Coalescence Rate Constants Research Articles

Kinetic Modeling of Flocculation and Coalescence in the System Emulsion of Water-Xylene-Terbutyl Oleyl Glycosides

The development of a mathematical model for explaining the kinetics of flocculation and coalescence of emulsion droplets is essential to study the stability of an emulsion system of the kinetics of emulsion stability. Mathematic models was developed from the equation Van Den Tempel by modifying emulsion systems. The emulsion was made by mixing water-xylene and surfactant tert-butyl oleyl glycosides. This research studied the effect of stirrer speed on the value of flocculation rate constant (a) and coalescence rate constant (K). The model identified the emulsion development condition whether controlled by coalescence or flocculation. It was observed that under lower agitation speed (1000 rpm) the emulsion development was controlled by flocculation mechanism, while a faster agitation (2000 rpm or higher) exhibited coalescence controlled mechanism. The results confirmed that the 1st model was the most appropriate for water-xylene-TBOG emulsion system. From four models after fitting with experimental data, the most suitable model is 4th model, because it has the smallest error of 2.22 %.

Novel population balance model for granule aggregation and breakage in fluidized bed granulation and drying

A novel population balance model for the fluidized bed granulation and drying process was developed taking into consideration moisture content for determining the coalescence and breakage probabilities. Experimental data of pharmaceutical powders manufactured at production scale was used to determine the coalescence and breakage rate constant. It was found that the calculated mean volume diameter and frequency distribution showed good agreement with the experimental ones observed during the coalescence growth and the breakage stages.

A kinetic approach to predict the potential effect of malaxation time-temperature conditions on extra virgin olive oil extraction yield

An original kinetic study of both oil coalescence phenomena and potential extra virgin olive oil extraction yield (i.e. apparent Extractability Index) was carried out at different malaxation time-temperature conditions using Abencor lab equipment to process olives (Frantoio cv) of a known degree of ripeness.The apparent Extractability Index was modelled at every malaxation temperature by pseudo first-order kinetics, where the yield rate constant was temperature dependent following the Arrhenius equation (k0 = 7.50 107 min−1; Ea = 54512 J/mol). Oil droplet coalescence, which was expressed as a relative variation in the percentage of oil droplets with a diameter of >30 μm, proved to be an time-dependent phenomenon only; the pseudo zero-order kinetics modelling was statistically significant, where the coalescence rate constant was equal to 0.033 min−1. The above kinetics were applied in order to propose a synoptic chart to predict the potential effect of malaxation in isothermal conditions on EVOO extraction yield.

Characterization of Chemical Demulsification of Oil in Water Emulsion: Comparison Between a Kinetics Model and Laboratory Experiments

In this study, kinetics of chemical demulsification of emulsion was studied. A series of experiments have been carried out with different demulsifiers and effect of temperature and demulsifier concentration on the destabilization process was examined. In the destabilization process, the separation efficiency of emulsion was determined by flocculation and coalescence rate constants measurement. When different dimulsifires were compared, the more coalescence and flocculation rate constants were obtained, the more efficient was demulsification. It was observed, as temperature increased, destabilization and coalescence behavior increased. Also, it was observed that an optimal demulsifier concentration exited to obtain a maximum coalescence rate constant.

Kinetics Model of Destabilization of Oil Droplets in Oily Wastewater Emulsions

In this article, a mathematical model that accounts for the kinetics of flocculation and coalescence of emulsion drops was developed to quantify the kinetics of emulsion stability. The model is similar to that developed by Borwankar et al. in 1992 with corrections in coalescence rate constant and collision efficiency factor. It includes a term to describe efficiency of collisions. Also, the coalescence rate constant was defined as a function of the total number of particles that were present in the system at the moment. The model has four adjustable parameters, and nonlinear least square optimization is used to obtain the adjustable parameters. The obtained adjustable parameters by the model served as parameters that can be used to quantitatively evaluate the effectiveness of a set of different demulsifiers by measuring total numbers of drops versus time and by determining the adjustable parameters and comparing them. The results of the presented model and the model of Borwankar et al. were compared with experimental data. The results of the new model were in good agreement with experimental data and showed the model's ability for dispalying the behavior of droplets during the destabilization processes of emulsions.

