Prediction of phase inversion in agitated vessels using a two-region model

Phase inversion in agitated vessels was studied using a two-region model. In this model, breakup and coalescence were assumed to take place in the vicinity of the impeller and away from that region, respectively. The mechanism of phase inversion was regarded as the result of an imbalance between the breakup and coalescence processes. Hence phase inversion was assumed to occur when the coalescence frequency exceeded that of breakup. In addition, the concept of a radial distribution function was adopted in the model in order to account for droplet coalescence in concentrated dispersions. Using the two-region model, the effect of interfacial tension, viscosity, density and impeller size on the width of the ambivalent range was investigated. The predictions agree well with experimental data particularly for the upper curve of the ambivalent range; however, the organic phase fraction of the lower curve is in some cases underestimated by the model.     

Predicting the diameters of droplets produced in turbulent liquid–liquid dispersion

The droplet size distribution in liquid–liquid dispersions is a complex convolution of impeller speed, impeller type, fluid properties, and flow conditions. In this work, we present three a priori modeling approaches for predicting the droplet diameter distributions as a function of system operating conditions. In the first approach, called the two-fluid approach, we use high-resolution solutions to the Navier–Stokes equations to directly model the flow of each phase and the corresponding droplet breakup/coalescence events. In the second approach, based on an Eulerian–Lagrangian model, we describe the dispersed fluid as individual spheres undergoing ongoing breakup and coalescence events per user-defined interaction kernels. In the third approach, called the Eulerian–Parcel model, we model a sub-set of the droplets in the Eulerian–Lagrangian model to estimate the overall behavior of the entire droplet population. We discuss output from each model within the context of predictions from first principles turbulence theory and measured data.     

Laser-Doppler measurements of the turbulent flow in stirred vessels to establish scaling rules

A laser-Doppler velocimeter, equipped with a frequency shift so as to eliminate directional ambiguity, has been used to measure the turbulent flow in stirred vessels with diameters of 0.12, 0.29 and 0.90 m of the same geometry. The vessels contained water and measurements were done in the impeller stream region. Scaling rules have been derived for average velocity, the periodic component, turbulent intensities and turbulence power spectra.It appears that close to the impeller the flow is dominated by the periodically fluctuating flow of the trailing vortices behind the impeller blades. The normalized mean velocity in the trailing vortices, and therefore the turbulence intensity close to the impeller, is very sensitive to impeller geometry and shows a slight increase with size of the vessel. In the greater part of the impeller stream region the power spectra have a section with a ?$\text{5}\text{2}$ slope on a log-log scale and consequently the energy of the small eddies decreases with increasing scale. At the vessel wall the vortices have decayed completely to random turbulence and the spectrum shows a ? $\text{5}\text{3}$ slope.     

Drop size distribution and holdup in a rotating impeller extraction column

A stagewise hydrodynamic model, applying drop population balance equations derived from models for breakage and coalescence of drops in a countercurrent liquid-liquid extraction system, was developed to predict the drop size distribution and the holdup of the dispersed phase in a rotating impeller extraction column. The drop size distributions were obtained by taking the photographs of the dispersions at the same locations through the rectangular shaped glass box filled with distilled water. The experimental variables were the impeller speed and flow rates of the continuous and dispersed phases. The solutions of the model equations were obtained by performing the computer simulation and the optimum parameter values were determined. The results predicted by the model were in good agreement with the experimental results obtained from the present rotating impeller extraction column.     

UTILIZATION OF POPULATION BALANCES IN SIMULATION OF LIQUID-LIQUID SYSTEMS IN MIXED TANKS

A simulation model has been developed to model drop populations in a mixed tank. A multiblock mixed tank model has been used with the drop population balance equations developed in the literature. The drop breakage and coalescence functions used in the population balance model take into account the local turbulent energy dissipation values. The drop breakage and coalescence function parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a mixed tank are used in the present model, the fundamental breakage and coalescence phenomena can be taken into closer examination. Furthermore, the present model is capable of predicting inhomogeneities occurring in a mixed tank. It is also considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is the transient data of the measured drop size distribution as the impeller speed is changed. The other is the time-averaged data measured at different locations of the mixed tank. Different flow regions can be chosen from direct measurements or from the CFD simulations in a straightforward manner. CFD flow simulation results can be used when no experimentally obtained flow conditions are available. This is especially useful for nonstandard vessels, such as reactors containing cooling coils.     

