Experimental study of drop size distributions at high phase ratio in liquid-liquid dispersions

An experimental investigation has been carried out in order to analyse the drop size distributions of a liquid-liquid dispersion in a stirred vessel at high phase ratio. Two liquid-liquid systems have been investigated: one at low and one at high coalescence rate. A sampling technique has been developed in order to measure the drop size distributions in the mixer with the help of a laser granulometer. A statistical approach has been attempted to derive the most probable drop size distribution in the mixer and the results have been compared with the experimental primary distributions. The comparison suggests that the energy dissipation cannot be considered as uniformly distributed in the mixer. The mean diameter of the distribution has been correlated to the global mechanical input power and to the volume phase fraction (phase ratio) for both systems in the frame of the classical Hinze-Kolmogorov theory. The results show that for each volume fraction studied, the mean diameter of the dispersion is a decreasing power law of the Weber number with an exponent equal to −0.6 at low phase ratio. However, it appears that for both systems studied this exponent is a decreasing function of the phase ratio. This result reveals the existence of a more complex breakup mechanism with high phase ratio than that assumed in the theory which has to be discriminated from dampening effect of the dispersed phase upon the turbulent energy of the bulk phase. The study of the secondary distributions mean diameter seems to be in good agreement with the numerical predictions of Stone (Annu. Rev. Fluid Mech. 26 (1994) 65). The ratio between the mean diameter of the primary distribution to the satellite drop mean diameter is a growing function of the viscosity ratio.     

Experimental studies and population balance equation models for breakage prediction of emulsion drop size distributions

A population balance equation (PBE) model for pure drop breakage processes was developed from homogenization experiments and used to investigate model extensibility over a range of emulsion formulation and homogenizer operating variables. Adjustable parameters in the mechanistic breakage functions were estimated from measured drop volume distributions by constrained nonlinear least-squares optimization. Satisfactory prediction of measured bimodal distributions was achieved by the incorporation of two different breakage functions that accounted for large drop breakage due to turbulent shear and for small drop breakage due to collisions between drops and turbulent eddies. Model extensibility to different emulsion compositions and homogenizer pressures was investigated by comparing model predictions generated with the base case parameters to drop volume distributions measured under different conditions. The PBE model satisfactorily accounted for changes in the dispersed phase volume fraction and the interfacial tension with the base case parameters. By contrast, significantly improved predictions for the continuous phase viscosity or multiple formulation variables were obtained through re-estimation of the model parameters using multiple data sets in which the associated variables were systematically varied. The model was not able to satisfactorily predict drop volume distributions resulting from homogenizer pressure changes, perhaps due to the assumption of a constant pressure throughout the homogenizer. We conclude that PBE models of drop breakage can be used to reasonably predict the effects of emulsion formulation variables on drop volume distributions and have the potential for guiding experimental efforts aimed at the design of novel emulsified products.     

An experimental study of immiscible liquid–liquid dispersions in a pump–mixer of mixer–settler

Drop size distribution(DSD) or mean droplet size(d32) and liquid holdup are two key parameters in a liquid–liquid extraction process. Understanding and accurately predicting those parameters are of great importance in the optimal design of extraction columns as well as mixer–settlers. In this paper, the method of built-in endoscopic probe combined with pulse laser was adopted to measure the droplet size in liquid–liquid dispersions with a pump-impeller in a rectangular mixer. The dispersion law of droplets with holdup range 1% to 24% in batch process and larger flow ratio range 1/5 to 5/1 in continuous process was studied. Under the batch operation condition, the DSD abided by log-normal distribution. With the increase of impeller speed or decrease of dispersed phase holdup, the d32 decreased. In addition, a prediction model of d32 of kerosene/deionized system was established as d_(32)/D = 0.13(1 + 5.9φ)We~(-0.6). Under the continuous operation condition, the general model for droplet size prediction of kerosene/water system was presented as d_(32)/D = C_3(1 + C_4φ)We~(-0.6). For the surfactant system and extraction system, the prediction models met a general model as d_(32)/D = bφ~nWe~(-0.6).     