Experimental study of turbulence-induced coalescence in aerosols

In this paper, measurements of the rate of aerosol coalescence in a well characterized turbulent flow are presented. The time dependence of the aerosol droplets’ mean radius upon initiation of flow in an oscillating grid generated turbulence chamber is determined using a phase-Doppler method. Together with a measurement of the aerosol number density from a light attenuation probe, the observed rate of change of the aerosol droplets’ mean radius can be related to the rate constant for the coalescence of two droplets. The Kolmogorov shear rate, which is the primary parameter in theories predicting coalescence rate, is determined from measurements of the root-mean-square fluctuating velocity and the integral length scale. Our experimental results are compared with theoretical predictions, obtained by solving of the population balance equation. Various expressions are considered for the coalescence rate constant to be used in the population balance equation. First, we considered various combinations of ideal coalescence rate constants, i.e. obtained theoretically neglecting particle interactions. Our data are then found to be in good agreement with theoretical predictions that take into account the simultaneous effects of turbulent shear induced and Brownian motion induced coalescence. Second, our results are compared with a theory that considers the effects of turbulent shear and Brownian motion as well as the non-continuum hydrodynamic and van der Waals interparticle interactions. The measured experimental values are generally 50–100% higher than those predicted by this theory. This discrepancy could be explained by the small polydispersity of the aerosol which may result in coalescence induced by differential sedimentation and turbulent acceleration.

A volume-based multi-dimensional population balance approach for modelling high shear granulation

A volume-based multi-dimensional population balance model based on the approach used by Verkoeijen et al. [2002. Population balances for particulate processes—a volume approach. Chemical Engineering Science 57, 2287–2303], is further developed and applied to a wet granulation process of pharmaceutically relevant material, performed in a high shear mixer. The model is improved by a generalization that accounts for initial non-uniformly distributed liquid and air among the different particle size classes. Only the wet massing period of the granulation process has been modelled and it is experimentally found that the pores in the granules are fully saturated by liquid, i.e., no air is present in the granules during this period. Hence, an alternative model formulation is used as no model for the air in the granules is needed. Particle volume distribution, liquid saturation, liquid-to-solid ratio and porosity of the granules can all be modelled, as these properties can all be expressed as combinations of three model parameters, i.e., the volume fraction of solid material, total liquid fraction and the liquid fraction inside the granules. The model is also improved by introducing a new coalescence kernel and by increasing the number of size classes used. The simulated results are compared to measurements from a series of five designed experiments where impeller speed and water content are varied. It is found that the evolution of the volume, liquid saturation and porosity distributions could all be explained by fitting the compaction and coalescence rate constants.

Population balance modelling of droplets in an oscillatory baffled reactor—using direct measurements of breakage rate constants

AbstractPopulation balance modelling (PBM) is a useful tool for design and prediction in a range of processes that involve dispersed phases, particulates or micro‐organisms. In the Inverse Problem approach, constants related to the rates of evolution and/or interaction of the individual components are optimized so as to match the experimentally observed distribution curves. However, the significance of these results may be slight, or several solutions may be possible. In this paper, a method is presented to circumvent this problem, and is applied to the breakage and coalescence of oil droplets in a continuous oscillatory baffled reactor (OBR). Direct observation of droplet breakage using a high‐speed camera should enable breakage rate constants to be obtained independently from the Inverse Problem approach, and thus obtain more reliable coalescence rate constants. An analysis of the droplet size distributions (DSDs) is also combined with direct observation with the high‐speed camera to allow the development of a breakage model specific to the OBR. It is expected that this method should yield parameters useful for prediction of steady‐state DSDs, and hence enhance the accuracy of design, scale‐up, and prediction of operation.© 2003 Society of Chemical Industry

Coalescence Rate Constant of Slug in a Gas Fluidized Bed.

