Mean drop size correlations and population balance models for liquid—liquid dispersion

Reliable models are required for accurate estimation of drop sizes which govern the interfacial area and rate of mass transfer in a system where various correlations and models have been improved for better accuracy and wider application breath. In this article, relevant semiempirical equations and population balance equation (PBE) models are reviewed. Semiempirical correlations are highly system dependent and limited to prediction of steady‐state drop size while PBE models could estimate transient drop size with considerations of inhomogeineity and flow spatial variation during drop size evolution. With appropriate model parameters determination, different PBE models can be used to reproduce experimental data for a similar system. © 2015 American Institute of Chemical Engineers AIChE J, 61: 1129–1145, 2015     

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.     

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.     

Investigation of hydrodynamic performance and effective mass transfer area for Sulzer DX structured packing

The hydrodynamic performance in terms of pressure drop (?P) and liquid holdup (h_L), and tshe effective mass transfer area (a_e) of Sulzer DX structured packing were investigated at 293.15 K and 101.3 kPa. In addition, the flooding velocity (u_F) was also calculated based on the experimental results of liquid holdup, and the effective voidage correction factor (?) was obtained by combining the Billet model and the experimental effective fraction. The liquid volume method and pressure difference from just below to above the column packing approach are used to describe the hydrodynamic performance in a structured packing column. Experimental results showed that the operational conditions in terms of gas flow rate, liquid flow rate, viscosity, and liquid systems strongly affect the hydrodynamic performance. The experimental comparison between the pressure drop profiles in air‐water (polyethylene oxide [PEO]) and MEA‐H₂O‐CO₂ systems indicated that both the reacting MEA and CO₂ partial pressure can enhance the pressure drop value. In addition, the Bain‐Haugen correlation model was developed to predict the flooding velocity data with an acceptable AARD of 8.1%, and a model was also successfully proposed to predict the values of liquid holdup with an AARD of 11.8%, which is lower than 14.7% in Billet model. Furthermore, the effective mass transfer area was found to be increased by increasing both the liquid and gas flow rate by using NaOH‐H₂O‐CO₂ system. A model was also proposed to calculate the experimental a_e with an acceptable AARD% of 19.52, and this built model (Eq. 39) can reasonably explain the experimental phenomenon. © 2018 American Institute of Chemical Engineers AIChE J, 64: 3625–3637, 2018     

CFD Modeling of Active Volume Creation in a Non‐Newtonian Fluid Agitated by Submerged Recirculating Jets

Computational fluid dynamics (CFD) models were employed to investigate flow conditions inside a model reactor in which yield stress non‐Newtonian liquid is mobilized using submerged recirculating jets. The simulation results agree well with the experimental results of active volume in the reactor obtained using flow visualization by the authors in a previous study. The models developed are capable of predicting a critical jet velocity (v_c) that determines the extent of active volume obtained due to jet mixing. The v_c values are influenced both by the rheological properties of the liquid and the nozzle orientation. The liquid with higher effective viscosity leads to higher v_c for a downward facing injection nozzle. However, an upward facing injection nozzle along with a downward facing suction nozzle generates enhanced complementary flow fields which overcome the rheological constraints of the liquid and lead to lower v_c.     

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.     

PREDICTION OF DROP SIZE IN PULSED PERFORATED-PLATE EXTRACTION COLUMNS

A single expression for the prediction of drop size in the mixer-settler, transition and emulsion regimes of operation in pulsed perforated-plate liquid/liquid extraction columns is presented. Analysis of 326 published drop size measurements both with and without mass transfer for 16 liquid/liquid systems from 12 different data sources show that the Sauter mean drop diameter, d ₃₂, in the dispersion is given in terms of column geometry, operating conditions and physical properties of the phases by:

in which ρ_* and σ _* are the density and surface tension of water at 20°C and α and 1 are the fractional plate free area and compartment height respectively. This equation predicts the drop diameter with an average deviation of 11·3% which is much better than the average errors obtained using other available correlations.     

Regime transition in viscous and pseudo viscous systems: A comparative study

A comprehensive quantitative study on the effect of liquid viscosity (1 ≤ µ_L ≤ 1149 mPa‐s) on the local flow phenomena of the gas phase in a small diameter bubble column is performed using ultrafast electron beam X‐ray tomography. The internal dynamic flow structure and the bubble size distribution shows a dual role of the liquid viscosity on the hydrodynamics. Further, the effect of solid concentration (C_s = 0.05, 0.20) on the local flow behavior of the gas phase is studied for the pseudo slurry viscosities similar to the liquid viscosities of the gas–liquid systems. The effects of liquid and pseudo slurry viscosities on flow structure, bubble size distribution, and gas phase distribution are compared. The bubble coalescence is significantly enhanced with the addition of particles as compared to the system without particles for apparently same viscosity. The superficial gas velocity at which transition from homogeneous bubbly to slug flow regime occurs is initiated by the addition of particles as compared to the particle free system for apparently same viscosity. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3079–3090, 2014     

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.     

