Experimental characterization and multi-scale modeling of mixing in static mixers. Part 2. Effect of viscosity and scale-up

Static micro-mixers are used in precipitation processes to avoid mixing limitations. The mixing performance of these mixers, which are used in this study to mix two streams of different viscosity, is characterized using competitive-parallel chemical reactions and computational fluid dynamics (CFD). This work is an extension of a previous paper where mixing of fluids with equal viscosity has been studied [Lindenberg, C., Schöll, J., Vicum, L., Brozio, J., Mazzotti, M., 2008. Experimental characterization and multi-scale modeling of mixing in static mixers. Chemical Engineering Science 63, 4135-4149]. It is found that the mixing performance in terms of reaction yield and mixing time decreases slightly with increasing viscosity ratio in a two jet vortex mixer (Roughton mixer). In the Y-mixer the trend is the same at low flow rates, but it is the opposite at large flow rates due to a symmetry breaking phenomenon. The Roughton mixer is scaled-up using the CFD model and a linear relationship between scale-up factor and mixing time is observed. Finally, it is shown that mixing times can be described satisfactorily as a function of velocity, jet diameter and viscosity.     

Experimental evaluation of gas mixing with a static microstructure mixer

Mixing plays an important role in chemical reaction engineering. In the last years several types of static microstructure mixers have been developed. The characterization of microstructure mixing is difficult to perform as the dimensions are too small for conventional methods. Therefore, we report a method to characterize the mixing of two gases directly by measuring the concentration of the gases at the outlet of the mixer. The experiments have been carried out up to gas flows of 5000 ml/min STP per passage. The mixing degree and mixing length were determined as well as the mixing time was calculated. These values depend on the properties of the gases and other parameters as temperature and gas velocity. Thus complete mixing is achieved after a mixing length, i.e., the distance to the microchannel outlet, of only 300-800 μm. Corresponding mixing times are just 100-600 μs. Furthermore, discontinuities in the mixing characteristic can be explained with the results obtained. Also design parameters for a further improvement of the mixer geometry individually for various applications could be set up.     

Combined static mixers for high viscous fluids mixing

A new static mixer Cross-over-Disc has been invented to strip off the boundary layer and to make strong radial mixing. The pressure drop of Cross-over-Disc is 12-26 times as large as that of empty pipe with equivalent diameter and length. The mixing performance of Cross-over-Disc with 14 elements has been investigated in the viscosity range of 190–250 Pa·s by decoloration method, and the gray analysis of images shows that mixing inhomogeneity is about 7.5% and 9.4% for the mixing ratio of 5:1 and 10:1, respectively. Furthermore, mixing inhomogeneity for a combination of static mixing elements (four from Cross-over-Disc and three pairs from Sulzer-type) can be decreased to 2.1%–3.1% within a reasonable range of pressure drop.     

Mechanisms of mixing of granular materials in drum mixers under rolling regime

Experimental investigations on mixing of non-ideal powders (granular tetraacetylendiamine (TAED)) are described. The evolution of mixing in rotating batch cylinders, in rolling regime has been addressed. Characterization and quantification of the local mixture composition have been obtained through an efficient solidification technique, coupled with computerized image analysis.Starting from a completely segregated configuration, the formation of a temporary, poorly mixed core at low rotation speed has been observed. Investigation of intermediate configurations during the mixing process allows to identify some unexpected granular mixing mechanism. The observed core has been explained in terms of transient axial convective fluxes superimposed on diffusive motion. Small differences of dynamic angle of repose between the two granular materials have been suggested to drive the axial convection, similarly to the mechanism reported in the literature to explain axial segregation phenomena. The differences in repose angle result from surface and shape irregularities typical of actual (i.e. non-ideal) granules.Convective fluxes due to the friction of powder with the end plates are also identified at the extremities of the mixer. Short-circuiting zones are created that hinder both axial diffusion and convection from the center of the vessel. Eventually, we suggest a mixing mechanism of non-ideal granular material where convection plays a major role.     

Drop breakage model in static mixers at low and intermediate Reynolds number

Drop break-up process for the flow of liquid-liquid dispersion in a static mixer has been investigated. Two new theoretical models for the drop break-up at low and intermediate Reynolds number for variant viscosity ratio of the dispersed phase to the continuous phase have been developed assuming that the flow through the static mixer elements is analogous to the flow through porous media. This concept has recently been established by Morançais et al. (Chem. Eng. Commun. 179 (1999) 77) and Legrand et al. (Chem. Eng. Res. Des. 79 (2001) 949). The boundary-layer shear force concept has been applied to predict the drop break-up at low Reynolds number and at intermediate Reynolds number, the effect of inertia on the drop break-up has been considered. The predicted drop sizes are in reasonable agreement with experimental results.     

