND BUBBLES IN A PERIODICALLY CONSTRICTED CAPILLARY

Buoyancy-driven motion of viscous drops and air bubbles through a vertical capillary with periodic constrictions is studied. Experimental measurements of the average rise velocity of buoyant drops are reported for a range of drop sizes in a variety of two-phase systems. The instantaneous drop shapes at various axial positions within the capillary are also quantitatively characterized using digital image analysis. Periodic corrugations of the capillary wall are found to have a substantial retarding effect on the mobility of drops in comparison with previous experimental results in a straight cylindrical capillary. For systems characterized by small Bond numbers, drop deformations are found to be periodic. In large Bond number systems, however, drop breakup eventually occurs as the drop size is increased beyond a critical limit. The observed mode of breakup is a tail-pinching process similar to that observed by Oibricht and Leal (1983) for pressure-driven motion of low viscosity ratio drops through a sinusoidally constricted capillary. In contrast to their results, however, the same mode of breakup was also observed for systems with O (1) viscosity ratios,     

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     

Primary breakup of shear-thickening suspension jet by an annular air jet

An experimental investigation is conducted to study the influence of shear-thickening behavior on the primary breakup process of suspension jets. The primary breakup morphologies of cornstarch–water suspension are observed via a high-speed camera. The unique hardened breakup mode only occurs when the suspension exhibits discontinuous shear thickening (DST). During hardened breakup mode, the oscillating portion of the suspension jet becomes perpendicular to the air direction and keeps cylindrical instead of deforming into a thin sheet or membrane structure. The suspension jets break off into large pieces rather than tiny droplets. The dimensionless number N is established to describe the relative magnitude of the increment of the viscous force and aerodynamic force during the primary breakup process. The primary breakup regime map of Newtonian fluids and shear-thickening suspensions is also promoted based on the dimensionless number N and the Weber number We.     

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     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part I: Droplet dispersion and coalescence—a review

The theoretical and experimental data on the breakup of droplets are reviewed. Several factors influence development of droplets: flow type and its intensity, viscosity ratio, elasticity of polymers, composition, thermodynamic interactions, time, etc. For Newtonian systems undergoing small, linear deformation, both the viscosity ratio and the capillary number control deformability of drops. On the other hand, the breakup process can be described by the dimensionless breakup time and the critical capillary number. Drops are more efficiently broken in elongational flow than in shear, especially when the viscosity ratio λ ? 3. The drop deformation and breakup seems to be more difficult in viscoelastic systems than in Newtonian ones. There is no theory able to describe the deformability of viscoelastic droplet suspended in a viscoelastic or even Newtonian medium. The effect of droplets coalescence on the final morphology ought to be considered, even at low concentration of the dispersed phase, ?_d ? 0.005. Several drop breakup and coalescence theories were briefly reviewed. However, they are of little direct use for quantitative prediction of the polymer blend morphology during compounding in a twin-screw extruder. Their value is limited to serving as general guides to the process modeling.     

Mass transfer to a drop stream from a field liquid

Mass transfer from a stream of drops falling freely in a stagnant liquid was investigated. Drop streams were produced by a dripping method and by a jet breakup method. Water and isobutanol, mutually saturated, were used as the dispersed and the continuous phases. Sodium hydroxide was transferred from isobutanol to water drops which were initially free of solute. The mass transfer resistance is on the continuous phase side. The mass transfer coefficient and terminal velocity of drop streams were measured experimentally. The experimental results show that the mass transfer coefficient in the drop stream is affected by the shielding effect of the previous drops. The experimental data have been correlated as K_t/U_t^0.5 versus interdrop distance l, a relationship describing the effect of the interdrop distance on the mass transfer coefficient in the continuous phase.     

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.     

Void transport in resin transfer molding

The transport of single drops through a hexagonal cylinder array is used to study the void movement and deformation in a resin transfer molding process. A transparent flow cell is used to visualize the transport of voids through a porous media model. Experiments are conducted with nearly inviscid water drops and viscous glycerol drops with drop sizes ranging from 0.4 to 80 μl, and with both a Newtonian fluid and Boger fluid with average resin velocities ranging from 0.011 to 0.140 cm/s. Two critical capillary numbers, which determine the breakup (Ca_b) and mobilization (Ca*) of drops, are measured to better understand the flow dynamics of voids. As demonstrated by the experiments, there is a critical drop size, below or above which a quite different flow behavior is observed. Such a transition is analyzed with consideration of the geometry characters in the flow field. Results expand the former studies in this area to a significantly larger range of drop sizes and capillary numbers. Particle Tracking Velocimetry is also used to quantify the local velocity, shear stress, extensional stress and energy dissipation in the flow field. Polym. Compos. 25:417–432, 2004. © 2004 Society of Plastics Engineers.     