Experimental study on drop formation in liquid-liquid fluidized bed

Drop formation in liquid-liquid fluidized bed was investigated experimentally. The normal water was injected via a fine-capillary spray nozzle into the co-flowing No. 25 transformer oil with jet directed upwards in a vertical fluidized bed. Experiments under a wide variety of conditions were conducted to investigate the instability dynamics of the jet, the size and size distribution of the drops. Details of drop formation, drop flow patterns and jet evolution were monitored in real-time by an ultra-high-speed digital CCD (charge couple device) camera. The Rosin-Rammler model was applied to characterize experimental drop size distributions. Final results demonstrate that drop formation in liquid-liquid system takes place on three absolutely different developing regimes: bubbling, laminar jetting and turbulent jetting, depending on the relative Reynolds number between the two phases. For different flow domains, dynamics of drop formation change significantly, involving mechanism of jet breakup, jet length pulsation, mean size and uniformity of the drops. The jet length fluctuates with time in variable and random amplitudes for a specified set of operated parameters. Good agreement is shown between the drop size and the Rosin-Rammler distribution function with the minimum correlation coefficient 0.9199. The mean drop diameter decreases all along with increasing jet flow rate. Especially after the relative Reynolds number exceeds a certain value about 3.5×10⁴, the jet disrupts intensely into multiple small drops with a diameter mainly ranging from 1.0 to and a more and more uniform size distribution. The turbulent jetting regime of drop formation is the most preferable to the dynamic ice slurry making system.     

A literature review of theoretical models for drop and bubble breakup in turbulent dispersions

This paper presents a literature review on mechanisms and models for the breakage of bubbles and drops (fluid particles) in turbulent dispersions. For the mechanisms, four categories are summarized, namely, turbulence fluctuation, viscous shear stress, shearing-off process and interfacial instability. The models for breakup frequency and daughter size distribution available in literature are reviewed thoroughly. The development and limitation of the existing models are studied and possible improvements are proposed.     

Modeling fluid behavior and droplet interactions during liquid-liquid separation in hydrocyclones

A mechanical separation process in a hydrocyclone is described in which disperse water droplets are separated from a continuous diesel fuel phase. This separation process is influenced by droplet-droplet interaction effects like droplet breakup and coalescence resulting in a change of droplet size distribution. A simulation model is developed coupling the numerical solution of the flow field in the hydrocyclone based on computational fluid dynamics with population balances. The droplet size distribution is discretized and each discrete droplet size fraction is assumed to be an individual phase within a multiphase-mixture model. The droplet breakup and coalescence rates are defined as mass transfer rates between the discrete phases by the aid of user-defined functions. All model equations are solved with the CFD software package FLUENT™. The investigations show the impact of the cyclone geometry on the coupled population and separation dynamics. Cyclone separators with an optimized geometry show less steep velocity gradients increasing the coalescence rates and improving the separation efficiency. The calculated droplet size distributions at the cyclone overflow and at the underflow show good accordance with experimental data. The basic modeling approach can be extended and adapted to other disperse multiphase flow systems.     

Modelling local bubble size distributions in agitated vessels

Photography and capillary suction probe were used to measure local bubble size distributions (BSDs) from Rushton turbine agitated (14/200 L) air-tap water and CO₂-n-butanol dispersions. A multiblock stirred tank model with population balances (PBs) for bubbles was created to describe local BSDs in agitated vessels. Unknown parameters in breakage and coalescence models were adjusted by comparing the predicted and measured local BSDs. The BSDs from both investigated systems and varying vessel-operating conditions were included simultaneously to the fitting. The adjusted models were incorporated to MUSIG PB model in CFX-5.7 and tested for the laboratory stirred tanks. The multiblock model showed to be an optimal trade-off between the accuracy and CPU time for the investigation of gas-liquid hydrodynamics and validation of closure models. As a result of fitting, the adjusted model seems to describe local BSDs more accurately in agitated vessels than the model of Lehr et al. [2002. Bubble-size distributions and flow fields in bubble columns. A.I.Ch.E. Journal 48, 2426-2443], which has been successful in bubble column studies. This shows that phenomenological breakage and coalescence closures need experimental validation for various flow environments.     

A state-of-the-art review on single drop study in liquid-liquid extraction: Experiments and simulations

The experimental and numerical investigations of single drop in liquid/liquid extraction system have been reviewed with particular focus on experimental techniques and computational fluid dynamic simulation approaches. Comprehensive surveys of available experimental techniques and numerical approaches for single drop rising and falling were given. Subsequently, single drop mass transfer was also reviewed both experimentally and numerically. Additionally, single drop breakage and coalescence process and the influencing factors were summarized and compared, so as to establish sub-models for population balance model. Future directions on single drop mass transfer, drop breakage and coalescence were suggested. It is believed that the single drop is a powerful tool to assist extraction process design from lab-scale to pilot-scale.     

A numerical procedure for calculating droplet deformation in dispersing flows and experimental verification

A three-step numerical procedure for studying droplet deformation in mixed, dispersing-type, flow fields is described. Finite element and numerical particle tracking techniques are used to obtain the history of shear and elongation rates along a particle trajectory in the flow field, and from this history, boundary integral techniques are used to determine the deformation a drop would experience along this path. This approach is then used to investigate the effect of a small change in geometry on the breakup behavior of drops in the annular gap flow between two eccentric cylinders. This flow geometry serves as an idealization of a rotor-stator dispersing device used for highly viscous fluid systems. It is found that an increase in eccentricity produces an increase in dispersing capability. Experiments in an eccentric cylinder geometry were performed to verify the simulation procedure. Under the experimental conditions considered, it is found that the simulations perform well, correctly predicting whether or not drop breakup occurs and the qualitative drop evolution behavior. The simulation procedure outlined in this paper can serve as an effective tool to determine drop breakup in dispersing geometries and hence to optimize dispersing procedures.     

