Population balance modelling of droplet coalescence and break-up in an oscillatory baffled reactor

This paper presents new population balance analysis to describe simultaneous coalescence and break-up in the formation of methylmethacrylate droplets in a batch oscillatory baffled reactor. It is concluded that the droplet data can very well be described by a model in which coalescence is taken to be shear induced, selection for break-up proceeds at a rate proportional to droplet volume and approximately four equally sized break-up fragments are produced per break-up event. It is shown that the experimental droplet size distribution data are self-similar in form and exhibit asymptotic behaviour characteristics also seen in the model. The coalescence rate is found to vary as the square of the oscillation frequency and the selection rate to vary with the oscillation frequency to the power five. As a result the asymptotic mean droplet volume is inversely proportional to the oscillation frequency.     

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.     

Determination of breakage rates of oil droplets in a continuous oscillatory baffled tube

Following on our previous studies, the population balance model that was built on the earlier work from Jareš and Procházka [Break-up of droplets in Karr reciprocating plate extraction column. Chemical Engineering Science 42, 283-292] was modified to include the viscoelastic effect on droplet size distribution and to evaluate the breakage rates of oil-in-water dispersions in a continuous oscillatory baffled tube. In this work, experiments were performed showing that the breakage of droplets is the dominant mechanism in the system, and the physical properties of different oils had no significant influence on droplet size distributions. Under those conditions the model can be used to focus only on breakage rate constants, keeping the number of fitted parameters in the modelling process to a minimum. The droplet breakage results from this work suggest that the oscillation amplitude has more influence on the breakage rates than the oscillation frequency. This work is a major extension and includes droplet data from our previous studies so that the breakage rates can be compared; and the consistency of the rate constants is examined.     

Numerical simulation of two-phase flow and droplet breakage of glycerin-water mixture and kerosene in the cyclone reactor

A liquid-liquid cyclone reactor(LLCR)was designed to achieve mixing-reaction-separation integration during isobutane alkylation catalyzed by ionic liquids.However,studies of the droplets deformation and breakage in the kind of reactors are lacking.In this work,the research studied the velocity distribu-tion,pressure field,and turbulent field to investigate the flow pattern and the main energy loss location in the LLCR through the computational fluid dynamics(CFD)method.The simulation results were verified by experiemnts to prove the correctness of the model.Then the deformation and breakage process of dro-plets,and the influencing factors of droplets breakage were studied by remodeling which was based on the tangential velocity distribution result of the three dimensional model.The three dimensional simu-lation results clearly showed that the pressure of the LLCR was mainly concentrated in the cone section and fluid turbulent motion was the most intense near the lateral wall,The reconstruct the results of the two dimensional model clearly showed that the deformation and breakage location of droplets were mainly occurred in the velocity boundary layer,while it was difficult to break in the mainstream region.In addition,low surface tension and high Weber number had a positive effect on droplet breakage.     

Modelling of high viscosity oil drop breakage process in intermittent turbulence

A multifractal model of the fine-scale structure of turbulence is applied to describe breakage of viscous drops of immiscible liquid immersed in a fully developed turbulent flow. A population of drops whose diameter falls within the inertial subrange of turbulence is considered here. The population balance equation is used to predict the drop size distributions. Calculations are performed for binary and multiple breakage. Several daughter distribution functions are applied and the results of their application are compared with experimental data. Experimental investigations of drop breakup were carried out in a flat bottom stirred tank having the diameter of and equipped with Rushton type agitator and four baffles. Silicone oils with viscosity of 10, 100, 500 and 1000 m Pa s were dispersed in the aqueous continuous phase. Measurements were performed using high resolution digital camera. Experimental results as well as numerical simulations show that after the initial period of multiple breakage, the strongly asymmetric type of binary breakage dominates.     

Optimal moving and fixed grids for the solution of discretized population balances in batch and continuous systems: droplet breakage

The numerical solution of droplet population balance equations (PBEs) by discretization is known to suffer from inherent finite domain errors (FDE). Tow approaches that minimize the total FDE during the solution of discrete droplet PBEs using an approximate optimal moving (for batch) and fixed (for continuous systems) grids are introduced. The optimal grids are found based on the minimization of the total FDE, where analytical expressions are derived for the latter. It is found that the optimal moving grid is very effective for tracking out steeply moving population density with a reasonable number of size intervals. This moving grid exploits all the advantages of its fixed counterpart by preserving any two pre-chosen integral properties of the evolving population. The moving pivot technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996b) 1333) is extended for unsteady-state continuous flow systems, where it is shown that the equations of the pivots are reduced to that of the batch system for sufficiently fine discretization. It is also shown that for a sufficiently fine grid, the differential equations of the pivots could be decoupled from that of the discrete number density allowing a sequential solution in time. An optimal fixed grid is also developed for continuous systems based on minimizing the time-averaged total FDE. The two grids are tested using several cases, where analytical solutions are available, for batch and continuous droplet breakage in stirred vessels. Significant improvements are achieved in predicting the number densities, zero and first moments of the population.     

