Affecting Separation Efficiency Research Articles

CFD-DEM simulation and experimental validation of air classification for tobacco particles

In cigarette processing, the challenge is particularly significant during the air classification of tobacco and stems due to their similar characteristics. This paper employs computational fluid dynamics (CFD) combined with the discrete element method (DEM) to analyze factors affecting separation efficiency and improve performance. The results were validated through laboratory and production line experiments at a 1:1 scale. The tobacco (length: 0 mm–4.75 mm, diameter: 0.32 mm) and stem (length: 0–25.145 mm, diameter: 1.51 mm) were modeled based on production samples. Findings suggest that particle feeding speed primarily impacts tobacco loss rate, while inlet air velocity mainly influences stem removal rate. Optimizing the chamber structure in the simulation resulted in a 63.66 % improvement in separation efficiency. Airflow streamlines, particle distribution, trajectory, and collision behaviors were discussed to illuminate motion characteristics. The flexible particle model moderately influenced separation efficiency and collision behaviors. These insights enhance the understanding of particle separation and the design of separation devices.

Industrial Textile Wastewater Treatment by Crossflow NF Membrane Filtration

Ineffective dyeing procedures frequently lead to the release of approximately 10–50% of the dye applied, which does not adhere to the fabric and is consequently discharged into the environment along with the effluent. This situation is undesirable both for potential recycling within the textile manufacturing process and because of its adverse environmental pollution effects. This study thoroughly examines nanofiltration (NF) membrane characteristics and their performance in textile wastewater treatment. Pristine NF membrane surfaces were revealing a web-like structure with well-defined pores predominantly in the membrane active region. This assessment confirms the membrane initial cleanliness, free from any external contaminants, which is vital for effective membrane-based filtration. Additionally, the study investigates how different feed flow rates affect water flux during NF membrane filtration. The results demonstrate a clear relationship, where the increasing flow rates boost water flux. This can be attributed to heightened cross-flow velocity and shear force on the membrane surface due to the increased water flux, minimizing external concentration polarization and reducing membrane fouling. The impact of feed flow rate on membrane separation efficiency is also examined, showing consistent efficiency at feed flow rates between 2 LPM and 5 LPM (approximately 80.8% to 82.22%). However, efficiency drops as the feed flow rate increases from 5 LPM to 6 LPM, likely due to increased pressure drop across the membrane, affecting separation efficiency.

Magnetic perlite based molecularly imprinted polymer on screen printed carbon electrode as a new tyramine electrochemical sensor

This paper describes the design and fabrication of a sensitive electrochemical sensor using a new magnetic pearlite-based molecularly imprinted polymer (MPt/MIP) for the voltammetric determination of tyramine (Tyr). MPt/MIP nanocomposite was synthesized by direct surface-based imprinting procedure using methacrylic acid (MAA) as monomer for MIP and also functional group for magnetic perlite (MPt). The structural properties of MPt/MIP nanocomposite were characterized using scanning electron microscopy (SEM), X-ray diffraction (XRD), FT-IR spectroscopy, vibrating sample magnetometry (VSM) and via adsorption kinetics and adsorption isotherms. The integrated analytical procedure consists of dispersion of synthesized MPt/MIPs for selective separation of target analyte from sample and their subsequent localization on the surface of a magnetic screen-printed carbon electrode (MSPCE) as a platform for determination of Tyr by differential pulse voltammetry (DPV). The experimental parameters which affect separation efficiency and electrochemical determination were optimized. The developed method provided a linear calibration range of 8.0 to 380.0 ng mL−1 (R2 = 0.998), and a detection limit of 3.8 ng mL−1. The intra-day and inter-day precision (%RSD) were in the range 3.1–4.4 %. The method was successfully applied to the determination of Tyr in real samples with recoveries ranging from 94.2 to 105.2 %.