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     

Investigation of flow parameters and efficiency of mixture separation on a structured packing

Results of experimental study of the effect of initial maldistribution of structured packing irrigation on efficiency of binary mixture separation are presented in this article. The studies were carried out in the experimental distillation column with the diameter of 0.9 m using the R114 and R21 freon mixture. Experiments were performed on the structured Mellapak 350.Y packing of stainless steel 316L, containing 19 layers with the total height of 4.016 m at the ratio of mole liquid and vapor flow rates L/V = 1 and 1.7, respectively, and the pressure in the upper part of the column p_top = 3 bars. Nonuniformity at the packing inlet was generated via the blocking of some holes in the liquid distributor. Here, we present some results on efficiency of mixture separation, pressure drop on the packing, distribution of local liquid flow rate under the packing over the cross‐section and on the column wall within the range of vapor loading factor (0.69 < F_v < 1.61 Pa^0.5), as well as experimental data on distribution of local concentration of the low‐boiling component over the cross‐section and along the height of the structured packing. It is found out that significant maldistribution of mixture concentration and liquid flow rate over the cross‐section slightly changes along the height in the lower part of the column at a change in the degree of packing irrigation nonuniformity at the inlet. It is shown that efficiency of mixture separation depends considerably on the value of parameter L/V, vapor flow factor F_v, and size of the zone underirrigated by liquid at the inlet. In the studied range of liquid and vapor flow rates, the relative pressure drop on the packing does not depend on the ratio of liquid and vapor flow rates L/V and degree of irrigation maldistribution. © 2013 American Institute of Chemical Engineers AIChE J 60: 690–705, 2014     

Numerical study of turbulent liquid‐liquid dispersions

A numerical approach is developed to gain fundamental insight in liquid‐liquid dispersion formation under well‐controlled turbulent conditions. The approach is based on a free energy lattice Boltzmann equation method, and relies on detailed resolution of the interaction of the dispersed and continuous phase at the microscopic level, including drop breakup and coalescence. The capability of the numerical technique to perform direct numerical simulations of turbulently agitated liquid‐liquid dispersions is assessed. Three‐dimensional simulations are carried out in fully periodic cubic domains with grids of size . The liquids are of equal density. Viscosity ratios (dispersed phase over continuous phase) are in the range 0.3–1.0. The dispersed phase volume fraction varies from 0.001 to 0.2. The process of dispersion formation is followed and visualized. The size of each drop in the dispersion is measured in‐line with no disturbance of the flow. However, the numerical method is plagued by numerical dissolution of drops that are smaller than 10 times the lattice spacing. It is shown that to mitigate this effect it is necessary to increase the resolution of the Kolmogorov scales, such as to have a minimum drop size in the range 20–30 lattice units [lu]. Four levels of Kolmogorov length scale resolution have been considered , 2.5, 5, and 10 [lu]. In addition, the numerical dissolution reduces if the concentration of the dispersed phase is increased. © 2015 American Institute of Chemical Engineers AIChE J, 61: 2618–2633, 2015     

Gas‐Liquid Mass Transfer in Fibrous Bed Reactor with Counter‐Current Liquid Recycle

In this work, the gas‐liquid mass transfer in a lab‐scale fibrous bed reactor with liquid recycle was studied. The volumetric gas‐liquid mass transfer coefficient, k_La, is determined over a range of the superficial liquid velocity (0.0042–0.0126 m.s^–1), gas velocity (0.006–0.021 m.s^–1), surface tension (35–72 mN/m), and viscosity (1–6 mPa.s). Increasing fluid velocities and viscosity, and decreasing interfacial tension, the volumetric oxygen transfer coefficient increased. In contrast to the case of co‐current flow, the effect of gas superficial velocity was found to be more significant than the liquid superficial velocity. This behavior is explained by variation of the coalescing gas fraction and the reduction in bubble size. A correlation for k_La is proposed. The predicted values deviate within ± 15 % from the experimental values, thus, implying that the equation can be used to predict gas‐liquid mass transfer rates in fibrous bed recycle bioreactors.     

Hydrodynamics and droplet size distribution of liquid–liquid flow in a packed bed reactor with orifice plates

A packed bed reactor with orifice plates (PBR@OP) was designed by adding orifice plates periodically in packed beds. Hydrodynamics and droplet size distribution in PBR@OP were experimentally investigated using fatty acid methyl esters (FAME)/water as the model liquid–liquid system. In PBR@OP, the flow pattern was close to plug flow. Droplets with Sauter mean diameter (d₃₂) of 150–550 μm were generated. The pressure drop of orifice, flow velocity and plate spacing were key parameters to control the droplet size. The reactor performance was evaluated by analyzing a FAME epoxidation process. At the same d₃₂ and residence time, the length and total pressure drop of PBR@OP were about 1/3 and 1/4 of those of PBR without orifice plates, respectively. Furthermore, a semi-empirical correlation describing the d₃₂ change in PBR@OP was developed, revealing a relative mean deviation of 8.64%. PBR@OP presents a cost-effective option for the intensification of liquid–liquid medium rate reactions.     

Prediction of CO2 gas permeability behavior of ionic liquid–polymer membranes (ILPM)

Predicting the gas permeability of ionic liquid‐polymeric membranes (ILPM) is of great importance for the design of efficient gas separation membrane materials. The available models for the prediction of CO₂ gas permeability through ionic liquid‐polymeric membranes were analyzed using the literature data. Maxwell model was selected for modification due to relatively accurate prediction capability. The Maxwell model was modified for ionic liquid‐polymeric membranes by incorporating model parameter k for the effectiveness of volume fraction of dispersed phase. The established methodology was tested for different ionic liquid‐polymeric membrane systems for validation. A satisfactory agreement was observed for predicted and experimental permeability by using the current approach. This method can be used for the prediction of CO₂ gas permeability through ionic liquid‐polymeric membranes. © 2017 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44761.