Laminar mixing of shear thinning fluids in a SMX static mixer

Flow and mixing of power-law fluids in a standard SMX static mixer were simulated using computational fluid dynamics (CFD). Results showed that shear thinning reduces the ratio of pressure drop in the static mixer to pressure drop in empty tube as compared to Newtonian fluids. The correlations for pressure drop and friction factor were obtained at Re_MR?100. The friction factor is a function of both Reynolds number and power-law index. A proper apparent strain rate, area-weighted average strain rate on the solid surface in mixing section, was proposed to calculate pressure drop for a non-Newtonian fluid. Particle tracking showed that shear thinning fluids exhibit better mixing quality, lower pressure drop and higher mixing efficiency as compared to a Newtonian fluid in the SMX static mixer.     

Pressure drop and mixing in single phase microreactors: Simplified designs of micromixers

Continuous flow microreactors can greatly improve the safety and product yields of processes in the pharmaceutical and fine chemical industry by overcoming many of the drawbacks of traditional batch and semi-batch stirred reactors. This study compares on a common scale the pressure drop and mixing performance of different size commercial microreactor plates composed of a tangential, SZ-shaped or caterpillar mixer followed by a rectangular serpentine main channel. The pressure drop was fitted to a friction factor model, which suggests that the mixing zone had significant chaotic secondary flow patterns, whereas the main channel did not. Moreover, the mixing zone was the main contributor to the overall pressure drop. Mixing performance was then characterized using competitive parallel reactions. Upon the formation of chaotic secondary flows, typically due to the interactions of artificially induced vortices, the mixer performance was found to be independent of geometry for a given energy dissipation rate. However, the mixer geometry will affect the critical Reynolds number that induces chaotic advection and changes the mixing time scale.     

Shortstopping and jet mixers in preventing runaway reactions

Runaway reactions are continuing to be a major problem in the chemical industry (26% of major accidents). One of the main reasons for runaways is power failure. Runaway reactions could be inhibited in two ways: by the addition of cold diluents and by the addition of an inhibitor (chemical reaction stopper). This technology is called shortstopping. After a power failure, the process of adding an inhibiting agent and mixing it with the reactor contents becomes a major problem in the shortstopping process. Jets or impellers, driven by a small generator, however, can be used for mixing the inhibitor with the reactor contents.Dakshinamoorthy et al. [2006. CFD simulations of shortstopping runaway reactions in vessels agitated with impellers and jets. Journal of Loss Prevention in the Process Industries 19, 570-581] compared the efficiency of using jet mixers versus impeller stirred vessels in shortstopping runaway reactions. On the basis of equal power consumption, this comparative study showed that jet mixers are ineffective when used for shortstopping. One needs to identify additional factors, to effectively shortstop when using jet mixers.Due to the hazardous nature of runaway reactions, these factors cannot be determined with lab scale or pilot plant scale experiments. Recent developments with CFD make it possible to carry out virtual experiments. The computational model is solved using FLUENT. Shortstopping studies via the addition of a reaction inhibitor and cold diluent are discussed in detail. The results reported in this study identify the major and minor factors, which contribute to effective shortstopping; i.e., power requirements, locations for adding the inhibitor, the quantity of inhibitor added, rate of the inhibition, the use of cold diluent and the use of multiple nozzles. These results especially demonstrate the value of using CFD simulations in situations that are experimentally prohibitive.     

Axial mixing in a ploughshare mixer

Motion is studied within a bladed 5 l ploughshare mixer for granular solids at two rotor frequencies, 2 Hz and 4 Hz, for fill levels between 12.5% and 70%. Positron emission particle tracking is used to follow the motion of a single radioactive tracer. Particles circulate around the bed in the transaxial plane in the direction of blade rotation. Axial motion perpendicular to this plane is significantly less and is largely contained in the region between the planes of rotation of adjacent blades. Axial mixing between these inter-plough regions is determined by calculating the transport rate across these planes. Transport is greater at 4 Hz than at 2 Hz, but decreases as fill level increases. Axial transport is further studied by recording the location of the tracer as it crosses each plane of blade rotation. These passages can be described as occurring either; (i), in defined regions of the bed; or (ii), by leading or lagging the blades by a constant angle. A transition from (i) to (ii) occurs as fill level increases. At 4 Hz or with oily rice, the transition occurs at lower fill levels.     