Optimising mechanical separation of anaerobic digestate for total solids and nutrient removal

Mechanical separation of anaerobic digestate has been identified as a method to reduce pollution risk to waterways by partitioning phosphorus in the solid fraction and reducing its application to land. Separators have adjustable parameters which affect separation efficiency, and hence the degree of phosphorous partitioning, but information on how these parameters affect separation performance is limited in the literature. Two well known technologies were investigated, decanter centrifuge and screw press, to determine the most efficient method of separation. Counterweight load and the use of an oscillator were adjusted for the screw press, while bowl speed, auger differential speed, feed rate and polymer addition were modified for the decanter centrifuge. Separation efficiency was determined for total solids, phosphorus, nitrogen, potassium, and carbon, and the total solids content of resulting fractions was measured. The decanter centrifuge had higher separation efficiency for phosphorus in all cases, ranging from 51% to 71.5%, while the screw press had a phosphorus separation efficiency ranging from 8.5% to 10.9% for digestate of ∼5% solids (slurry/grass silage mix). Separation by decanter centrifuge partitioned up to 56% of nitrogen in the solid fraction leaving a reduced nitrogen content in the liquid fraction available for land spreading; this nitrogen would most likely need to be replaced by chemical fertiliser which would add to the cost of the system. The decanter centrifuge is better suited to cases where phosphorus recovery is the most important factor, while the screw press could be advantageous in cases where cost is a limiting factor.

Combination of the insulator‐based dielectrophoresis and hydrodynamic methods for separating bacteria smaller than 3 μm in bloodstream infection: Numerical simulation approach

AbstractBloodstream infections have a high mortality rate with >80,000 deaths per year in North America. The inability to detect pathogens quickly in the early stages of the infection causes high mortality. Such inability has led to a growing interest in developing a rapid, sensitive, and specific method for identifying these pathogens. The rapid detection of bloodstream infections requires the rapid and efficient separation of bacteria from the blood. But the problem is that the number of bacteria is much lower than other blood components. The blood culture step needs to be accomplished first for bacteria identification and antibiotic susceptibility testing. As the blood culture is time‐consuming, a method based on the insulator‐based has been presented that increases the number of bacteria by combining the blood culture method and increasing the concentration. In this model, the dielectrophoresis technique was utilized in a curved microchannel with a constriction for sorting three particle sizes including 9, 7–4 μm, as well as smaller than 3 μm. The results showed that the applied voltage and the channel dimensions affect separation efficiency. Suppose these values are properly selected (for example, a voltage of 110 V that was causing the maximum electric field of 200 V/cm). The proposed model can completely (100%) separate larger than 9 μm and smaller than 3 μm particles. The proposed model has simple geometry and is considered an appropriate technique for sorting all bacteria separation in bloodstream infection.

Separator performance modeling and analysis using artificial neural network and response surface method

The performance of swirl-vane separator is mainly obtained by experiments or numerical simulation, which is expensive and time-consuming. ANN models based on a back-propagation neural network (BPNN), a generalized regression neural network (GRNN), and an Elman neural network (Elman NN) have been developed. 127 experimentally obtained separator performance data points are used for model training and verification. The results show that GRNN model demonstrated the highest prediction accuracy. Furthermore, parametric analysis for the gas–liquid separator is carried out by GRNN model incorporated with response surface method (RSM) which shows advantage to reflect the multivariate interaction of separator. It is found that three items (Rewater, Regas × d and Rewater × d) play the key roles in affecting separation efficiency. Quadratic polynomial correlations for separation performance have been developed by RSM and have discrepancies less than 7.5% compared with the experimental results, which show good performance to quickly and accurately predict the performance of separators.

Polyacrylonitrile/poly(acrylic acid) layer-by-layer superimposed composite nanofiber membrane with low iron ion leaching-out and stable methylene blue-removing performance

Membrane process is used to decontaminate dye wastewater. In the process of separation, the adsorbed and/or rejected dyes can greatly foul the membrane and negatively affect separation efficiency. Fenton oxidation can non-selectively mineralize dyes to prevent fouling the membrane. Therefore, this work focused on synthesizing the membrane coupled with Fenton catalyst for dye wastewater treatment. Polyacrylonitrile (PAN)/poly (acrylic acid) (PAA) composite nanofiber membrane was first prepared by layer-by-layer sequential electrospinning and then served as the substrate to load iron ions by the coordination of carboxyl groups of PAA with iron ions, after which a catalytic membrane was successfully prepared. During the application process, water would inevitably elute some iron ions from the catalytic membrane. In order to minimize the loss of iron ions, another PAA/PAN composite nanofiber membrane with the function of rejecting iron ions was then designed and superimposed onto the catalytic membrane using the adhesiveness of upper PAA layer. In this sense, the obtained composite membrane can stably catalyze H2O2 to effectively oxidize methylene blue (MB) due to low leaching-out of iron ions. The results showed that the iron ion loading ratio of PAN/PAA composite nanofiber membrane was increased by 167% compared to that of PAN nanofiber membrane, and the total iron ion elution ratios of PAN nanofiber membrane and PAN/PAA composite nanofiber membrane were 27 times and 6 times higher than that of superimposed composite membrane, respectively. As a result of high loading and low elution of iron ions, the superimposed composite membrane exhibited considerably stable efficiency for MB removal within 30 operation cycles, which reached up to 97.0%. Additionally, the superimposed composite membrane presented better mechanical property and more adjustable permeation flux than the control membranes, so that it would show a great potential for the application in the field of dye wastewater treatment.

