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.     

Elaboration of PEG/PA66 blends in a twin-screw batch-type mini-extruder: Process study and modelling

This paper deals with the development of the morphology in polyethylene glycol (PEG) and polyamide 66 (PA66) immiscible blends exhibiting an extremely low viscosity ratio (η_PEG/η_PA66=3-4×10^-5). These materials were obtained by melt mixing, under different operating conditions, using a twin-screw batch-type DSM mini-extruder.Scanning electron microscopy, followed by quantitative image analysis was used to determine PEG particles size distribution (PSD) as a function of blends composition and screw rotation speed. Experiments carried out with two mixing time (5 and 10 min) showed no significant difference of PSD. So, to avoid thermal degradation of the products, the mixing time was set up at 5 min for all experiments. The influence of PEG concentration and screw rotation speed on PSD appeared to be similar to that obtained in a previous study for the same blends elaborated in a Haake internal mixer. The results clearly showed that the average particle diameters decreased as screw rotation speed increased and as PEG concentration decreased. However, this decrease is less important using the twin-screw batch-type mini-extruder with which the particle sizes are smaller. The particles sizes were then correlated to blend composition, shear rate and viscosity ratio owing to an extension of Serpe's model. The unknown parameters of the corresponding model were estimated on the basis of experimental data. This enabled then to predict with a good precision the influence of the process operating conditions on the morphology of the dispersed phase.     

Fast liquid mixing by cross-flow impingement in millimeter channels

A fast liquid mixing process was implemented by the cross-flow impingement of thin liquid sheets in the confined mixing channels with the width of millimeter(s). The species transport between the two liquids was studied by visualizing the 2-D concentration field of Rhodamine dye with the planar laser induced fluorescence (PLIF) technique, on which the intensity of segregation (IOS) and the 95% mixing time (τ₉₅) were calculated to evaluate the mixing quality. Due to the reduced spatial scale of liquid mixing and the high energy dissipation rate of ∼1000 to produced by the strong impingement between the liquid sheets, fast mixing of liquids was achieved at a time scale of milliseconds. The effects of operating conditions and the mixer geometry on the mixing behavior were investigated comprehensively by both experiments and computational fluid dynamics (CFD) simulations. Good agreement of the CFD predictions with the experimental data was obtained by the k-? model with species transport, where dependence of the CFD predictions on the turbulent Schmidt number (i.e. Sc_t) was discussed in detail. The results show that for this turbulence-induced mixing procedure the momentum ratio and the cross-flow angle between the two liquids play significant roles in the mixing efficiency. The absolute liquid velocity has little effect on the species transport in space, i.e. the mixing distance to reach IOS of 5%. Nevertheless, the mixing time is shortened at higher velocity conditions. The fluctuation of the transient concentration signals shows stronger interaction at the interface between the two liquid sheets. And the local concentration fluctuations can be well described by the β-PDF (probability density function) model.     

Characterization of the granular-to-fluid state process during mixing by power evolution in a planetary concrete mixer

Adding product into the mixer exerts a strong and rapid impact during concrete mixing. Experimental data obtained from a planetary mixer in a full-scale concrete plant under laboratory conditions show that the state of mixture progress with mixing time is well described by the mixing power evolution. More specifically, a reliable method for detecting the time corresponding to the transformation of a mixture from a cohesive granular material into a granular paste (i.e. the so-called “transition time”), through use of a mixing power measurement, will be presented herein. Moreover, once this transition has been achieved, mixing power consumption will be related to mixture rheology and then to mixer geometry by means of a simplified hypothesis. This equation can also be obtained via a dimensionless analysis. Lastly, it will be shown that mixture behavior beyond the transition point is well fitted by a hyperbolic equation. The corresponding mixing power evolution can then be predicted by the level of power at this transition time. These results are suitable for application to online process monitoring.     