Characterization and optimization of an oscillatory baffled reactor (OBR) for ozone-water mass transfer

Ozone-water mass transfer was investigated using an oscillatory baffled reactor (OBR) operated as a semi-batch and as a co-current up flow continuous reactor. The effects of input ozone concentration, input gas and water flow rates, and oscillation conditions on gas hold up, volumetric mass transfer coefficient and mass transfer efficiency were determined. The same reactor was operated as a baffled column (without oscillation) and as a bubble column to assess the effect of the reactor arrangement on the mass transfer. The results show that the OBR was 5 and 3 times more efficient for ozone-water mass transfer than the baffled and bubble columns, respectively. The enhancement obtained with OBR over the baffled column reactor was found to decrease with gas flow rate due to changes in bubble flow pattern from homogenous to heterogeneous. Under continuous flow conditions, the performance of the baffled reactor and the OBR were found to be twice efficient for ozone-water mass transfer than when operating under semi-batch conditions. The mass transfer effeciency (MTE) was found to increase from 57% using the baffled reactor to 92% with OBR under continuous flow at water and gas superficial velocities of 0.3 and 3.4 cm s⁻¹, respectively.     

Solution of the droplet breakage equation for interacting liquid-liquid dispersions: a conservative discretization approach

A conservative discretization approach for the population balance equation (PBE) with only droplet breakage describing the hydrodynamics of a continuously interacting liquid-liquid dispersion is presented. The approach is conservative in the sense that it conserves any two integral properties associated with the number droplet distribution and thus it is considered internally consistent. The discrete set of equations is laid down through applying the subdomain method where it is shown that this set of discrete equations is only internally consistent with respect to one integral property. The internal consistency is enforced by introducing a set of two auxiliary functions that are uniquely determined by matching the integral properties obtainable from the discrete set against those from the continuous PBE. However, it is shown that this conservation of integral properties is not exact for all the subdomains and hence it results in what we call the intrinsic discretization error (IDE). This IDE is not only associated with this approach, but also it is found inherently existing in the fixed-pivot (FP) technique of Kumar and Ramkrishna (Chem. Eng. Sci. 51 (1996a) 1333). The derived equations of the IDE for the present discretization approach and the FP technique generalized to continuous flow systems show that the present approach enjoys a small value of the IDE. To validate the discretization approach, two analytical solutions for the continuous PBE are presented, where good agreement is found between the predicted and the analytical solutions. To assess the reliability of the present discretization approach two experimentally validated breakage frequency functions describing droplet breakage in a turbulent continuous phase as well as two daughter droplet distributions are considered. The convergence characteristics show that the present discretization approach has an identical convergence rate as that of the FP technique, and in some cases it is superior to it. This rate of convergence is found approximately proportional to the square of the inverse of the number of subdomains.     

Computational fluid dynamic modelling of flow patterns in an oscillatory baffled column

Numerical simulations to date within the context of oscillatory flow in a baffled column have been limited to flows in a symmetrical regime, i.e. eddies are generated symmetrical to the central line of the column where the oscillatory Reynolds numbers are below 400. In this paper, 3-D computational fluid dynamic (CFD) simulation of flow patterns of oscillatory flow in a baffled column has, for the first time, been carried out and the results extended to all regimes of oscillatory Reynolds numbers covering from symmetric to asymmetric flows. The flow patterns simulated have also been validated by both direct flow visualisation and by digital particle image velocimetry measurements. The success of such CFD simulations opens doors for many potential studies, from optimisation of geometry for plug flow to suspension of particles, and from droplet breakage and coalescence to mass/heat transfer of particles.     

Effect of oscillation amplitude on velocity distributions in an oscillatory baffled column (OBC)

This paper presents a numerical study of the effect of oscillation amplitude in oscillatory baffled column (OBC) using computational fluid dynamics. The numerical work was carried out for single phase liquid flow for an unsteady 3-D model using commercial software, Fluent (2006). This work was concentrated on the effect of oscillation amplitude. Three amplitudes of 5, 10 and 15 mm with constant frequency of 1 Hz are applied. Vortex and cycle average velocities at different points are analyzed. The studies show the maximum velocity for 5 mm, 10 mm and 15 mm in an OBC are 0.11 m/s, 0.25 m/s and 0.40 m/s respectively in the first cycle of oscillation. At a constant frequency, greater oscillation amplitude displaces the liquid to a further distance and builds a larger vortex. Vortex length was 1.5 times bigger when oscillation amplitude changes from 5 mm to 10 mm and 2 times when the amplitude is triple from 5 mm. The detailed validation is presented somewhere else; this research is focused on the effect of oscillation.     