Simultaneous determination of fungicides and carbamates in tobacco by ultra performance convergence chromatography-tandem mass spectrometry coupled with modified QuEChERS

This study concerned the development and validation of a green and rapid method for the analysis of 23 pesticides in tobacco using ultra performance convergence chromatography-tandem mass spectrometry (UPC2-MS/MS) combined with modified QuEChERS. The sample was extracted with acetonitrile, purified by graphene, and then determined by UPC2-MS/MS. In this paper, optimization was made on factors affecting separation efficiency including chromatographic column, modifier, column temperature, and back pressure. With CO2-ethanol as mobile phase, all pesticides were adequately separated on a Viridis HSS C18 SB column, and the whole analysis process was completed within 6 min. Under optimal conditions, the calibration curves showed good linearity in the range of 10–200 ng/mL with the regression coefficients higher than 0.9946. The limit of detection and limit of quantification were 1.04–7.07 and 3.32–23.16 μg/kg, respectively. At three spiked levels (0.2, 1.0 and 2.0 mg/kg), mean recoveries for 23 pesticides were ranging from 80.2% to 110.6% and relative standard deviations were 2.2%–7.2%. The proposed method, being fast, sensitive, and practical, can be used for rapid detection of fungicides and carbamates in tobacco.

EFFECT OF LIQUID-VAPOR SEPARATION ON THE THERMAL-HYDRAULIC PERFORMANCE OF AN AIR-COOLED CONDENSER

This work characterizes the use of liquid-vapor separation inside air-cooled condensers and its effect on thermal-hydraulic performance. A series of 3 mm inner diameter U-tubes were installed in the condenser for the liquid-vapor separation with 6 mm inner diameter and 215 mm long-finned condenser tubes. R134a was used as the working fluid. During operation, condensed R134a was separated by the liquid-vapor separation device to significantly improve the heat transfer compared to that of a serpentine condenser without liquid-vapor separation. In addition, fewer tubes were required inside the air-cooled condenser due to its high heat transfer rates, which indicated a potential for reducing the condenser size. This study investigated the key factors affecting the liquid-vapor separation process, such as the number of liquid-vapor separation devices, the wind velocity, and the total mass flow rate. The results indicated that in-tube pressure drop is the dominant parameter affecting separation efficiency. This liquid-vapor separation condenser design had better thermal-hydraulic performance than a serpentine condenser due to the enhanced heat transfer. Adding an additional liquid-vapor separation structure changed the separation conditions of the previous separation structure and made the condensation heat transfer more uniform.

Screening of 5′-Methylthioadenosine Nucleosidase Enzyme Inhibitors from Traditional Chinese Medicine and Small Molecular Compounds by Capillary Electrophoresis After Enzymatic Reaction at Capillary Inlet

A capillary electrophoresis (CE) method was developed for the screening of 5′-methylthioadenosine nucleosidase (MTAN) inhibitors in traditional Chinese drugs and small molecular compounds. In this method, reaction occurred at the capillary inlet during a predetermined waiting period, followed by electrophoretic separation of the reaction substrates and products. Parameters affecting separation efficiency and enzyme activity were evaluated systematically. The optimized conditions were as follows: 30 mM phosphate (pH 3.0) running buffer, 25 kV applied voltage, 20 mM HEPES (pH 6.0) reaction buffer, and 4 min incubation time. Under the optimized conditions, the Michaelis–Menten constant (Km) of MTAN was 3.44 μM, which agreed with the documented data. The proposed method was successfully applied for MTAN inhibitor screening from 21 natural extracts and 8 small molecular compounds. The results demonstrated the practical applicability of the at-inlet reaction-based CE method in screening of MTAN inhibitors from natural products and small molecular compounds.