Dimensional analysis for planetary mixer: Mixing time and Reynolds numbers

Mixing time number is a convenient parameter to characterize mixing performance of stirred tanks. This dimensionless number is now well established for agitated vessels equipped with vertically and centrally mounted impeller for Newtonian as well as for non-Newtonian fluids. To our knowledge, there is more ambiguity concerning its definition for planetary mixers especially when they have dual motion (around two perpendicular axes) to achieve homogenization. In this study, dimensional analysis of mixing time and reliability of the modified Reynolds and mixing time numbers are proposed for such a planetary mixer particularly named as TRIAXE^® system. These two numbers are based on the maximum tip speed of mixer as the characteristic velocity. Modified dimensionless numbers are consistent with the definition of conventional Reynolds and mixing numbers (when only one revolving motion around the vertical axis of the mixing device occurs in the vessel).Mixing time experiments with TRIAXE^® mixer for highly viscous Newtonian fluids showed that the proposed modified Reynolds and mixing time numbers succeeded to obtain a unique mixing curve irrespective of the different speed ratio chosens. This agreement proves that the proposed modified dimensionless numbers can be well adapted for engineering purposes and they can be used to compare the mixing performance of planetary mixers.     

A modified coalescence—dispersion model for the axial mixing of segregating particles in a motionless mixer

A modified coalescence—dispersion model has been developed for the axial mixing of segregating particle systems in a motionless mixer (Kenics mixer). This model is capable of generating the concentration distribution as a function of time and its applicability is not constrained by the initial concentration distribution in the mixture. Two important parameters in this model are the coalescence rate and the distribution ratio. It has been found that the former can be correlated as a linear function of the number of helices in the mixer, and the latter depends heavily upon the physical properties of the individual particles. The validity of the present model has been tested against the available experimental data [16].     

The recirculating screw mixer: A new small-volume mixer for the polymer laboratory

The recirculating screw mixer (RSM), a new small-volume intensive mixer for the polymer laboratory, is designed, built, modeled, and tested. This type of batch mixer is intended for the mixing of 1 to 30 cm³ of viscous material at high shear rates. A material element in the mixer experiences alternating screw pump and tubular flows with reorientation between these flows. A mixer with a 10 cm³ sample capacity is built for testing and evaluation. Flow visualization experiments are used to investigate the quality of the distributive mixing achieved. The flows in the mixer are modeled for the cases of a Newtonian fluid and a power law fluid. The Newtonian model accurately predicts the recirculation time for particles suspended in Newtonian silicone oils. The power law model accurately predicts the screw torque obtained with a polystyrene and polyethylene. A method for the measurement of fluid rheology from the operating conditions of the RSM is proposed and tested. The mixing achieved by the RSM is compared to that obtained by a batch mixer with roller blades. Both mixers are used to prepare blends of ethylene-propylene rubber in polystyrene. The morphologies of the resultant blends are compared and differences in the mixing action are discussed. The mixers are also used to prepare composites of fumed silica in polyethylene. The quality of mixing obtained in the RSM compares quite favorably with that obtained in the batch mixer with roller blades for polystyrene/ethylene-propylene rubber reactive blends and polyethylene/silica composites.     

Pyrolysis of hydrocarbons in a heat-carrier flow with fast mixing of the components

A scheme of autothermal pyrolysis of hydrocarbons in a reactor with fast mixing of the feedstock with a high-temperature heat-carrier flow is considered. The possibility of providing fast mixing of the components is verified in a series of aerodynamic experiments in a model setup, where the optimal geometry of the mixer for operation conditions of the pyrolysis reactor is determined. An experimental reactor is designed and manufactured for verification of the concept proposed. A scheme of the propane pyrolysis reactor is given. Products of combustion of a hydrogen-air mixture are used as a heat carrier. Experimental distributions of the flow temperature and concentration of the injected substance at the exit of the reactor agree with results obtained in the model setup. The mixing time is demonstrated to be smaller than the residence time of the mixture in the reactor mixer by more than an order of magnitude, which allows the process to be arranged under controlled conditions. In addition to experimental research, several detailed kinetic schemes of hydrocarbon pyrolysis are tested on the basis of available experimental data. Results of kinetic calculations for the operation conditions of the experimental setup are presented. __________ Translated from Fizika Goreniya i Vzryva, Vol. 44, No. 5, pp. 38–44, September–October, 2008.     

A study on the mixing of flour in a motionless Sulzer (Koch) mixer using a radioactive tracer

This work was concerned with the evaluation of the motionless Sulzer (Koch) mixer for radial mixing of flour. A radioactive tracer technique was employed. The tracer employed, mainly radiosotope ⁵⁶Mn, was created by neutron activation with a neutron flux of 1.44 × 10¹² n/cm² sec. The method has a high degree of accuracy and the advantage that no physical differences exist between the bulk and tracer materials. The concentration distribution in the radial direction was measured, and the resulting degrees of mixedness of the mixture after passing through the mixer for 1, 2, 3, 5 and 10 passes were determined. The degress of mixedness in the radial direction increased with the number of passes. The experimental results were compared to the same mixture passing through an empty column without mixing elements inserted. The comparison indicated that the mixing elements enhanced the mixing process in a predictable way. Finally, a mechanistic model was developed and verified by the experimental results.     

