Design and characterization of a Low-pressure-drop static mixer

Four-blade static mixer was designed for inline mixing of Newtonian fluids at Reynolds numbers from 700 to 6800. The mixer consists of four equally spaced blades mounted on cylindrical housing with 45° rotation relative to the circumference. It was tested in three different compartments of 6, 8, and 10 mixing elements; each element rotated 45° relative to the adjacent one. Multipoint sampling was used to measure concentration downstream the mixer. The mixing quality was measured by the coefficient of variance (CoV). The CoV decreases as the energy input per unit mass increases. This effect is more pronounced when the number of mixing elements increases. For the case of 10 mixing elements, a good mixing performance (typically more than 95% mixedness or CoV < 0.05) achieved, although a marginally good mixing performance could also be achieved by eight mixing elements. The friction factors were correlated as f = C₁/Re + C₂/Reⁿ with an average deviation of ±10% from experimental data. Furthermore, experimental friction factors were compared with existing models. For a wide range of Reynolds numbers, the friction factors are apparently smaller than those from SMV, KMX, and baffle-type static mixers. © 2018 American Institute of Chemical Engineers AIChE J, 65: 1126–1133, 2019     

Stochastic modeling of segregation in a motionless mixer

The mixing of particles with different characteristics is generally accompanied by segregation which prevents the particles from attaining the randomly mixed state. A discrete steady-state Markov chain model was employed to model the axial segregation of solid particles in a motionless mixer. Three systems containing particles of different sizes and/or densities were studied. One step transition probabilities of the model were experimentally determined. The model can predict the concentration profiles, the degrees of mixedness, and the equilibrium states of these particle systems blended by passing the particles through a motionless mixer. Experimental results are in good agreement with those predicted from the model.     

Residence Time and Concentration Distribution in a Kenics Static Mixer

Static mixers, often referred to as motionless mixers, are in-line mixing devices that consist of mixing elements inserted into a length of pipe. Most of the experimental works in this field have concentrated on establishing design guidelines and pressure drop correlations. Due to experimental difficulties, few articles have been published on the investigation of the flow and mixing mechanisms. In this work, a Kenics KMX static mixer was utilized to study concentration and residence time distribution (RTD) and effect of Reynolds number on mixing. The static mixer had six mixing elements arranged in-line along the length of the tube, and the angle between two neighboring elements was 90°. The length of the mixer was 0.98 m with internal and external diameters of 5.0 cm and 6.0 cm, respectively. The main continuous fluid was water, and NaCl solution was used as a tracer. All experiments were conducted with three replications at three Reynolds numbers, Re = 1188.71, 1584.95, and 1981.19. A dispersion model was used to model the RTD data. The experimental results were compared with the model results and reasonable agreement was achieved.     

The effect of mixing aids on the kinetics of mixing in a rotating drum

The batch mixing of particulate solids in a rotating drum mixer has been investigated with various numbers of Lucite balls added as mixing aids. Two experimental systems have been studied. One involved the mixing of dolomite particles of two sizes, 28 × 32 and 42 × 48 mesh, while the other consisted of mixing calcite and silica of the same size range, namely 65 × 100 mesh. The progress of mixing was followed by a simple sampling and assaying technique which permits accurate determination of the composition of the powder in sections along the axis of the mixer. The role of mixing aids on the mixing process was quantified by evaluating their effect on the diffusion coefficient and the degree of mixedness. An empirical relationship between the diffusion coefficient and the number of balls added to the mixer was obtained.     

Development of positron emission particle tracking for studying laminar mixing in Kenics static mixer

Positron emission particle tracking (PEPT) is a flow visualisation technique that has found application in a wide range of processes. In this work, PEPT has been used to study laminar flow of a high viscosity Newtonian and non-Newtonian fluid in a Kenics static mixer (KM). Through analysis of the trajectories of many hundreds of passes of the tracer particle through the mixer, it is possible to compute the overall flow field and to visualise how the fluid twists and folds as it passes along the mixer. Eulerian velocity maps plotted for the Newtonian and non-Newtonian fluids showed that the length required for the flow to develop is shorter for the non-Newtonian fluid than the Newtonian. The stretching and folding mechanism of mixing was observed by grouping the trajectories into clusters according to whether the trajectory passes to the left or right of the blade at the transition between elements. Those trajectories making the same L–R–L decision tended to remain in the same striation through two or three elements until that striation became stretched and folded back on itself, sandwiching other layers. It is clear that the PEPT data is rich and powerful. We are hopeful that the techniques we develop for the flow and mixing in the Kenics mixer will be applicable to studying more complex laminar flows.     

Macroscopic estimation method of the mixedness of Kenics type static mixer

We investigated the mixing process of the Kenics type static mixer, in which the mixing is enhanced by both advective mixing and mixing due to molecular diffusion in order to propose an estimation method of the mixedness. The results show that the element divides, folds and stretches the mixing fluids and forms a lamellar structure with striation width l _a . The value of l _a decreases with an increase in the number of elements by l _a -(2 ⁿ⁻¹)⁻¹, which represents the characteristics length of advective mixing. The characteristic length of mixing due to molecular diffusion l _d can be estimated by solving the one-dimensional unsteady species conservation equation analytically. The macroscopic estimation and prediction method of mixedness is proposed as function of l _a and l _d . When l _a >l _d , the advective mixing is dominant, while, when l _a <l _d , the mixing due to molecular diffusion plays an important role.     