Demulsification of crude oil emulsions tracked by pulsed field gradient NMR. Part II: Influence of chemical demulsifiers in external AC electric field

Crude oil emulsions can reach stability levels that pose severe challenges for the processing industry. Certain conventional methods are used to deal with these challenges, such as chemical demulsification. In this article, two chemicals were mixed with crude oil emulsions to study their separation capabilities in the presence and absence of external AC fields. Experiments were conducted at 65 ⁰C to lower crude oil viscosity, which in turn affects separation efficiency. Effects from the chemical and electrical constituents on the crude oil emulsion was tracked by a pulsed field gradient NMR method, developed in a previous study. The NMR measured emulsified water content for 2 h, continuously, as a function of sample height. Given the water content, droplet sedimentation and free water layer kinetics could be quantified. Droplet size distributions from the top half oil phase were obtained at the beginning and end of each experiment, with the intent of mapping coalescence and sedimentation development of droplets. However, tracking droplet size evolution proved challenging due to rapid changes within the emulsion. The main focus with the NMR technique was therefore on sedimentation and free water layer kinetics. A synergy was observed between the two chemicals and low AC fields. The two chemicals showed varied degrees of separation efficiency, where limited amounts of water was resolved by chemical 1 without electric field, though it improved separation past the limit of electrical treatment when used in combination with AC field. Above a given electric field, sedimentation by electrocoalscence dominates, and the effect of chemical demulsifier is marginal. Chemical 2 achieved promising results as a lone separation method, while further enhancing separation in collaboration with AC fields.

Stereoselective supercritical fluidic chromatography –mass spectrometry (SFC-MS) as a fast bioanalytical tool to assess chiral inversion in vivo and in vitro

The stereoisomers of a chiral drug can exhibit great differences in pharmacodynamic and/or pharmacokinetic properties. Chiral bioanalytical assays are necessary to measure the concentrations of individual enantiomers and/or their chiral metabolites in biological samples in order to assess the absorption, distribution, metabolism, excretion, and toxicity of the individual enantiomers. In addition, chiral assays are required to evaluate potential chiral inversion caused by the biotransformation process. While normal phase or reversed phase chromatography remains the common choices for chiral bioanalytical assays, supercritical fluid chromatography (SFC) demonstrated shorter analysis time without affecting separation efficiency, due to the lower viscosity and faster mass transfer properties of supercritical or subcritical carbon dioxide than traditionally used mobile phases. In this paper, we present examples for developing chiral SFC-multiple reaction monitoring (MRM) assays to measure the pharmacokinetic profiles of stereoisomers of drugs in three distinct cases. Furthermore, these assays can be used to investigate the potential chiral inversion of the small molecule drugs from in vivo or in vitro sources.

Fast extraction of chloramphenicol from marine sediments by using magnetic molecularly imprinted nanoparticles.

A straightforward method has been developed for selective separation of chloramphenicol (CAP) from marine sediment samples. Magnetic molecularly imprinted nanoparticles (NPs) of type Fe3O4@SiO2 were prepared via surface imprinting with CAP. The NPs were characterized by Fourier transform infrared spectroscopy, transmission electron microscopy and thermogravimetric analysis. They have perfect core-shell structure, excellent thermal stability, high affinity and selectivity to CAP. The imprinting factor and Scatchard analysis also reveal good specific recognition to the template. The imprinted NPs were applied as sorbents for fast and selective extraction of CAP from marine sediment samples. The experimental parameters affecting separation efficiency were optimized. Three marine sediment samples were analyzed. Following desorption with methanol/water (90/10,v/v), CAP was quantified by HPLC withDAD detection. The limit of detection is 0.1μgL-1 with a good linear response between 0.1-20mgL-1 of CAP concentration (R2 = 0.999, n = 3). The method exhibits satisfactory recoveries from spiked samples (77.9-102.5%) and has low relative standard deviations (<6.3%). The magnetic material can be used at least 5 times by the regeneration without any loss of selectivity and adsorption capability. Graphical abstract Schematic presentation of magnetic molecularly imprinted nanoparticles (MMIPs) as sorbent for fast extraction and chromatographic analysis of chloramphenicol (CAP) from marine sediments. CAP-MMIPs are synthesized by surface imprinting method using 3-methacryloxy propyl trimethoxy silane (MPS) as the silane coupling agent.