Finite element modeling of the laminar and transition flow of the Superblend dual shaft coaxial mixer on parallel computers

The macro-mixing mechanisms of the Superblend coaxial mixer consisting of a Maxblend impeller and a double helical ribbon agitator mounted on two independent coaxial shafts rotating at different speeds are numerically investigated. The simulations are based on the resolution of the Navier-Stokes equations with help of a parallel three-dimensional finite element solver exploiting the capabilities of high performance computers. To model the rotation of agitators a hybrid approach based on a novel finite element sliding mesh and fictitious domain method is used. The power consumption, the flow patterns, the shear rate distribution, the pumping capacity and the mixing time of the Superblend mixer are calculated from the simulated hydrodynamics. The simulations allow observing the flow as it evolves from deep laminar (Re=0.1) to transition (Re=520) regime. As Reynolds number increases, several recirculation zones above and below the middle of the tank are formed. It is found that operating the agitators in co-rotation mode requires less power consumption and exhibits equal or shorter mixing time than counter-rotation mode. The larger power consumption in counter-rotating mode is caused by the presence of high shear vortices generated between the two coaxial agitators. Furthermore it is shown that the shear distribution throughout the Superblend coaxial mixer operating in co-rotation mode is almost homogenous, which is highly desirable for shear sensitive products. In view of the results obtained in this work, the Superblend coaxial mixer is found as a good alternative for tough mixing applications.     

Simulation of supercritical water–hydrocarbon mixing in a cylindrical tee at intermediate Reynolds number: Formulation,numerical method and laminar mixing

The objective of this work is to study the flow dynamics and mixing of supercritical water and a model hydrocarbon (n-decane), under fully miscible conditions, in a small scale cylindrical tee mixer (pipe ID = 2.4 mm), at an intermediate inlet Reynolds number of 500 using 3-D CFD simulations. A Peng–Robinson EoS with standard van der Waals mixing rules is employed to model the near-critical thermodynamics with the mixture binary interaction parameter obtained from a Predictive Peng–Robinson EoS using group contribution theory (PPR78). The n-decane stream is introduced at the colder temperature of 700 K to ensure operation above the Upper Critical Solution Temperature (UCST, 632 K) of the water n-decane system while the water stream enters at a higher temperature of 800 K. Under these conditions, the flow in the tee mixer remains laminar and steady-state is reached. Mixing occurs predominantly due to the circulating action of a counter-rotating vortex pair (CVP) in the body of the hydrocarbon jet entering from the top. This CVP is formed due to the reorientation of the streamwise vorticity pre-existing within the hydrocarbon jet as it flows down the vertical pipe of the tee junction. The advective transport is further assisted by a secondary flow of water from the bottom stream, around the hydrocarbon jet, toward the space vacated near the top of the downstream pipe section by the downward motion of the HC jet. The CVP becomes progressively weaker due to vorticity diffusion as it is advected downstream and beyond 10–12 diameter lengths downstream of the mixing joint, transport is mainly controlled by molecular diffusion. It was found that the variations of density and transport properties with temperature do not have a significant impact on the flow and mixing dynamics for a ΔT = 100 K between the two streams. Local cooling of the fluid mixture was also observed in the mixing of water and n-decane streams entering at the same temperature (initially isothermal). This cooling effect is due to the diffusion of species along a gradient in their partial enthalpy in the mixture. Such gradients in species partial enthalpies are non-zero under near-critical conditions even for initially isothermal flows due to the non-ideality of the fluid mixture under these conditions. This local heating/cooling effect at near-critical conditions could give rise to unexpected formation of phases when operating close to critical points.     

