The effect of pH on experimental and simulation results of transient drop size distributions in stirred liquid-liquid dispersions

A novel parameter study with experimental and numerical investigations of transient drop size distributions was carried out in order to study published model approaches for dispersed systems on the basis of the population balance equation. In terms of breakage and coalescence behaviour the dependency of the drop size distributions on power input, phase fraction, and especially pH was studied with the system toluene-water. With higher pH, coalescence is hindered considerably. As a consequence, the transient evolution of drop size distributions after starting the stirrer is changing and the time for reaching the stationary distribution increases. For the simulation applying the breakage and coalescence models a very efficient solver for the population balance equation (PBE), the program PARSIVAL^® is used. The simulation results of transient drop size distributions are in good agreement with the experimental data for various power inputs. The influence of the dispersed phase fraction is not characterized correctly.A proportionality between the Sauter mean diameter and the Weber number d₃₂∼We^-0.5 was measured for pH 13 and different phase fractions. The commonly reported exponent -0.6 for systems with low coalescence seems to be not applicable with higher pH and increased dispersed phase fraction.     

Drop size distribution in highly concentrated liquid–liquid dispersions using a light back scattering method

New data are presented on drop size distribution at high dispersed phase fractions of organic‐in‐water mixtures, obtained with a light back scattering technique (3 Dimensional Optical Reflectance Measurement technique, 3D ORM). The 3D ORM technique, which provides fast, in‐situ and on‐line drop distribution measurements even at high concentrations of the dispersed phase, is validated using an endoscope attached to a high‐speed video recorder. The two techniques compared favourably when used in a dispersion of oil (density (ρ) = 828 kg m^?3, viscosity (µ) = 5.5 mPa s, interfacial tension (σ_i) = 44.7 mN m^?1) in water for a range of 5–10% dispersed phase fractions. Data obtained with the ORM instrument for dispersed phase fractions up to 60% and impeller speeds 350–550 rpm showed a decrease in the maximum and the Sauter mean drop diameters with increasing impeller speed. Phase fractions did not seem to significantly affect drop size. Both techniques showed that drop size distributions could be fitted by the log‐normal distribution. Copyright © 2005 Society of Chemical Industry     

Drop size distribution in a mixer–settler reactor for the gold chloride/DBC system

An experimental investigation was carried out in order to analyze the drop size distributions of liquid–liquid dispersion in a horizontal mixer–settler. Two aqueous chemical systems were studied: synthetic gold solution and gold solution prepared from the leaching of copper anode slimes. The dependency of the drop size distributions on impeller speed, 335–600 rpm, and phase fraction, 0.167–0.54, were studied for gold chloride–DBC system. The Sauter mean diameter, D₃₂, was correlated for both systems in the frame of classical Hinze–Kolmogorov theory. The results showed that, for each volume fraction in the studied range, D₃₂ is decreasing as a power function of Weber number with an exponent equal to −0.73 and −0.65 for leach and synthetic solution, respectively. This corroborates that the mentioned theory may not be the most adequate to correlate drop size diameters, particularly when reaction occurs in the system. Also such a variation of the exponent may be interpreted as a different combination of the continuous phase. However, for both systems studied, correlation to show the effect of reaction on D₃₂ has been represented. By comparing the results, the prediction of mean drop size diameter in the leach solution is possible by using synthetic solution data with AARD <10%.     

Drop break-up in turbulent pipe flow downstream of a restriction

This work addresses the drop fragmentation process induced by a cross-sectional restriction in a pipe. An experimental device of an upward co-current oil-in-water dispersed flow (viscosity ratio λ≈0.5) in a vertical column equipped with a concentric orifice has been designed. Drop break-up downstream of the restriction has been studied using a high-speed trajectography. The first objective of this work deals with a global analysis of the fragmentation process for a dilute dispersion. In this context, the operating parameters of the study are the orifice restriction ratio β, the flow Reynolds number, Re and the interfacial tension, σ. The break-up domain has been first mapped on a β(Re) graph and drop size distributions have been measured for different flow Reynolds numbers. It was observed that the mean drop diameter downstream of the restriction linearly increases as a function of the inverse of the square root of the pressure drop. This behaviour is in agreement with the observations previously made by Percy and Sleicher [A.I.Ch.E. Journal, 1983, 29(1), 161-164]. In addition, experiments based on the observation of single drop break-up downstream of the orifice have allowed the identification of different break-up mechanisms, and the determination of statistical quantities such as the break-up probability, the mean number of fragments and the daughter drop distribution. The drop break-up probability was found to be a monotonous increasing function of the Weber number based on the maximal pressure drop through the orifice. The mean number of fragments is also an increasing function of the Weber number and the reduced mean daughter drop diameter decreases as the Weber number increases. The daughter drop distributions are multimodal at low and moderate Weber numbers as a result of asymmetrical fragmentation processes. The statistical analysis of single drop break-up experiments was implemented in a simple global population balance model in order to predict the evolution of the size distribution across the restriction at different Reynolds numbers, in the limit of dilute dispersions.     