Drop size distribution and mean drop size in a pulsed packed extraction column

Drop size distribution and mean drop size are used for calculation of interfacial area available for mass transfer. In this study, the drop size distribution and Sauter mean drop diameter (d₃₂) have been investigated using three different liquid systems in the absence of mass transfer in a pilot plant pulsed packed column. The drop size was measured at four different points along the active column height. Three operating variables have been studied including the pulse intensity (af) and flow rates of both liquid phases. The effect of liquid properties and height of the active column were also investigated. A combination of the pulse intensity and interfacial tension had the largest effect on the drop size distribution while none of the flow rates were of significance. The height of the column played an important role at the bottom of the active column, but the associated effect was reduced with increase of the height. Finally, a normal probability function of number density was proposed for prediction of the drop size distribution with an Average Absolute Relative Error (AARE) of 8.8% for their optimized constant. Furthermore, two correlations were presented involving height or flow rates of the two phases along with operating variables and physical properties of the liquids. These correlations had AARE values of about 8.5 and 7.8%, respectively.     

Drop breakage and coalescence in the toluene/water dispersions with dissolved surface active polymers PVA 88% and 98%

The influence of two PVAs of the same molecular weight (13,000–23,000) and different degree of hydrolysis equal to 88% and 98% on breakage and coalescence of toluene droplets in the liquid/liquid dispersion were considered for PVA concentration range 0.001–0.01%. Analysis of experimental results shows that drop coalescence is significant only in the system containing 0.001% PVA. Drop coalescence for polymer concentration range 0.002–0.01% is strongly limited. Therefore, population balance was solved using breakage and coalescence expressions with assumed partially mobile drop interfaces for the lowest PVA concentration. For c ≥ 0.002% drop size distributions were properly predicted using only breakage model. Multifractal formalism was used to take into account intermittent character of turbulence and explain drop behavior. Larger drop size reduction by PVA of lower degree of hydrolysis observed experimentally was confirmed by the model.     

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.     

Inferential closed-loop control of particle size distribution for styrene emulsion polymerization

In this work, a new control strategy for controlling the particle size distribution (PSD) in emulsion polymerization has been proposed. It is shown that the desired PSD can be achieved by controlling the free surfactant concentration which in turn can be done by manipulating the surfactant feed rate. Simulation results show that the closed-loop control of free surfactant concentration results in a better control of PSD compared to open-loop control strategy, in presence of model mismatch and disturbances. Since the on-line measuring of ionic free surfactant concentration is difficult, conductivity which is related to it is measured instead and used for control purposes. The closed-loop control of conductivity also results in a better control of PSD compared to open-loop control strategy, but its performance is not as good as controlling free surfactant concentration in presence of model mismatch.     

Population balance modeling of bubble size distributions in a direct-contact evaporator using a sparger model

The study of bubble size distributions in direct-contact evaporators was addressed both theoretically and experimentally. Recently developed models for calculating bubble coalescence and breakage frequencies in isothermal bubble columns were adapted to the population balance equation using the bubble mass as the internal coordinate which was discretized using an expansion of the number density function by impulse functions. A sparger model was developed based on experimental data for a non-coalescing system and using bubble formation models for isothermal and non-isothermal conditions. Bubble size distributions in a direct-contact evaporator operating in the quasi-steady-state regime for four different gas superficial velocities, including the homogeneous and heterogeneous regimes, together with the sparger model, were used for estimating the three empirical parameters from the population balance model, which were observed to be functions of the gas superficial velocity. In all cases considered, the population balance model fitted the experimental data rather well and the regressed parameters exhibit the physically expected behavior with changes in the gas superficial velocity.     