An overlapping crisscross micromixer

We propose a grooved micromixer incorporating an overlapping crisscross inlet port that is located at the intersection of two patterned channels crossing one above another. Both numerical analysis and experimental verification of the flow structure of this design have substantiated the superior mixing features over the existing herringbone mixer. Because of the symmetric feature of this microstructure, fabrication becomes simplified through assembling two identical PDMS-based slabs oppositely. Both experimental results for flow visualization and numerical simulation reveal significant cross flow at the intersection of the two channels and vertical tumbling of the flow. This activated flow feature supplies downstream fluids with vertical momentum to enhance the chaotic advection and enlarges the interfacial area between the two mixing fluids. All these features improve the mixing performance of this novel overlapping crisscross micromixer by 46% compared with the mixing indices of the staggered herringbone mixer for the longitudinal distance . Furthermore, on modulating the ratio of volumetric flow rates between the two inlet streams, an excellent mixing function with a specific prearranged concentration of a mixture and a decreased pressure loss are achieved. The divided ratios Q_t/Q_l, defined as diverted flow rate over forward flow rate, are between 1.86 and 2.88 for fluid A and between 0.52 and 0.67 for fluid B with a variable initial flow rate ratio.     

Rheological behavior of reactive miscible polymer blends: Influence of mixing and annealing before crosslinking

We followed crosslinking reactions in the blends of two miscible reactive polymers by either torque rheometry or dynamic rheological measurements. Functional polymers with controlled glass‐transition temperatures (T_g's), chain lengths, and number of reactive groups per chain were synthesized by bulk radical polymerization. The blends were prepared either in a batch mixer or directly in the parallel plate geometry of a dynamic rheometer. Because of the low T_g of the blend components, it was possible to separate the mixing step from the crosslinking reaction, which was followed by small amplitude dynamic measurements at a higher temperature. The kinetics of the crosslinking reaction were determined by the study of the variations of the storage modulus (G′) as a function of the reaction time. In this study, we focused on investigating the influence of blend composition, crosslinking reaction temperature, and amount of shear generated during the mixing step on the reaction kinetics. The influence of annealing time after the preshear step was also investigated. We found that the mixing procedure in the internal mixer produced homogeneous blends for which G′ was dependent on the reaction time. Moreover, the reaction rate increased as the temperature and the chain functionality increased. A first approach showed that reduced variables could be defined from G′ and reaction time with the initial concentration of the functional units to obtain a master curve independent of the species concentration. For blends prepared directly between the parallel plates of the dynamic rheometer, G′ and the subsequent reaction rate were strongly dependent on the amount of shear generated during the mixing step. However, at high enough shear, the blend was perfectly mixed and the increase in G′ versus reaction time was comparable to that obtained for the blend prepared in the internal mixer. Surprisingly, the higher the annealing time was, the lower the increase in G′ was. However, we could explained this by considering the fact that the reaction started during the annealing step, which therefore, led to a thin crosslinked layer, which prevented any further diffusion of the polymer chains. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 98: 1978–1995, 2005     

Crystal Growth in Drowning‐Out Crystallization using a T‐Mixer

The kinetics of nucleation and crystal growth in drowning‐out crystallization using a T‐mixer were estimated using crystal size distribution, taking into account a size‐independent growth. At the conditions of the feed compositions investigated, the product weight mean size changed from 7–29 μm when the residence time varied between 0.32 and 0.61 s. Nucleation and growth rates were expressed simply as a function of the residence time. The T‐mixer can be used to generate high levels of supersaturation due to inducing micro‐mixing effects. The particle size correlated well with the ratio of growth rate to nucleation rate. Finally, the particle size obtained in drowning‐out crystallization using a T‐mixer was found to be proportional to the 1.69^th power function of the residence time.     

The mixed-bed ion exchange performance at ultralow concentrations 1. Variable feed concentration and incomplete mixing of resins

Experimental data were obtained to evaluate the performance of mixed-bed ion exchange for the cases of variable feed concentration and incomplete mixing of anion and cation resins observed in large scale industrial units. For variable feed concentration, step changes in feed concentration were arbitrarily introduced into a test column. For incomplete mixing, only anion resin was loaded in the upper 20% of the column and more cation resin in the lower portion. Feed concentrations of 5.0× 10⁻⁵−2.0×10^-4 M NaCl were used for the experiments, with flow rates of 0.665-7.0 ml/sec. The effluent from the column was collected periodically and analyzed using on-line/off-line ion chromatography. The step changes in feed concentration affect the breakthrough times of sodium and chloride. Sodium breakthrough curve is more sensitive to the step changes than chloride breakthrough curve. With the same volumes of cation and anion resins, incomplete mixing of resins increases the cation exchange rate slightly and decreases the anion exchange rate slightly. As the cation resin volume increases, the effect of the incomplete mixing of resins decreases. The breakthrough curves of both ions, plotted as the ratio of effluent to the influent concentration versus run time in hour, give some detailed results about the effects of the conditions.     