Kinetics of oil dispersion in the absence and presence of block copolymers

A phenomenological model proposed describes droplet breakup in the turbulently agitated lean oil-in-water dispersions and provides a correlation between the median droplet size in an agitated vessel of standard geometry and the time of dispersion. It was assumed that the droplet breakup takes place in the dispersion-only region and coalescence is negligible. The model described the data from this study and the literature quite satisfactorily under these conditions. The effect of adding triblock PEO/PPO/PEO copolymeric surfactants on the dispersion kinetics of oil was also investigated. Addition of surfactant reduced the median oil droplet size significantly, and the extent of this reduction was a strong function of surfactant concentration. Application of the model on these data demonstrated that the change in the median droplet size could be divided into two distinct regions. The breakage rate was high initially, most probably due to continuous adsorption of surfactant molecules at the oil/water interface. A lower breakage rate was attained at longer times, as the surfactant molecules were depleted from the solution. The time of transition between the two was affected strongly by the concentration of the surfactant added. Furthermore, the time of addition of the surfactant did not affect the final droplet-size distribution in the system.     

Prediction of average droplet size in flowing immiscible polymer blends

The paper is focused on calculation of the average droplet size in immiscible blends during their steady flow. Available theoretical and experimental results of studies of the droplet breakup and coalescence are utilized to derive the equations describing dynamic equilibrium between the droplet breakup and coalescence. New expression for the coalescence efficiency, reliably reflecting recent theoretical results, is proposed. The equation for the average steady droplet size, controlled by the stepwise breakup mechanism and coalescence of droplets with not very different sizes, is derived for blends containing up to 10–20 vol % of the droplets. For blends with above approximate 20 vol % of the droplets, the breakup by the Tomotika mechanism and coalescence in highly polydisperse system is modeled. Results of the derived equations are compared with experimental data; qualitative agreement is found for the dependence of the droplet size on the amount of the dispersed phase. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 45250.     

Theory of competition between breakup and coalescence of droplets in flowing polymer blends

The Smoluchowski equation for the breakup and coalescence of dispersed droplets has been solved for flowing polymer blends. A scaling form for the distribution of droplet sized derived and published for a system of clusters with fragmentation and coagualation was used in our dervation. Equations are developed here for the average droplet size and for the characteristic time of transition to steady state flow of blends with a high content of the dispersed phase. Expressions reasonably describing the average size of droplets for all concentrations were obtained by a theory modification. Measured dependences of droplet size on the blend composition can be matched only if simultaneous collisions of three and more droplets are considered. The results of the theory indicate that the mechanism of droplet breakup (formation of pieces with the same or different volumes) has only a small effect on their average size in concentrated systems. The dependence of droplet size on the shear rate in flow is determined by properties of the blend components, and is generally nonmonotonic.     

Coalescence and break-up in dilute polydispersions

Functional relationships for coalescence rate dependence on drop size and hold-up were derived via the collision rates and coalescence efficiency. Experiments in an agitated vessel indicated the coalescence rate to be controlled by the viscous flow regime and, per unit drop concentrations, to be proportional to the third power of the sum of the diameters of the two coalescing drops. By combining the experimentally known coalescence rate dependence on drop diameter with the independently determined dependence of the latter on the dispersed phase hold up, the breakup rate was found to depend on d^2.0.     

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     

Simulation of the population balances for liquid-liquid systems in a nonideal stirred tank. Part 2—parameter fitting and the use of the multiblock model for dense dispersions

In the previous part of this work (Chem. Eng. Sci. 54 (1999) 5887), a multiblock simulation model was developed in order to allow the close examination of different regions of a stirred tank for drop size distribution calculations. In this paper, that model is tested in a parameter fitting procedure. The drop breakage and coalescence parameters are fitted against drop size measurements from dense liquid-liquid dispersions, which were assumed fully turbulent. Since the local turbulence and flow values of a stirred tank are used in the present model, the fundamental breakage and coalescence phenomena can be examined more closely. Furthermore, the present model is capable of predicting inhomogeneities occurring in a stirred tank. It is also to be considered as an improved tool for process scale-up, compared to the simple vessel-averaged population balance approach, or use of correlations of dimensionless numbers only. The present model can use two sources of data for fitting parameters in the drop rate functions. One is to use transient data of the measured drop size distribution as the impeller speed is changed. The other is to use time-averaged data measured at different locations of the stirred tank. It is shown in this paper that the different flow regions can be chosen from the CFD simulations in a straightforward manner. CFD flow simulation results can be used to select the flow regions when no experimentally obtained flow conditions are available. This is especially useful for non-standard vessels, such as reactors containing cooling coils. After fitting the parameters with a multiblock model, the population balance model can be rather easily incorporated into a commercial CFD program to investigate different flow conditions.     