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.     

Effect of Impeller Blade Height on the Drop Size Distribution in Agitated Dispersions

A common method to achieve a contact of two liquid phases – required for many chemical engineering operations – is the dispersion of one into the other by mechanical agitation. The drop size distribution in such an agitated dispersion is a result of the dynamic equilibrium existing between the breaking and coalescing drops. A comparison has been made of drop diameters produced by four disk type impellers differing only in blade height (D_W = 1, 2, 4 and 6 cm). Measurements in situ at 200, 250, 300, 350, 400, 450 rpm and at holdup fractions 0.02, 0.05, and 0.07, showed that the Sauter mean drop diameters increased up to 140 % as the impeller blade height decreased from 6 to 1 cm. Plots of ln α₃₂ vs. ln N, lnα₃₂ vs. ln D_T and ln α₃₂ vs. ln α_max gave straight lines.     

A CRITICAL REVIEW: SURFACE AND INTERFACIAL TENSION MEASUREMENT BY THE DROP WEIGHT METHOD

The drop weight method has been used as a standard method for surface and interfacial tension measurement. However, lack of appropriate guidelines in using this method has resulted in errors. The specific objective of this critical review is to present the experimental setup, the limitations on the correction factors, and the principle of the drop weight method. Mathematical models of correction factors were evaluated by using a proposed error analysis. The use of the proposed Lee-Chan-Pogaku model and HG-Equation 2 for correction factor determination is suggested. However, further investigations would be required to justify the validity of the correction factors at low r/V ^1/3 range and their use for viscous fluids. The physics of drop detachment is complicated; more investigations would be required to form a rigid theory of this method.     

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.     

Size distribution of drops formed from nozzles in liquid-liquid systems at velocities below jetting

The size distribution of drops formed from four different diameter nozzles (d=l.O, 1.6, 2.6 and 3.5 mm) was measured over the flow rate range of 0.17 to 3.0 cm3/s (below jetting). Kerosene was used as the dispersed phase and distilled water was used as the continuous phase. The experimental drop size distributions were described adequately by the upper limit number and volume distributions. Plots of the maximum and the minimum diameters versus the mean diameter yielded straight line with slopes of 1.11 and 0.87, respectively.     

Experimental and analytical study of countercurrent flow limitation in vertical gas/liquid flows

An experimental and analytical study of adiabatic countercurrent flow limitation (flooding) in single vertical ducts is reported. The experiments were carried out in a rectangular channel using saturated liquid and vapour of Refrigerant 12 (CCl₂F₂). The steady-state liquid delivery (flooding) curves as well as local pressure drop and void fraction distributions in the countercurrent flow were measured in a range of system pressures from p/p_crit = 0.16 to p/p_crit = 0.31, and for various total liquid injection rates and locations. The measured flooding curves j₁ = f(j_g) as well as pressure drop and void fraction during partial liquid delivery (j₁ < j₁ⁱⁿ) were not affected either by the axial liquid feed location or by the excess liquid rate carried upwards by the vapour. Moreover, for given flow conditions during flooding pressure drop and void fraction were essentially the same at different axial positions. Radial void fraction distributions evaluated from optical fibre probe data indicate an annular-type flow pattern. Based on this experimental evidence, a mechanistic core/film flow model was developed for the calculation of flooding. The analytical results are compared with the present high pressure and with comparable atmospheric pressure experimental data, showing reasonable overall predictions not only of the flooding curves, but also of the pressure drop in countercurrent flow.     

On the effect of phase fraction on drop size distribution of liquid–liquid dispersions in agitated vessels

The theory of Kolmogorov–Hinze is the base for many studies that have been done on mean drop size and drop size distribution of liquid–liquid dispersions in agitated vessels. Although this theory has been used extensively in the literature, but it does not always give a satisfactory result in the studies and therefore needs to be modified. This paper addresses the effect of phase fraction on drop size distribution in agitated vessels and on the proportionality coefficient and Weber number exponent in the relation d₃₂/D ∝ We^m. The experimental data that were taken from Pacek et al. (1998) and Desnoyer et al. (2003) have been applied to this relation to investigate the effect of phase ratio. It is shown that even at low phase fractions, the Kolmogorov–Hinze theory necessarily does not give the best result with the −0.6 exponent for the Weber number. Furthermore, for the non-coalescing system, a range of exponent for the Weber number typically from −0.6 to −0.43 can be considered where the system may be approximated as a pseudo-coalescing system at Φ = 0.4 in which the obtained results are in good agreement with the results of Pacek et al. (1998).     