Modeling and simulation of polypropylene particle size distribution in industrial horizontal stirred bed reactors

This work aims at developing a steady-state particle size distribution (PSD) model for predicting the size distribution of polypropylene particles in the outflow streams of propylene gas-phase horizontal stirred bed reactors (HSBR), on the one hand and investigating the effect of the catalyst residence time distribution (RTD) on the polymer PSD, on the other hand. The polymer multilayer model (PMLM) is used to describe the growth of a single particle. Knowing the PSD and RTD of a Ziegler–Natta type of catalyst and polymerization kinetics, this model allows calculating the polymer PSD of propylene polymerization in the HSBRs. The calculated polypropylene PSDs agree well with those obtained from the industrial reactors. The results reveal that both the PSD and the RTD of the catalyst affect the polymer PSD but in different manners. The effect of RTD on the PSD is less significant in the case of a nonuniform size catalyst feed. This model also allows investigating the effects of other process parameters on the polymer PSD under steady-state conditions, including intraparticle mass- and heat-transfer limitations, initial catalyst size, and polymer crystallinity. © 2012 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Using discrete simulation of microprocesses in dispersed phases in analyzing multiphase flows with reactions

An approach to define collisional properties and kinetic coefficients for simulating multiphase flows with reactions by integrating discrete and continuum models is developed. Accordingly, the microprocesses are investigated separately by numerical simulations of a discrete system in order to obtain information about collision frequencies, diffusion rates, etc., and then this information is incorporated into a continuous population balance model. The approach is demonstrated on a two-phase turbulent flow in a pipe type reactor where a single irreversible coalescence reaction between the identical species of the dispersed phase takes place and on diffusion of droplets in a turbulent field. A generalization of the approach to a polydispersed system of species is outlined.     

The effect of coalescence on drop size distribution in an agitated liquid-liquid dispersion

A procedure involving high speed cine photography and novel optical probes has been used to study droplet interaction phenomena in liquid-liquid dispersions. Coalescence and breakup events were observed and the rate of coalescence was measured at various positions in a stirred tank for dispersions of methylisobutylketone in water. For the conditions studied, drop breakup occurred near the impeller and droplet coalescence predominated at other locations, as expected. However, the extent of this behavior was unexpected. Beyond distances from the impeller region of order of only $\text{1}\text{6}$ the impeller diameter, breakup was virtually nonexistent. Outside the impeller region, extensive coalescence measurements showed (1) collisions between droplets are extremely inefficient for this chemically equilibrated system—at most 10% of collisions result in a coalescence, (2) only binary coalescence occurs even at the highest dispersed phase concentration investigated, (3) coalescence rate shows little preference on drop size, and (4) the coalescence rate is directly proportional to turbulence level; that is, the highest coalescence rates occur closest to the impeller. On the basis of these measurements, drop balance methods and a circulation path model were used to relate the drop size distribution at various locations in the region where coalescence predominates. In this case good agreement was obtained between measured and predicted drop size distributions.     

群体平衡方程在搅拌反应器模拟中的应用

群体平衡方程（population balance equation,PBE）是描述多相流体系中分散相大小与分布随时空变化的通用方程。搅拌反应器内多为多相流体系,考虑到颗粒聚并、破碎等微观机制对颗粒大小、分布、粒数密度等宏观参量的影响,采用PBE对搅拌槽内多相流体系进行数值模拟,可以较准确预测搅拌槽内流场和颗粒的大小与分布。对群体平衡方程在搅拌反应器数值模拟中的应用进行了综述,在简要介绍PBE的基本形式后,讨论了PBE的主要数值求解方法,然后着重介绍近年来采用PBE对搅拌槽内液固沉淀过程、气液及液液体系进行数值模拟的情况,并对今后的研究方向进行了展望。     

Numerical simulation and experimental study of emulsification in a narrow-gap homogenizer

The present experimental and theoretical study investigates the fragmentation of the oil phase in an emulsion on its passage through a high-pressure, axial-flow homogenizer. The considered homogenizer contains narrow annular gap(s), whereupon the initially coarse oil drops break into fine droplets. The experiments were carried out using either a facility with one or two successive gaps, varying the flow rate and the material properties of the dispersed phase. The measured drop size distributions in the final emulsion clearly illustrated that the flow rate, as well as the dispersed-phase viscosity, and the interfacial tension can significantly affect the drop size after emulsification. The larger mean and maximum drop diameters obtained for the homogenizer with one gap in comparison to those obtained with two gaps (at the same Reynolds number and material parameters of the emulsion phases), highlighted the strong relevance of the flow geometry to the emulsification process. The numerical simulation of the carrier phase flow fields evolving in the investigated homogenizer was proven to be a very reliable method for providing appropriate input to theoretical models for the maximum drop size. The predictions of the applied droplet breakup model using input values from the numerical simulations showed very good agreement with the experimental data. In particular, the effect of the flow geometry—one-gap versus two-gaps design—was captured very well. This effect associated with the geometry is missed completely when using instead the frequently adopted concept of estimating input values from very gross correlations. It was shown that applying such a mainly bulk flow dependent estimate correlation makes the drop size predictions insensitive to the observed difference between the one-gap and the two-gaps cases. This obvious deficit, as well the higher accuracy, strongly favors the present method relying on the numerical simulation of the carrier phase flow.