Microencapsulation of hydrophilic solid powder as fire retardant agent with epoxy resin by droplet coalescence method

To give water resistance to Bistetrazol–diammonium (BHT–2NH₃) as a fire retardant agent, microencapsulation with epoxy resin was tried by the droplet coalescence method. In this method, two kinds of epoxy resin droplets were prepared; one is the larger epoxy resin droplet containing BHT–2NH₃ as a core material and the other the smaller droplets containing Imidazole as a gelation agent. The larger epoxy resin droplets were made to coalesce with the many smaller droplets during the microencapsulation process to prepare microcapsules. In the experiment, the agitation velocities for preparation of the droplets and for coalescence were mainly changed. With increase in the impeller speed, the content of core material increased, became maximum because of increase in the coalescence frequency, and then decreased because of breakup of droplets. With increase in the impeller speed, the leakage ratio of core material decreased, became minimum, and then increased. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2008.     

Dispersion behaviour of droplets in circular loop reactors

A circular loop reactor was built for application to a heterogeneous liquid-liquid reaction. In order to investigate the dispersion behaviour of droplets in the reactor, basic experiments were performed using a number of liquid-liquid dispersions. Droplets discharged form the impeller region were found to grow due to coalescence in the circulation region. Mean droplet diameter decreased exponentially with elapsing time. An expression correlating the steady-state mean droplet diameter with the operating conditions was derived. Moreover, the transition time required for the droplet diameter to reach the equilibrium value was determined and correlated with the operating conditions.     

Analysis of droplet expulsion in stagnant single water-in-oil-in-water double emulsion globules

Double emulsions created by phase inversion can be used for fast liquid–liquid separation; therefore, the coalescence behaviors of these types of multiple emulsions need to be predictable for different physical properties and drop size ratios. The aim of this study is to determine the influence of the effective overall drop diameter and the internal droplet size on the coalescence time and the coalescence behavior. Experimental investigations on the physical stability of single stagnant water-in-oil-in-water (W₁/O/W₂) double emulsion globules are performed. For this investigation, a formation device to inject one water droplet into an oil drop inside a water bulk phase is developed. The coalescence process of the sole internal water droplet floating on the O/W₂ interface with the water bulk phase, often termed droplet expulsion or external coalescence, is recorded with a high speed camera. Based on image analysis, the diameters of the effective overall drop D, containing the oil and entrapped water volume, and the internal water droplet d are determined. Additionally, the coalescence time τ, including the time from the first contact of the internal droplet and the drop-bulk interface to the film rupture is measured. A large increase in coalescence time with increasing water droplet diameters is found. For the investigated paraffin oil–water system and initial drop sizes, partial coalescence occurs. In this case, the diameter ratio of daughter-to-mother droplet ψ is determined.     

A theoretical model for droplet breakup in turbulent dispersions

A theoretical model for the prediction of droplet breakup rate and daughter size distribution in turbulent dispersions has been developed. It considers the breakup contributed by a novel breakup criterion based on surface energy density increase, the droplet surface oscillation from previous collision and the eddies larger than original droplets. The breakup rate and daughter size distribution predicted by this model show a good agreement with the experimental data reported recently.     

Effect of impeller geometry on drop break-up in a stirred liquid—liquid contactor

Drop size measurements were made in the break-up zone at the tip of three 6 bladed disc turbines of different geometries in a 0·30 m dia. vessl. Three systems kerosene, methyl iso-butyl ketone (MIBK) and n-butanol at a volumetric fractional hold-up of 0·05 in water were examined. Power input and circulation time characteristics were determined and a new dimensionless group (?^{?$\text{1}\text{3}$}t_c/T^{$\text{2}\text{3}$}) is proposed to account for the effect of geometric parameters in the correlation of the drop size.     

Local droplet diameter variation in a stirred tank

The local variation of droplet diameter in a stirred tank was measured in the vicinity of the impeller and at another region. The degree of difference in droplet diameter between regions increases with the impeller speed. A correlation equation between the local difference in droplet diameter and the frequencies of coalescence and circulation of the droplet was derived according to the circulation interaction model. The degree of local difference in droplet diameter was found to be controlled strongly by the ratio of coalescence to circulation frequency.     

Continued self-similar breakup of drops in viscous continuous phase in agitated vessels

Drop breakup in viscous liquids in agitated vessels occurs in elongational flow around impeller blade edges. The drop size distributions measured over extended periods for impellers of different sizes show that breakup process continues up to 15–20 h, before a steady state is reached. The size distributions evolve in a self-similar way till the steady state is reached. The scaled size distributions vary with impeller size and impeller speed, in contrast with the near universal scaling known for drop breakup in turbulent flows. The steady state size of the largest drop follows inverse scaling with impeller tip velocity. The breadth of the scaled size distributions also shows a monotonic relationship with impeller tip velocity only.