The measurement of mixing efficiency of continuous mixers

A radiotracer method for testing the mixing characteristics of industrial continuous mixers in actual process conditions is described. The tracer is fed into the input of the mixer at a constant rate and the radiation in the output is measured by two properly collimated radiation detectors. The measurement yields data in the form of two time series which contain information about the radial and axial homogeneity of the tracer in the measuring point. The formulas connecting the information in the measurement data and the axial and radial concentration variation of tracer are derived by the methods of statistical mathematics. The values for experimental parameters are obtained by computer simulation of the radiation measurement geometry.The method was tested by measuring the increase of the homogeneity as a function of mixing distance in a static tube chlorine mixer in a pulp bleaching plant. Also some results obtained on another type of mixers showing the effect of pulp type on mixing are given.     

Powder mixing in a horizontal batch mixer

The mixing process in a horizontal batch mixer with a twin spiral rotor has been investigated.A mixture of crushed wheat and sodium chloride was mixed in a model mixer. The concentration of sodium chloride in mixture samples was checked as a function of the mixing time and sampling place for various degrees of mixer filling. The sample composition was determined by conductometric determination of sodium chloride in water extracts of the sample. From the values obtained, the mixing degree was calculated as defined by the variation coefficient along the whole mixer, as a function of the mixing time.In analysing the data and empirical correlation between the concentration of component under study and the place and time of mixing, C/C? = f(x, t) was obtained and compared with industrial experiments using radionuclides as tracers.     

Solids mixing in a fluidized bed riser

The solids mixing in a riser with a height of 10 m and 0.186 m inner diameter was investigated by using pneumatic phosphor tracer technique. Considering the shielding effect of the bed material on the light emitted from the phosphor tracer particle, a modified method for the phosphor tracer measurement is proposed. And then the curves of particle residence time distribution were obtained. The experimental results show that the particle diffusion mechanism can be explained by the dispersions of dispersed particles and particle clusters in the axial direction, and as well the core-annulus nonuniform distribution of the solids fraction in the radial direction of the riser. Moreover, based on the experimental results, a two-dimensional dispersion model was established to predict the solids axial and radial diffusion. Furthermore, the effects of superficial gas velocity and solids circulating flux on the axial and radial Peclet number of the particles were discussed; two empirical correlation formulas about the axial and the radial Peclet numbers were given; the calculated values agree well with the experimental results.     

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.     

Characterization of the Mixing Quality in Micromixers

The laminar flow patterns and mixing performance of two different micromixers have been investigated and quantified using CFD. The micromixer geometries consist of a channel with either diagonal or asymmetric herringbone grooves on the channel floor. The numerical results show that a single helical flow is produced for the diagonal mixer, whereas the herringbone mixer creates a double helical flow, composed of an alternating large and small vortex. Particle tracking of a tracer shows that very little convective mixing occurs in the diagonal mixer. However, in the herringbone mixer, very good mixing occurs. Quantitative analysis methods that are traditionally used for characterizing macro‐scale static mixers have been employed. Calculation of the variance of tracer dispersion and the stretching has shown to be well adapted for quantifying the mixing in the micromixers. However, methods based on the deformation rate appear to be less suitable. The results are in excellent agreement with previous experimental findings.     

The effect of interparticle cohesion on powder mixing in a ribbon mixer

The effect of interparticle cohesion on powder mixing in a ribbon mixer was studied by means of the discrete element method. It is shown that with an increase in the cohesion, the mixing rate and uniformity of mixing deteriorate, the coordination number increases indicating the loss of the ability of particles to be engaged in free flowing motion, and a majority of particles have a stronger tangential velocity allowing bulk angular motion of particles. Conversely, with a decrease in the cohesion, more particles have larger axial velocities, which will increase convective motion in the axial direction. When the cohesion is reduced, the number of particles having large radial stresses increases, and normal stress in the axial direction remains mostly unchanged. The ribbon mixer can mix cohesive particles in a wide range of the Bond numbers without causing large stresses. © 2015 American Institute of Chemical Engineers AIChE J, 62: 1023–1037, 2016     

无序环流混合器的流体力学特性和颗粒混合特性

在内径为Φ286 mm的无序环流混合器装置中,研究了无序环流混合器的流体力学特性和颗粒混合特性。以催化裂化(FCC)平衡剂为颗粒相,在中心区表观气速为0.3~0.5 m/s,边壁区表观气速为0.1 m/s,系统循环强度为0.25~1.00 kg/s的操作条件下,采用PV-6D型颗粒速度密度测量仪测量了混合器内床层各截面密度,并给出不同操作条件下的截面不均匀指数(RNI);采用热颗粒示踪技术给出了混合器内各测量截面的无因次温度分布,并引入混合指数用来定量描述不同操作条件下的颗粒混合程度,同时对比了传统环流混合器与无序环流混合器的混合能力。结果表明,无序环流混合器内部床层密度呈现中心低,边壁高的分布模式。随着循环强度的增加,RNI先减小后增大,随着表观气速的增加,RNI增大。预混合区混合指数为0.7~0.9,在高循环量,低中心区表观气速条件下(G_s为1.00 kg/s,u_(gd)为0.3 m/s),下料管进料影响区的截面混合指数低于其他操作条件。另外,无序环流混合器混合能力优于传统环流混合器。     