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.     

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.     

Drop Detachment from a Micro‐Engineered Membrane Surface in a Dynamic Membrane Emulsification Process

Drop size distribution is an important characteristic of emulsions, probably the most crucial one for their use in various applications. Here, a pilot‐scale apparatus with a cone‐shaped flow geometry is introduced. The plate contains a micro‐engineered membrane manufactured from silicon allowing for the production of emulsions with narrow drop size distributions. The process is characterized by producing model emulsions of the oil‐in‐water type under laminar rheometric flow conditions and by accessing the regime of drop detachment as a function of the wall shear stress applied, by means of high‐speed imaging in a separate flow cell. Furthermore, clear evidence is given of the crucial influence of the membrane wetting properties on the emulsification results, by comparing the performance of micro‐engineered membranes composed either of silicon, silicon nitride, or nickel, for pore diameters from 1 to 12 μm, in the flow cell.     

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.     

Laboratory Evaluation of a TSI Condensation Particle Counter (Model 3771) Under Airborne Measurement Conditions

The performance of a condensation particle counter (CPC, Model 3771, TSI Inc.), which has a nominal minimum detectable particle size (d ₅₀) of 10 nm, has been tested in the laboratory for the purpose of airborne measurements. First, the effects of particle coincidence at concentrations above the upper limit specified by the manufacturer (>10⁴ cm^-3 were evaluated. By applying a correction factor derived from experimental results, the CPC can quantify particle concentrations of as high as 5 × 10⁴ cm– 3. Second, the effects of inlet pressure (p) on the size dependence of the detection efficiency were investigated (particle diameter (d)= 8–100 nm, p= 1010–300 hPa). The asymptotic detection efficiency and d ₅₀ showed decreasing and increasing trends with decreasing pressure, respectively, especially at p < 600 hPa. It is likely reduction of the 1-butanol saturation ratio in the condenser at decreased pressures can explain the observed pressure dependence. Finally, the temporal variation of the detection efficiency during continuous operation of the CPC without the supply of 1-butanol was investigated (d= 10 and 100 nm, p = 1010, and 600 hPa). The detection efficiencies did not show significant change, at least over 6 h, without the supply of 1-butanol, which ensures stable performance of the CPC for flight durations of 4–5 h. Based on our laboratory evaluations, possible errors in airborne measurements were estimated assuming typical particle number size distributions of ambient aerosols.     

A Model of dispersion hydrodynamics in a vibrating plate extractor

A stagewise polydisperse model of the Karr vibrating plate extractor hydrodynamics is presented. It describes the drop size distribution and the dispersed phase hold-up as functions of drop transport, breakage and coalescence. ¹ The predicted stationary hold-up profiles and drop size distributions are proved to be in good agreement with the experimental data.     

油水两相分散流液滴粒径预测模型

油水两相分散流的液滴粒径及其分布在很大程度上影响管路压降等流动参数,研究液滴粒径预测模型对揭示油水两相流的流动特性具有重要意义。通过研究湍流脉动动能与乳状液的界面能之间的平衡、管流径向速度脉动与摩擦速度之间的关系以及泵的剪切作用,建立了油水两相管流中分散相液滴粒径预测模型;在水平管道上对油水两相分散流的液滴特性进行了实验研究,采用高速摄像和显微镜拍摄获得液滴数据,探索含油率、流量和温度等因素对粒径的影响。预测模型计算结果与不同流量、温度和含油率条件下的实验数据吻合较好。根据预测模型计算了有泵和无泵情况下分散流液滴粒径,发现泵的剪切和扰动作用使得分散液滴具有更小的粒径,泵对液滴粒径及其分布起到了显著作用。     

Droplet size and velocity profiles in liquid-liquid horizontal flows

The size and vertical distribution of drops were studied experimentally in dispersed liquid-liquid pipeline flows. Under most conditions the pattern was dual continuous where both phases retain their continuity and there is entrainment in the form of drops of one phase into the other. The investigations were carried out in a stainless steel test section with 38 mm ID with water and oil (density and viscosity ) as test fluids. Mixture velocities from 1.5 to and input oil volume fractions from 20% to 80% were used. A dual sensor impedance probe allowed drop chord length and drop velocity measurements at different locations in a pipe cross section.It was found that in dual continuous flows drop concentration and size decreased with increasing distance from the interface. There were only small differences in size between oil drops in the lower water continuous layer of the flow and water drops in the upper oil continuous layer. Mixture velocity did not affect significantly the drop size of either phase since higher velocities that would result in smaller drops were accompanied by increased entrainment of one phase dispersed into the other that favoured larger drops. The Rosin-Rammler function was found to fit satisfactorily the experimental drop size distributions, while literature correlations on entrained and maximum drop sizes in a turbulent field underpredicted the values found experimentally.