Performance of Kenics static mixer over a wide range of Reynolds number

The present study deals with the numerical simulation of flow patterns and mixing behaviour in Kenics static mixer over a wide range of Reynolds number. Three different sets of Kenics mixer (aspect ratio = 1.5) comprised of 3, 9 and 25 elements each have been characterized. The Reynolds number was varied in the range of 1 to 25,000 (i.e., from laminar to turbulent flow regime). The numerical approach takes into account the aspects of the fluid flow at higher Reynolds number values including circumferential velocity profiles at different cross-sections within the Kenics mixer, which were neglected in previous studies. It was observed that cross-sectional mixing in the turbulent flow regime takes place up to 30% of each element length at element-to-element transition; beyond that velocity profiles were uniform. The experiments were also carried out to measure the circumferential and axial velocity profiles and pressure drop in three different Kenics Mixers using air as fluid. The pressure drop per unit element (ΔP/η) was found to be independent of the number of Kenics mixing elements used in the system. The total pressure drop across Kenics mixer obtained by CFD simulations were compared with the experimental pressure drop values and correlations available in the literature. The numerical results were found in good agreement with the experimental as well as the results reported in the literature. A new pressure drop correlation in the Kenics static mixer has been developed.     

Laboratory RO and NF processes fouling investigation by residence time distribution curves examination

The fouling phenomena of nanofiltration of calcium sulfate saturated feed solution in the presence of magnesium and carbonates as well as the reverse osmosis of saturated silica feedwater with magnesium chloride content at different pH levels, was investigated by analyzing the membrane residence time distribution curves (RTD) in our laboratory. The fraction of degraded membrane (parameter a), the fraction of active membrane area (parameter b) and the fraction of membrane blocked by impermeable layer (parameter c) as a function of permeate recovery was determined. It was found that not only surface blockage affects permeate efficiency, but also other factors, such as module retentate chamber pressure drop and osmotic pressure increase. The membranes RTD measurements as well as fouling, a, b and c parameters, gathered with ion-selective electrodes (chloride, calcium and cupric ion-selective) and appropriate tracer solutions (sodium chloride, calcium chloride and cupric nitrate) were compared with commonly used conductivity sensor and sodium chloride tracer solution. We found that both the tracer and detector type strongly affects membrane mean residence time and its variance, but at the same time no influence of detector and tracer type on membrane fouling a, b and c parameters was observed.     

Phase diagram of poly(vinyl chloride) and solution chlorinated polyethylene

The behaviour of mixtures of poly(vinyl chloride) (PVC) and solution chlorinated polyethylene (SCPE) has been investigated as a function of temperature. These polymers have been found to be compatible over some ranges of composition and exhibit the phenomenon of a lower critical solution temperature (LCST). The thermally-induced phase separation has been investigated by optical, dynamic mechanical, and electron microscope techniques. The single phase mixture has been investigated by scanning analytical electron microscopy. Some investigation of the thermodynamics of the mixture has been made and the heat of mixing term has been found to be negative and small, i.e. favouring mixing. It has been shown that the technique of in situ polymerization overcomes many of the problems of preparing these polymer mixtures in the solid state.     

Effect of operating conditions and design parameters in a continuous powder mixer

An experimental investigation was carried out to study the mixing performance and flow behavior in a continuous powder mixer for a typical pharmaceutical mixture. Blender performance, characterized by the relative standard deviation (RSD) of composition of blend samples taken at the blender discharge and by the variance reduction ratio (VRR) of the blender, was measured as a function of impeller rotation rate, flow rate and blade configuration. The flow behavior in the continuous mixer was characterized using the residence time distribution (RTD) and powder hold-up measurements. To quantify the strain applied to the powder in the blender, the number of blade passes experienced by the powder in the blender was calculated using the residence time measurements. The relationship between different experimental parameters and mean residence time and mean centered variance was examined. The mixing performance was largely dominated by the material properties of the mixture, which had a larger effect than the ingredient flow rate variability contributed by the feeders. Holdup was strongly dependent on impeller rotation rate; as impeller rotation rate increased, holdup (and therefore, residence time) decreased sharply. As a result, intermediate rotation rates showed the best mixing performance. Blade configuration affected performance as well; blade patterns where some of the blades push the powder backwards improved the mixing performance.