Analysis of Evodiae Fructus by capillary electrochromatography-mass spectrometry with methyl-vinylimidazole functionalized organic polymer monolilth as stationary phases

Evodiae Fructus is used as a traditional Chinese medicine for the treatment of several kinds of diseases with its bioactive constituents. In this study, a capillary electrochromatography-mass spectrometry (CEC-MS) method was developed to determine three bioactive compounds including evodiamine, rutaecarpine and limonin in Evodiae Fructus fruit. Home-developed monolithic columns with methyl-vinylimidazole functionalized organic polymer monolilth as stationary phases were used in CEC-MS with excellent separation selectivity and high efficiency. The CEC-MS methods provided 4–16 folds improvement of LODs when compared with CEC-UV method. The conditions, which could affect separation efficiency and detection sensitivity, were optimized. Under optimum conditions, baseline separation with high detection sensitivity was obtained. The method showed good linearity (R2 >0.99) of 0.8–160 μg mL−1 with low limits of detection of 0.15-0.31 μg mL−1. Relative standard deviations of migration time and relative peak areas were <13.89%. Recoveries of evodiamine, rutaecarpine and limonin in Evodiae Fructus fruit were tested and calculated, which ranged from 102% to 113%. Finally, the three bioactive compounds in Evodiae Fructus herb samples from different regions were analyzed and studied. It has been demonstrated that the developed method has great potential for quality control of Evodiae Fructus herb.

Steady-state recycling chromatography in the purification of weakly acidic lignocellulosic hydrolysates

Abstract Purification of monosaccharides from lignocellulosic hydrolysates using mixed recycle steady-state recycling chromatography (SSR) was studied experimentally on a pilot scale and via simulations. A hydrophilic, weak cation exchange resin was used as separation material, enabling the removal of lignin, formic acid, acetic acid, hydroxymethyl furfural, and furfural in a single step. Lignin concentration had only a minor effect on separation efficiency. The exchange of the Na+ ions of the resin with Ca2+ ions from the hydrolysates was found to decrease separation efficiency. The full recovery of separation efficiency could be obtained via a natrium citrate treatment of the resin. Very strong sorption of some lignin molecules led to coloring of the resin but did not affect separation efficiency. Simulations showed that depending on the monosaccharide concentration of the hydrolysates, the SSR mode yielded 13–20% higher monosaccharide productivity than the batch mode. The experimental investigation of the fractionation on a pilot scale revealed that viscous fingering due to a highly concentrated feed (≥360 g/L) lowered the separation efficiency in single-column batch mode but not in SSR mode. Thus, in practice, SSR is even more efficient than the batch process than was suggested by the simulations.

Preparation of molecularly imprinted polymer based on the magnetic multiwalled carbon nanotubes for selective separation and spectrophotometric determination of melamine in milk samples

A new molecularly imprinted polymers coated on magnetic multiwalled carbon nanotubes (MIPs/MMWCNTs) was synthesized. Synthesized sorbent were characterized by scanning electron microscopy, X-ray diffraction, FT-IR spectroscopy and via adsorption kinetics and adsorption isotherms. The application of this sorbent was investigated in preconcentration and determination with a simple and selective spectrophotometric determination of melamine (MEL) by charge transfer complexation. The method is based on the adsorption of MEL on MIPs/MMWCNTs and subsequent reaction of desorbed MEL with tetrachloro-p-benzoquinone (TCBQ) reagent for final spectrophotometric detection. The effect of experimental parameters affecting separation efficiency and spectrophotometric detection were investigated and optimized. Under optimum conditions, the calibration curve for MEL determination showed a good linearity in the range of 10.0–600.0 ng mL−1 (R2 = 0.999) and the limit of detection (S/N = 3) was estimated to be 3.0 ng mL−1. The intra-day and inter-day precision (RSD%) of MEL were in the range of 2.8–3.9%. This method was successfully applied to determination of MEL in milk and milk powder samples. The good spiked recoveries ranging from 94.6 to 102.3% were obtained.