The axial dispersion performance of an oscillatory flow meso-reactor with relevance to continuous flow operation

A laboratory scale continuous oscillatory flow meso-reactor was developed and residence time distribution (RTD) studies were carried out in order to establish certain process characteristics of the system. In particular, the dispersion coefficient as a function of the primary variables was established. Using optical probes the axial dispersion was investigated by monitoring the response of a pulse dye tracer at different locations within the meso-reactor. Three cases, net flow without oscillation, oscillation without net flow, and oscillation plus net flow were studied over a range of oscillation frequencies, amplitudes, and net flow rates. Both the imperfect and the perfect pulse injection methods were used to determine the axial dispersion coefficient for the system with and without net flow. The axial dispersion coefficient and the dimensionless dispersion number were analysed in the context of different flow conditions. A correlation was established and demonstrated that the axial dispersion within the meso-reactor could be quantified as a function of flow conditions. The results showed that the laboratory continuous flow meso-reactor was able to produce plug flow with modest axial dispersion over a wide range of parameter space, thereby indicating efficient mixing and effective RTD performance.     

Inverse phase suspension polymerization of acrylamide in a batch oscillatory baffled reactor

We report, for the first time, our experimental investigation of inverse phase suspension polymerization of acrylamide in a batch oscillatory baffled reactor. In such a reactor, the oscillatory motion is achieved by moving a set of orifice baffles up and down the column at the top of the reactor. The effects of both operational and design parameters on the mean particle size and size distribution of polymer beads were investigated, including oscillation amplitude, oscillation frequency, baffle spacing, baffle free area, and monomer addition time. The experimental results indicated that the mean particle size and size distribution of the polymer beads depended predominantly on the product of oscillation frequency and amplitude, i.e., the oscillation velocity. The size distributions are narrow and of essentially a Gaussian distribution. The level of fines produced is consistently less than 1% for all 100 experiments performed. We demonstrated that the mean particle size and size distribution in an oscillatory baffled reactor can be controlled precisely by simply selecting the appropriate oscillation velocity. The effect of the baffle spacing on the mean particle size is much less compared with that of the baffle free area. The monomer injection time has a noticeable influence on the mean particle size, but the rate of change is relatively small. © 2000 John Wiley & Sons, Inc. J Appl Polym Sci 76: 1669–1676, 2000     

The influence of mixing on lysozyme renaturation during refolding in an oscillatory flow and a stirred-tank reactor

Protein refolding is a key unit operation in many processes that produce recombinant biopharmaceuticals using Escherichia coli. Yield in this step generally controls overall process yield, and at industrially relevant protein concentrations is limited by aggregation. While most refolding operations are optimised with respect to chemical environment, the physical processes affecting yield have been neglected. In this study, we demonstrate that refolding yield for the model protein lysozyme is dependent on mixing intensity during dilution refolding. This is shown for two different reactor configurations: a standard stirred-tank reactor and a novel oscillatory flow reactor. We further show that the effect of mixing is dependent on the type of chaotrope employed for denaturation. Yield falls significantly when mixing intensity is decreased following urea denaturation, while the effect of mixing is not apparent when guanidine hydrochloride is employed as the denaturant. In batch tests we further confirm that, for urea, the “path” of dilution affects yield, and hence the observed sensitivity to mixing is not unexpected. We conclude that mixing is a critical parameter that must be optimised in industrial reactors, along with the usual chemical and protein-specific parameters.     

Characterisation of flexible baffles in an oscillatory baffled column

In our previous studies the volume‐averaged strain rates, of 2–22 s^?1, were obtained in an oscillatory baffled column (OBC) based on velocity measurements over a half baffled cell for oscillatory Reynolds numbers of 1000–4030. These values are very low compared with those in a traditional stirred tank vessel (at least >100 s^?1) for similar operational conditions and the same power consumption. It was also observed that the volume‐averaged strain rates in the OBC fluctuated with the phase of oscillation over any cycle, with high values coinciding with eddy generation, and low values with eddy cessation. The objective of this study is to show that such fluctuations can be attenuated by employing innovative flexible baffles, whose inside edges move with the fluid oscillation. In this paper experimental measurements of velocity vector maps and strain rate distributions using Digital Particle Image Velocimetry (DPIV) are presented for both conventional and flexible baffles in an OBC. Mixing characterisation, in terms of axial dispersion coefficients, are compared for both baffle designs. The results show that the flexible baffles can reduce the fluctuations and magnitudes of the volume‐averaged strain rates in the OBC without compromising the mixing performance. Low and uniform strain rate distributions in time and space are essential biochemical, biomedical and pharmaceutical applications where shear sensitive cultures are involved. © 2001 Society of Chemical Industry     