Experimental study on drop breakup time and breakup rate with drop swarms in a stirred tank

The direct experimental data for breakup parameters of drop breakup time, multiple breakage, and breakup rate are urgently required to understand drop breakup phenomena. In this regard, drop breakup experiments were carried out in a stirred tank using a high-speed online camera. The influences of the rotating speed, interfacial tension, and drop viscosity on the above breakup parameters were then quantitatively investigated. An mechanism correlation for the breakup time is proposed and is further verified by comparing with the results of Solsvik and Jakobsen (Chem Eng Sci, 2015;131:219-234). The percentage of multiple breakage comparing to binary breakup was statistically counted. The results indicated that the dimensionless drop diameter η = d/d_max can be adopted to characterize the proportion of binary breakup. Finally, the breakup rate was experimentally measured and the breakup probability was calculated using the inverse method.     

An experimental study of Mesler entrainment on a surfactant‐covered interface: The effect of drop shape and Weber number

Mesler entrainment is the formation of large numbers of small bubbles which occurs when a drop strikes a liquid reservoir at a relatively low velocity. Existing studies of Mesler entrainment have focused almost exclusively on water as the working fluid in a nominally clean state, where even very small levels of contamination can cause significant changes in surface tension that affect the repeatability of the results. Herein water combined with the soluble surfactant Triton X‐100 is used as the working fluid in an attempt to stabilize the state of the water surface. Despite this approach, nominally identical drops did not always result in the same bubble formation event. Accordingly, Mesler entrainment was quantified by its frequency of occurrence for drops having the same nominal diameter and impact velocity. This frequency of occurrence was found to be well correlated to both the Weber number and the shape of the drop on impact. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

An experimental study of air entrainment at a solid/liquid/gas interface

Some data from an experimental study of air entrainment into a fluid bath by a continuous moving plane tape is presented. The separate effects of surface tension and viscosity are described and the various modes of air entrainment are given in the context of fluid properties. The velocity of air entrainment is found to be a function of surface tension and viscosity for viscosities less than 4.65 poise. For viscosities greater than this value, the air entrainment velocity tended to a constant value of 9.5 cm sec^?1 independent of surface tension. Relationships of the form: We = k Re^a and We = c (Bo + 1)Re^d, are suggested by analogy to describe air entrainment data without and with buoyancy effects. Data from studies on four tapes and nine fluids gave a very high correlation when plotted in the above form. The data is in substantial agreement with that from similar studies, and shows that the condition Ca = We/Re = constant is not a global criteria for air entrainment by a plunging surface. The experimental data shows that air entrainment velocity may be estimated from the relationship V_AF = 67.679 (μ√(g/ρσ))^?0.672 for the normally plunging plane tapes studied.     

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.     

Coupled two-phase mass transfer to spherical drops — Trace gas absorption and oxidation by a single drop

Mass transfer across gas and liquid boundary layers into the core of drops with liquid phase first order chemical reaction has been analyzed for spherical drops in the Reynolds number range of 50 < Re_g < 400. The realistic and computationally efficient simulation of this gas absorption system is applicable in a variety of engineering fields including gas-liquid mass transfer in drops and sprays. The present paper deals with the fluid mechanics and mass transfer with chemical reaction of a single drop. In computer experiments good predictive agreement has been achieved with measured data. The theoretical results were generalized to show the influence of three major system parameters: Peclet number Pe_g or Pe_l Damköhler number Da and the distribution coefficient at the gas-liquid interface, M, on mass transfer and to demonstrate the importance of coupled gas- and liquid-phase resistances to gas absorption under practical conditions.     

Forced Oscillations of Pendant Drops

Abstract

The efficiency of droplet/bubble breakup in multiphase contactors can be increased by applying external fields at resonance frequencies of the drops/bubbles. Experimental and theoretical techniques, developed for the study of forced oscillation of pendant drops on nozzles, are used to gain a fundamental understanding of drop response as a function of forcing frequency. Preliminary results of drop oscillations caused by electrical and flow perturbation techniques indicate that the relationship of resonance frequency to drop size for a given fluid system is not affected by the means of excitation. Computational techniques may be used to gain insight into phenomena which are difficult to probe by experiment, such as internal flow fields. The understanding gained by use of these techniques will be indispensable in design and operation of future multiphase contacting devices.     

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.     