In order to understand the characteristics of slug coalescence, the slug frequency has been measured by a differential pressure method in a gas-fluidized bed of i.d. 0.1 m and height 2.25 m, at ambient temperature and pressure, and with respect to variations of bed height (0.23–0.93 m) and gas velocity (U – Umf = 0.0190–0.139 m/s). Air was used as fluidizing gas and a fresh FCC catalyst (Geldart’s group A particle, dp = 0.070 mm, ρs = 1600 kg/m3, Umf = 0.0113 m/s) and glass bead (Geldart’s group B particle, dp = 0.168 mm, ρs = 2486 kg/m3, Umf = 0.0303 m/s) as bed materials.The slope of a frequency decrease accompanying with a gas velocity increase at different bed heights was similar in the bed of Geldart’s group-A particle. So was the slope of frequency decrease with bed height at different constant gas velocities. The mechanism controlling slug coalescence was found to be different between Geldart group-A and B particles. The slug coalescence model proposed by Yamazaki et al. (1984) was extended to the case with gas velocity as a variable. The slug coalescence rate constant leveled off after an initial decrease in the bed of Geldart’s group-B particle. However, it increased in the bed of Geldart’s group-A particle as the gas velocity increased. Correlation on the slug coalescence rate constant that includes effects of gas velocity, temperature and particle properties has been proposed in each different slug growth regime.

Model for Formation and Growth of Vesicles in Mixed Anionic/Cationic (SOS/CTAB) Surfactant Systems

The dynamics of vesicle formation and growth following the mixing of cationic cetyltrimethylammonium bromide (CTAB) and anionic sodium octyl sulfate (SOS) surfactant solutions were determined using static and dynamic light scattering. The results are well-described by a two-stage model in which initial nonequilibrium vesicles are generated rapidly following the mixing of the surfactant solutions and the subsequent vesicle growth is by slower vesicle fusion. The formation of the initial vesicles is based on a balance between the unfavorable edge energy of disklike aggregates and the bending energy required to form spherical structures. The sizes of the initial vesicles correlated well with the equilibrium sizes determined after 2 months, in accordance with the model predictions. The growth of both the disklike bilayers (bilayer−bilayer fusion) before their transition to the initial vesicles and of the nonequilibrium vesicles (vesicle−vesicle coalescence) was modeled using Smoluchowski's theory for colloid coagulation. Estimates of the coalescence rate constants showed that the fusion of bilayer disks is at least an order of magnitude faster than the coalescence of nonequilibrium vesicles, with rate constants of ∼200 and ∼5−10 (Ms)-1, respectively.

On the evaluation of droplet breakage and coalescence rates in an oscillatory baffled reactor

A numerical model is developed to evaluate droplet breakage and coalescence rates in a continuous oscillatory baffled reactor (OBR). The structure of the model is similar to that of the population balance approach, but concentrates on droplet interactions with simpler assumptions of a functional form for breakage and coalescence rate constants. The OBR is a relatively new reactor technology and offers enhanced and more uniform mixing than traditional reactors, making some model assumptions more closer to the reality. In this paper, we present the development, robustness and validation of the modelling process together with the predicted results for the OBR system.

Drop Coalescence during Emulsion Formation in a High-Pressure Homogenizer for Tetradecane-in-Water Emulsion Stabilized by Sodium Dodecyl Sulfate

The present study investigates the effects of homogenizer pressure, surfactant concentration, ionic strength, and dispersed phase fraction on the coalescence rate of tetradecane-in-water emulsions during their formation in a high-pressure homogenizer. Experiments were conducted in a recirculating system consisting of a Rannie laboratory-scale single-stage homogenizer and a stirred vessel for tetradecane-in-water emulsions stabilized by sodium dodecyl sulfate (SDS). The initial evolution of the number concentration of droplets in the stirred tank was measured when subjected to a negative stepchange in the homogenizer pressure. The average drop coalescence rate constant in the homogenizer was inferred by fitting the experimental evolution of the number concentration of drops to a simple model accounting for the coalescence in the homogenizer under the assumption of a quasi steady state in the homogenizer. The residence time of the emulsion in the homogenizer was evaluated from the analysis of radial turbulent flow between disks. The step down homogenizer pressure was varied in the range 20.7–48.3 MPa, the drop size in the range 174–209 nm, the dispersed phase fraction in the range 5%–15%, SDS concentration in the range 0.0033–0.25 wt%, and ionic strength in the range 0.01–0.1 M. The coalescence rate constants were found to be in the range from 3.34×10−17 to 2.43×10−16 m3 s−1. The coalescence rate constant was found to be higher for higher homogenizer pressures, smaller drop sizes, lower dispersed phase fractions, and lower SDS concentrations and was insensitive to variations in ionic strength.