Mass transfer in external-loop airlift bioreactors using static mixers

The influence of static mixers on the overall gas-liquid volumetric mass transfer coefficient (K_La_L) was examined in an external-loop type airlift bioreactor (approximately 15 L volume, 1.8 m static liquid height, A_r/A_d = 0.444). The study was conducted with aqueous salt solution (0.15 kmol ? m^?3 NaCl) and with pseudoplastic solutions of carboxymethyl cellulose (0.2 ? 0.6 wt./vol. % (g/100 mL) CMC). Over a broad range of power law parameters K (10^?3 ? 10 Pa ? sⁿ) and n (0.5 ? 1.0), the presence of static mixers in the riser was found to enhance the K_La_L relative to mixer-free mode of operation. The extent of increase in K_La_L depended on the fluid “thickness”, K: the higher the K, the greater the K_La_L intensification due to static mixers. For otherwise identical conditions, the presence of static mixers improved K_La_L by 30-500%, depending on the fluid. The boost in K_La_L was associated with increased gas holdup and gas-liquid interfacial area, which arose due to bubble breakup accomplished by the static mixing elements. Potential advantages of static mixers in upgrading the performance of oxygen-limited fermentations were pointed out.     

Hydrodynamics and mass transfer in gas-liquid flow through static mixers

The objective of this study was to characterize the two-phase flow hydrodynamic behaviour and mass transfer in a static mixer in a horizontal pipe. Different arrangements of elements of the static mixer were tested and their performances compared. The pressure drop, bubble diameters and mass transfer coefficient were measured. The influence of operating conditions was also studied. A different correlations are proposed and compared with other correlations found in the literature.     

Experimental study of the mixing kinetics of binary pharmaceutical powder mixtures in a laboratory hoop mixer

As increasingly commented by the literature during the last 5 years, estimating the homogeneity of a powder mixture and following powder mixing processes is not a simple task. In this paper, we present the development and statistical validation of a sampling methodology for defining the number of samples required to provide a reasonable estimation of the homogeneity attained in a laboratory scale tumbler mixer. This method is then used to follow the mixing kinetics of a dilute binary powder mixture in a hoop mixer. Special attention is paid to the statistical meaning of the values obtained and the influence of the physical characteristics such as particle size and shape. The role of the particle shape of the majority powder is particularly emphasised and it is quantitatively demonstrated that spherical particles are harder to mix and more ready to segregate than particles with irregular shapes. The different mixing mechanisms at play are identified; the practical limits of use of such tumbler mixers with pharmaceutical powders are discussed.     

Scale-up of pump-mix mixers using CFD

Effect of scale on the drop size distribution in a pump-mix mixer has been studied. A network of zones model was developed to predict the drop size distribution at different locations in the mixer. Computational fluid dynamics model was used to obtain the flow patterns in the mixer and to identify zones based on the flow patterns. Population balance equation was solved for all the zones of the mixer. The model was validated with the experimental data over a wide range of parameters as well experimental data from the published literature. The model was further extended for scale-up studies. Two different scale-up criteria were studied. It was observed that equal power consumption per unit mass and geometrical similarity is a better scale-up criterion as compared with equal tip speed criterion for pump-mix mixers.     

CFD simulation of liquid-phase mixing in solid-liquid stirred reactor

A comprehensive CFD model was developed to gain an insight into solid suspension and its implications on the liquid-phase mixing process in a solid-liquid stirred reactor. The turbulent solid-liquid flow in a stirred reactor was simulated using a two-fluid model with the standard k-ε turbulence model with mixture properties. The multiple reference frames (MRFs) approach was used to simulate impeller rotation in a fully baffled reactor. The computational model with necessary sub-models was mapped on to a commercial solver FLUENT 6.2 (of Fluent Inc., USA). The predicted solid concentration distribution was compared with the experimental data of Yamazaki et al. [1986. Concentration profiles of solids suspended in a stirred tank. Powder Technology 48, 205-216]. The computational model was then further extended to simulate and understand the implications of the suspension quality on liquid-phase mixing process. The computational model and the predicted results discussed here will be useful for understanding the liquid-phase mixing process in stirred slurry reactors in various stages of solid suspension.     

Pressure drop and mixing behaviour of non‐Newtonian fluids in a static mixing unit

Static or motionless mixers have received wide application in chemical and allied industries due to their low cost and high efficiency. The pressure drop and mixing behaviour of such mixers have been widely studied. However, the available information for non‐Newtonian fluids is scanty. The results of pressure drop and mixing studies conducted with a locally made motionless mixer (MALAVIYA mixer) and four non‐Newtonian fluids—aq. CMC, PVA, and PEG solutions are reported in this article. The new mixer causes less pressure drop compared to some of the commercial mixers. Mixing behaviour of the unit is more closer to plug flow and a two‐parameter model correlates the dispersion data.     