Numerical study of the flow pattern and heat transfer enhancement in oscillatory baffled reactors with helical coil inserts

Oscillatory baffled reactors (OBRs) are a means of process intensification as they allow processes with long residence time to be converted from batch to continuous processing. Helically baffled OBRs have only been developed at “mesoscale” so far, but at this scale have displayed significant advantages in terms of the increased range of conditions over which plug flow is achieved. Scale-up studies are underway to determine whether this is replicated at larger scales. This paper reports fluid mechanical modeling of a helically baffled oscillatory flow for the first time. Time-dependent flow structures induced in tubular reactors have been analyzed on the basis of periodic, laminar flow numerical simulation. A reversing swirled core flow and its interaction with the unsteady mechanism of vortex shedding downstream of the wires has been described. This has allowed greater understanding of the flow structures, which will underpin optimal design and scale-up. The potential for heat transfer enhancement is discussed, considering the compound effect of oscillatory motion and helical coil inserts. The results show that the heat transfer for the helical baffled tube could be enhanced by a factor of 4 compared to a smooth tube in the tested range of oscillation conditions.     

Modelling the morphological evolution of nanosuspension droplet in constant-rate drying stage

A novel mathematical model of constant-rate stage of nanosuspension droplet drying is proposed. In contrast to previously published literature studies, the developed model considers two morphologically different periods of the constant-rate drying: before the shell formation and after the shell formation; the latter was named “transition period”. The point of initial “locking” between nanoparticles on the droplet surface and beginning of the shell formation is associated with theoretical maximum of solid volume fraction. It is postulated that shrinking and thickening shell of nanoparticles occurs fast, and thus the shell virtually remains submerged in the liquid during the overall transition period. Because of the submerged shrinking shell, in the transition period, the evaporation process still takes place from the droplet surface and the drying rate remains unchanged as it was before the shell formation. Correspondingly, the droplet temperature retains at the level of equilibrium evaporation temperature. The developed theory was successfully validated by the published experiment of silica nanosuspension droplet drying. Finally, the developed model proposes a simple morphology criterion based on comparison between the calculated droplet volume at the end of transition period and the corresponding volume of solid final particle with the given porosity.     

A rigorous breakage matrix methodology for characterization of multi-particle interactions in dense-phase particle breakage

Broadbent and Calcott's breakage matrix methodology has been used for more than 50 years to model various comminution processes and to determine breakage functions from experimental data. The methodology assumes first-order law of breakage and neglects mechanical multi-particle interactions that are especially prevalent in dense-phase comminution processes and breakage tests. Although several researchers severely criticized this aspect of the methodology, Baxter et al. (2004, Powder Technol. 143–144:174–178) were the first to modify the methodology toward determining the elements of a feed-dependent breakage matrix. However, no non-linear breakage matrix has ever been constructed from experimental data using the modified approach. In this study, a critical analysis of this modified approach has been performed, and the non-linear breakage matrix was fundamentally derived from a non-linear population balance model. Different approaches were proposed to identify the breakage functions based on the nature of available breakage tests on multiple mono-dispersed feed samples and at least one poly-dispersed sample. Using the derived equations, available experimental data on the breakage of a binary mixture of coarse and fine limestone particles in uniaxial compression test were fitted to quantify the multi-particle interactions. Superior fitting capability of rational approximation to the effectiveness factor was demonstrated.     

On the characterisation of wax deposition in an oscillatory baffled device

Deposition from viscous fluids in industrial processes is a major nuisance during production of many useful materials ranging from oil to foodstuffs. In a cold‐wall scenario rapid deposition of gel‐like material causes restriction, processing delays and potentially reduction in product quality. One well‐known example of this phenomenon is paraffin wax deposition, which is one of the greatest challenges in the petroleum industry, where the main implication is the blockage of oil. The aim of this work was to investigate the effect of applying oscillation on wax deposition, with the main focuses on the effects of oscillation frequencies and amplitudes, as well as the volume of the wax‐oil mixture. Wax deposit formation was measured gravimetrically. The results indicate that baffles and oscillation reduce wax deposition; increasing both oscillation frequency and amplitude result in a decrease in wax deposition; and the degree of reduction is greater with changing oscillation amplitude than with frequency. It was also found that deposition on the column wall rather than the baffles was the main contribution to the total wax deposit. Copyright © 2006 Society of Chemical Industry