Coalescence of Protein-Stabilized Emulsions in a High-Pressure Homogenizer

Coalescence rate constants in a high-pressure homogenizer were inferred for pure emulsions of a neutrally buoyant mixture of carbon tetrachloride and benzene dispersed in aqueous medium, as well as for emulsions stabilized by sodium caseinate or whey protein, from the temporal evolution of number of drops per unit volume in the exit stream of the homogenizer in a recirculating system consisting of the homogenizer and a stirred tank when subjected to a negative step change in applied homogenizer pressure (Ph). The homogenization pressure was varied in the range 6.9 to 41.4 MPa, pH in the range 5 to 7, dispersed phase fraction in the range 0.05 to 0.15, ionic strength in the range 0.01 to 0.05M,and protein concentration in the range 0.01 to 0.05 wt%. Functional dependence of drop coalescence rate on the homogenizer pressure was derived for pure emulsions for mechanisms of drop collisions due both to turbulence and to shear. The inferred collision rate constant for pure emulsions was found to be proportional toPh0.722, which was closer to the functional dependence for drop collisions due to turbulence. The coalescence rate constant was found to be higher for higher homogenizer pressures, larger drop sizes, and higher dispersed phase fractions. For emulsions stabilized by proteins, drop coalescence rate constant was found to be higher at lower protein concentrations, near the isoelectric point of the protein, and higher ionic strengths because of the smaller interdroplet colloidal repulsive forces, thus clearly demonstrating the effect of colloidal forces on drop coalescence. Sodium caseinate was found to result in a lower coalescence rate constant than whey protein.

Kinetic study and characteristic curve of the reactive noranda tailings agglomeration process

The kinetics of agglomerate growth in a batch disc pelletizer has been studied using fine reactive Noranda tailings. The effect of operating variables such as moisture content, angle of inclination and agitation (rpm) on the agglomeration process was studied. Higher moisture content, lower inclination angle and higher agitation improved the agglomeration behavior. The growth of agglomerates was observed to follow first-order kinetics. The nuclei coalescence rate constant was fitted with moisture content in a semi-logarithmic manner. The agglomerate size distributions were found to fit log-normal size distribution and followed a self-preserving growth. A Rosin-Rammler type of equation was used to quantify the characteristic curve of the Noranda tailings agglomeration process. This can be utilized to predict the complete agglomerate size distribution irrespective of the operating conditions and the size of the pelletizer if a relationship such as agglomerate median product size as a function of the operating conditions and agglomeration time is made available.

Orthokinetic coalescence of protein-stabilized emulsions

A phenomenological model of orthokinetic stability, which combines a second-order coalescence process and a first-order disruption process, is tested against experimental results for β-lactoglobulin oil-in-water emulsions. Numerical data in the form of plots of average volume—surface diameter as a function of shearing time are presented for different values of the various model parameters: the coalescence and disruption rate constants, the critical droplet size for disruption, and the fractal dimensionality characterizing the ‘reactivity’ term in the orthokinetic rate equation. Satisfactory agreement between theory and experiment requires a low fractal dimensionality ( D ≈ 2) similar to that encountered for perikinetic reaction-limited cluster—cluster aggregation, and much less than the classical Smoluchowski value ( D = 3) for immediate full coalescence. Adjusting the pH of the β-lactoglobulin emulsion after formation but before shearing leads to changes in the protein surface coverage and the degree of flocculation. Experimental results are presented for the effects of shearing intensity and pH on the destabilization time of the β-lactoglobulin emulsions, and the trends are compared with those predicted by the phenomenological model. Adjusting the pH towards the isoelectric point of the protein induces substantial perikinetic flocculation of the emulsions and a correspondingly enhanced rate of orthokinetic destabilization. Changes in interdroplet interactions during the shearing process due to ageing of the adsorbed protein layer may have to be included in any refinement of the model.