Development of polymer blend morphology during compounding in a twin-screw extruder. Part II: Theoretical derivations

In Part II of the work, the intermeshing twin-screw extruder is briefly described and the theoretical procedures used to model its operation are summarized. Based on the microrheological considerations discussed in Part I, a predictive procedure of the morphology evolution during compounding of two immiscible polymers is proposed. In this first generation model, only the shear flow effects are considered. Furthermore, to avoid complications due to coalescence a low concentration of the dispersed phase was assumed. In the procedure, two drop breakup mechanisms are discussed. The first assumes that the drops do not break under flow while the second postulates that breakup occurs under flow. Two dispersion mechanisms are considered, the first postulating continuously increasing polydispersity of drop size and the second postulating that drop polydispersity is inversely proportional to deformation strain. The influence of the screw configuration and operating conditions on blend morphology evolution is studied. It is expected that the computed drop size distribution provides limiting values for the experimental data. Dependency of predicted morphology on operating conditions is also investigated. Increasing screw rotating speed (resulting in increasing energy consumption) and decreasing throughput (resulting in decreasing productivity) lead to prediction of finer drop size. In practice, therefore, a compromise would be required. The proposed procedure is limited to melt flow (excluding the die region) within the region of large capillary parameter values, k > 4k_crit.     

Investigations on the Droplet Entrainment in a Forced Circulation Flash Evaporator

This contribution presents results from entrainment measurements in a forced circulation flash evaporator which was designed to systematically investigate the droplet entrainment under real evaporating conditions. Operating pressures in a range of 100 to 800 mbar(a) and temperature differences between 5 and 55 K were conducted. Gas load factors up to f_G = 4.0 Pa^0.5 were achieved with glycerol-water and water as evaporating liquids. A conductivity measurement was used to determine the absolute entrained liquid and entrainment ratios. The results show an exponential behavior between entrainment, gas load factor, and heat flux due to superimposing effects. Investigation on the pressure drop across the orifice plate showed no influence for operation at gas load factors of f_G < 2.5 Pa^0.5.     

Flow characteristics of large oscillating drops in liquid-liquid systems

A study was made of the flow characteristics of large oscillating drops of pure liquid-liquid systems, using a thermostatically-controlled, rising drop column, 50 mm in diameter and 1000 mm in length. Mirrors in the jacket enabled front and side views of drops to be photographed simultaneously. Single drops in the size range 5–10 mm were investigated with both mutually-saturated phases and when the solute was being transferred from the dispersed phase. The systems studied were (1) toluene and acetone (dispersed)-water (continuous), and (2) n-heptane and acetone (dispersed)-water (continuous). Acetone concentrations were varied up to 3.75 kmol/m³. The oscillations of a travelling drop were asymmetrical; therefore, the amplitude cannot be expressed accurately in terms of only two axes. The area change of the drop compared to that of a sphere of equal volume ‘ε’, was shown to represent the amplitude accurately. The periods of droplet oscillation were uniform for the mutually saturated systems of constant physical and flow properties but changed when mass transfer was taking place. The interfacial tension exerted a marked effect on the amplitude, which also depended upon the oscillation frequency. The amplitude changed with droplet size in a similar manner to the terminal velocity, i.e. it increased with increasing size until it reached a maximum, subsequently decreasing less rapidly. The drag coefficient increased with increasing rate of mass transfer from the drop. Correlation of the results and the area eccentricity ‘ε’ by dimensional analysis embracing all possible parameters and physical properties affecting drop oscillation, resulted in the correlation ε = 0.22 Sr^0.42 We^?0.53 M^0.13 with a mean deviation of ± 14%. This will facilitate more accurate prediction of the interfacial area for mass transfer calculations, relating to equipment containing droplets in the oscillating regime.     

An experimental analysis of the influence of the ink properties on the drop formation for direct thermal inkjet printing of high solid content aqueous 3Y-TZP suspensions

Direct inkjet printing (DIP) of ceramics as a novel solid freeform fabrication (SFF) method has been subjected to extensive research in the recent years. The studies have focused either on the simulation of the drop ejection or the production of demonstration objects. The aim of this study was to close the gap between the simulation results and product oriented studies. 3Y-TZP inks of 24 vol.% solid content were prepared and characterized in terms of physical properties as well as dimensionless quantities (Re, We, Ca, and Oh). The drop volume and velocity were estimated by considering a constant ejection pressure but varying physical properties of the ejected inks. A thermal inkjet printer was used to eject arrays of single drops as well as three-dimensional 3Y-TZP demonstration objects. The drop arrays were analyzed to determine the relation between the ink properties and the drop formation. The demonstration object was sintered close to the full density.     

Newtonian power curve and drop size distributions for vibromixers

Power input data are presented for a twin flat disk up-and-down moving (vibromixer) impeller operating in a small vessel with a range of Newtonian liquids. Vibromixer power number and Reynolds number are defined and are used to establish the Newtonian power curve for this type of mixer. Drop size distributions are presented for xylene-in-water dispersions under turbulent flow conditions in the vibromixer and are shown to vary with the maximum velocity of the disk (2πAf). The Sauter mean drop diameter of the distribution is related to the vibromixer Weber number, (We =ρ(2πAf)²D/σ), by an equation of the type d₃₂/D = C (We)^?3/5 with the coefficient C = 0.37.