Relationship between shear energy input and sedimentation properties of exopolysaccharide-producing Streptococcus thermophilus strains

Besides fermentation, the production of bacterial starter cultures includes another crucial step, namely, the separation of the bacteria cells. This separation is most commonly carried out with disc stack separators and needs to be adjusted to the respective strain to obtain a high cell recovery rate. Exopolysaccharides (EPS) produced by several starter cultures, however, have a large negative impact on the separation properties of the cells. These EPS can be divided into cell-bound capsular EPS or free EPS that are released into the surrounding fermentation medium. To improve the separation step, shear forces were applied after fermentation with a gear ring disperser to simulate the impact of a homogenizer and the influence on the separation properties of six Streptococcus thermophilus strains was examined. In case of capsular EPS, the sedimentation velocity of the bacteria increased due to shearing off the capsular EPS layer. Shearing media with free EPS resulted in a viscosity decrease and, hence, in a higher sedimentation velocity, as was determined using a disc centrifuge and a LUMiSizer. Sediment compression as measured with the LUMiSizer was also affected by the shearing step. The results of this study suggest that a defined shear treatment of EPS producing bacterial starter cultures leads to improved separation properties and, hence, higher bacteria yields. We assume that both EPS types affect separation efficiency of the bacteria cells, free EPS because of increased media viscosity and capsular EPS because they act like a friction pad.

Novel method of air distributor design for enhancing bed stability and reducing impurities in gas–solid fluidized bed system

ABSTRACTCoal plays a key role in the economic development of China. It is greatly significant to improve the efficient use of coal through high-efficiency dry separation. In this paper, a porous sponge was used to optimize the air distributor, and its fluidization characteristics were studied. Response surface methodology was used to study the collaborative optimization effects of gas velocity, separation time, and bed height on the fine coal separation. Gas velocity was the main factor which affects separation efficiency. When separation is in operation parameters, the yield and ash content were 65.48 and 10.89% as to the clean coal product and 9.24 and 80.47% as to the gangue product, respectively. Furthermore, the yield and ash content of middlings were 25.29 and 20.32%, respectively. The probable error, E, values were between 0.085 and 0.100 g/cm3. Using XRF and FTIR analysis, it was observed that the harmful elements and impurities in coal were reduced during the separation process.

Pneumatic jig: effect of airflow, time and pulse rates on solid particle separation

This paper aims to provide insights into the factors contributing to the efficiency of separation of solids particles in pneumatic jigging. A batch pneumatic jig was constructed at the University of Nottingham, UK, for solid waste recycling. Synthetic materials (density tracers), colour coded for density, were used as the bed materials in a series of experiments. The bed was analysed layer by layer using image analysis technique, utilizing colour difference among density tracers to calculate separation efficiency. In general, the pneumatic jigging movement depends on two important factors which are airflow rate and pulse rate. The former lifts the bed, and the latter creates intermittent air current. Airflow rate, pulse rate and time were studied to identify the significant parameters affecting separation efficiency in pneumatic jigging. Any changes in one of these parameters could influence separation efficiency. Process optimization was performed using Box–Behnken design to determine optimal conditions for obtaining high percentage of separation yield. Results from the software (Design-Expert® 7.1) suggested that optimal conditions could be attained at a pulse rate of 120 rotations per minute, time of 7 min and airflow rate of 30 cm/s, with the produced yield expected at 82.4%. Actual experiments generated a separation efficiency of greater than 80% by varying the tested parameters.

Hydrocyclone Separation Efficiency Modeled by Flow Resistances and Droplet Trajectories

The growing demand to optimize the deoiling performance for offshore oil & gas gives the incentive to improve existing control solutions by means of model-based control solutions. This paper proposes a separation efficiency grey-box model of a deoiling hydrocyclone. Grey-box modeling of deoiling hydrocyclones aims to combine knowledge from fluid dynamics with the data-driven parameter estimation to yield better accuracy than black-box derived models while keeping the computational load much lower than CFD-simulations. The model has to be reasonably accurate in all likely operating conditions and be computed in real-time, in order to be beneficial for advanced model-based control. The developed grey-box model is based on flow resistance and oil droplet trajectory analysis. The model functionally describes how the valve openings, inflow rates, and PDR set-points affect separation efficiency of the considered generic deoiling hydrocyclone. The results are reasonable and provide a fundamental overview of how the operational conditions affect separation efficiency. The model can be extended to account for changes in the axial velocity distribution, coalescence and breakup of droplets.