Electrostatic and steric stabilization of PVC primary particles

AbstractProblems related to the formation and stability of primary particles in VCM suspension and bulk polymerization were theoretically analyzed, based on the DLVO (Deryaguin‐Landau‐Verway‐Overbeek) and HVO (Hesselink‐Vrij‐Overbeek) theories of stability of colloidal systems. In the absence of secondary stabilizers, PVC primary particles were solely stabilized by negative electric charges, as a result of the presence of HCl formed by a chain transfer reaction of chloride redicals to PVC polymer chains. The dependence of the stability of primary particles on the ionic strength of the medium, temperature, and total particle charge was quantitatively investigated in terms of the stability ratio and the particle coalescence rate constant. The steric stabilization of primary particles, arising from the addition of surfactants or polymers to the monomer phase, was examined, using the HVO theory. It was shown that PMMA improved the stability of primary particles and, thus, could alter the particle agglomeration kinetics. The effects of molar mass and the amount of the absorbed PMMA, as well as the influence of solvent quality on the steric stabilization of primary particles, were also investigated. The experimental results, published on the electrostatic and steric stabilization of PVC primary particles, were in good agreement with the theoretical predictions obtained in this study. © 1993 John Wiley & Sons, Inc.

Modeling of Emulsion Polymerization of Vinyl Chloride

Abstract A survey of the principles of emulsion polymerization modeling of vinyl chloride is presented. Experimental results and model equations for particle nucleation, particle coalescence, and particle growth are discussed. A mechanism for particle coalescence in the course of polymerization is proposed based on the assumption that radical desorption from a particle is the rate-determining step for coalescence. Equations for the coalescence rate and velocity constant are derived based on this assumption. The resulting population balance equations for describing the change of particle size distribution during emulsion polymerization of vinyl chloride can be applied to different polymerization procedures, e.g., discontinuous, continuous, and seeded polymerizations. Examples of model calculations are given for several polymerization procedures and compared with experimental data.

Dispersing Behaviour of Droplets in (W/O)/W Emulsion. II.

In a (W/O)/W emulsion, the dispersion behavior of (W/O) droplets was observed following sudden reduction in impeller speed. The rates of both coalescence and breakup of (W/O) droplets were quantitatively estimated, and then the dependence of coalescence and breakup rate constants on operating conditions such as impeller speed and droplet diameter was determined.As the impeller speed increased, coalescence and breakup also increase. As (W/O) droplet diameter increased, coalescence decreased and breakup increased.Leakage of the inner aqueous phase into the outer aqueous phase was found to occur mainly as a result of (W/O) droplet breakup.

Dispersing Behavior of Droplets in (W/O) /W Emulsions. I.

In a (W/O)/W emulsion, the dispersion behavior of (W/O) droplets was observed following sudden reduction in impeller speed. The rates of both coalescence and breakup of (W/O) droplets were quantitatively estimated, and then the dependence of coalescence and breakup rate constants on operating conditions such as impeller speed and droplet diameter was determined.As the impeller speed increased, coalescence and breakup also increase. As (W/O) droplet diameter increased, coalescence decreased and breakup increased.Leakage of the inner aqueous phase into the outer aqueous phase was found to occur mainly as a result of (W/O) droplet breakup.

PREDICTION OF OIL SATURATION IN FIBROUS BED-COALESCER BY DYNAMIC PULSE TECHNIQUE

Average oil saturation in fibrous bed coalescer has been measured experimentally using pulse response technique. Comparable results were obtained with saturation values obtained under steady-state condition. The experimental technique involved the injection of small amount of toluene-water dispersion in the upstream side of the coalescer and following the inlet and outlet concentration count for this dispersion. As a result of this work a coalescence rate constant, k, could be measured which gives an indication of the rate of coalescence in the bed.