CFD simulation of mixing and reaction: the relevance of the micro-mixing model

The aim of this work is to understand the role of the micro-mixing model in computational fluid dynamics (CFD) simulations of fast reactions. Using CFD, in fact, the reactor is modelled through a computational grid and the governing equations are discretised using numerical methods. However, the mixing phenomena that occur at scales that are smaller than the grid size remain unresolved. This means that the probability density function (PDF) of all scalars is assumed to be a delta function centred at the mean value. In order to take into account micro-mixing effects a model must be added. In this work the finite-mode PDF approach is used to predict the selectivity of a parallel reaction in a Taylor-Couette reactor working in semi-batch conditions. Experimental data are compared with model predictions in order to investigate the relevance of the micro-mixing model. The case of precipitation is also discussed.     

CFD analysis of turbulence non-homogeneity in mixing vessels: A two-compartment model

A two-compartment model has been developed for calculating the droplet/particle size distribution in suspension polymerization reactors by taking into account the large spatial variations of the turbulent kinetic energy and its dissipation rate in the vessel. The two-compartment model comprised two mixing zones, namely an impeller zone of high local energy dissipation rates and a circulation zone of low kinetic energy. Computational fluid dynamics (CFD) was employed for generating the spatial distribution of energy dissipation rates within an unbaffled mixing vessel agitated by a flat two-blade impeller. A general methodology was developed for extracting, from the results of the CFD simulations, the volume ratio of the impeller over the circulation zone, the ratio of the average turbulent dissipation rates in the two zones, and the exchange flow rate between the two compartments. The effect of agitation rate, continuous phase viscosity, impeller diameter, and mixing vessel scale on the two-compartment model parameters was elucidated. The two-compartment model was then applied to a non-homogeneous liquid-liquid dispersion process to calculate the time evolution of the droplet size distribution in the mixing vessel. An excellent agreement was obtained between theoretical and experimental results on droplet size distributions obtained from a laboratory-scale reactor operated over a wide range of experimental conditions.     

Formation of O/W emulsions by static mixers for pharmaceutical applications

Oil-in-water (O/W) emulsions produced by static mixers in the laminar flow regime are characterized for their oil drop size spectra. The emulsions are used in the first process step for the production of microspheres for pharmaceutical applications by the emulsion extraction method. However, emulsion generation by static mixers in the laminar flow regime is rarely discussed in the scientific literature. Here we deduce a non-dimensional correlation for predicting the Sauter mean oil drop size as a function of the static mixer operation parameters and the liquid properties. First, the material properties of the organic and water phases are characterized. Second, the oil drop size spectra of the emulsions are measured by laser diffraction. Dimensional analysis is used to describe the relationship between the process parameters of the static mixer and the Sauter mean oil droplet size. Emulsion production experiments using SMX static mixers with two different diameters are carried out with the mixing of the two liquids taking place in the laminar flow regime. We provide results covering a wide range of all process parameters, which were identified influencing the droplet size of the emulsion. The correlation achieved is related to the non-dimensional drop-size based Ohnesorge number of the emulsification process and allows for the prediction of the mean oil droplet size with good accuracy, which is an essential information about the emulsion properties relevant for the pharmaceutical application.     

Experimental investigations of velocity fields in packed bed static mixers

Experimental investigations of velocity fields have been carried out in static mixers filled by Inzhekhim random packings of various sizes and Rashig rings. Studies have been performed on a laboratory setup by stereoscopic particle image velocimetry using a Polis multiphase flow measurement system. Experimental data have been supplemented by the results of numerical modelling of the hydrodynamics of flow, which were obtained using ANSYS Fluent software.     

Scaling inline static mixers for flocculation of oil sand mature fine tailings

Operations to reclaim mature fine tailings (MFT) ponds involve flocculation using high‐molecular‐weight polymers, for which inline static mixers are suited. Three different commercial static mixers were utilized to determine mixing parameters corresponding to optimal dewatering performance of flocculated MFT. MFT was treated with polymer solution under different mixing conditions. The dewatering rates passed through a peak with increasing mean velocity, V and Reynolds number, Re of the fluid. The greater the number of mixer elements, the lower the V and Re at which the peak dewatering rate occurred. Mixing parameters such as G‐value, residence time, and mixing energy dissipation rate of the most rapidly dewatering flocculated MFT were dependent on mixer type and setup. In contrast, peak dewatering rates converged when scaled with respect to specific mixing energy, E, demonstrating that E is a suitable scale‐up parameter for inline static mixing to produce optimally dewatering MFT. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4402–4411, 2015