Mixing of pharmaceutical solids. I. Effect of particle size on mixing in cylindrical shear and V-shaped tumbling mixers

The mixing of a cohesive drug with a cohesive, non-cohesive and free-flowing excipient was studied using two types of mixers, cylindrical shear and V-shaped tumbling. Two mixing indices, one based on complete random mixing, s/σ_R, and the other based on standard specifications, s/σ_A, were used to evaluate the data. Both indices gave similar results for mixing cohesive drug with a free-flowing or non-cohesive excipient and were suitable for evaluating homogeneity. However, for mixing a cohesive drug with a cohesive excipient, s/σ_R was not a suitable index, while s/σ_A could be used. The ‘mixing margin’, a concept proposed by Hersey [3], is not a very useful tool in assessing mix-ability of powders having too large or too small particle size distributions. Because of electrostatic charging, preferential sticking of the drug to the walls of the mixer resulted in a lower mean value of the drug in the mixture. Although the mixing indices suggested that the desired mixedness was reached, it is proposed that the mean percent of the active ingredient should be checked in addition to the mixing indices for ensuring the uniformity and potency of the drug content in solid state mixtures.     

Improving mixing performance by curved-blade static mixer

This article addresses design modification to a flat-blade static mixer to enhance mixing performance. The static mixer elements used in this work consist of four blades with curvature made to intensify turbulent-like flow, while reducing the pressure drop. The blades were mounted on a cylindrical housing with 45° rotation relative to the axial direction. The mixer assembly was used in three different arrangements of 8, 10, and 14 elements for a range of Reynolds number between 600 and 7,000. The coefficient of variance (COV) of samples was used to measure the mixing quality. The curved-blade mixer provides considerable improvement in mixing quality compared with the flat-blade mixer and comparable to the SMX mixer. Compared with the flat-blade static mixer, the new design reduces the COV by up to about 50%. This effect is more pronounced when the number of mixing elements increases. Furthermore, the friction factors for the modified mixer, obtained at a wide range of Reynolds number, were apparently smaller than those for the flat-blade, SMX, and SMV mixers. The correlation presented for the friction factor, when all mixer arrangements and aspect ratios were considered, supports the experimental data with ±15% deviation.     

Radial Gas Mixing in a Fluidized Bed with a Multi‐Horizontal Nozzle Distributor using Response Surface Methodology

The gas mixing in the radial direction within a fluidized bed equipped with a multi‐horizontal nozzle distributor was studied using response surface methodology (RSM), which enables the examination of parameters with a moderate number of experiments. All experiments were carried out in a circular fluidized bed of 0.29 m I.D. cold model fluidized bed. The distributor is placed beside twenty‐two horizontal nozzles that are arranged in three concentric circles with all existing discharge directed clockwise. The tracer gas (CO₂) was discharged into the bed as a tracer gas and the analysis was performed with a gas chromatograph. In order to compare the different internal circulations, the tracer gas was discharged in the center area or annular area of the bed. In RSM, the static bed height, superficial velocity and the open area ratio of the distributor are chosen as the research variables, and the standard deviation of the time averaged radial tracer concentration is used as the objection function. A mathematical model for the gas mixing as a function of the operating parameters was empirically proposed. The results show that the standard deviation of time averaged radial tracer concentration is well correlated with the operating and geometry parameters, (U – U_mf)/U_mf, H_s/D and ψ_d, and that the tracer gas injected to the center position has a better dispersion than when injected to the annular position. This model can be used for optimizing the design of fluidized bed reactors at a required performance level.     

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.     

Numerical characterisation of folding flow microchannel mixers

Micromixers have been considered in numerous recent studies with the aim of mixing different liquid streams for the common circumstance of non-inertial flow, i.e., in the Stokes flow regime. Under such conditions, the diffusion of momentum is dominant but the diffusion of species remains weak because the Schmidt number of liquids is large. Most mixers that have potential for application in the Stokes regime make use of a folding flow pattern that approximates the baker's transformation. In the work presented here, the general scaling of mixers of this type is developed from the exact equation for species transport and computations are made for a specimen mixer geometry to test the effectiveness of the resulting scaling. The scaling relation developed is found to give an excellent representation of the actual mixing characteristics of the specimen mixer over the entire range of Péclet number of practical interest. Finite volume computations are employed to solve the governing equations up to around Pe=10³. At higher Péclet numbers, where finite volume numerical solution becomes inaccurate with affordable mesh sizes, the species equation is solved using a Monte Carlo method instead. Finally, the scaling relation is used to develop the design relations needed to determine the number of mixing elements, the pressure drop incurred and the Péclet number of operation to achieve a given mixture uniformity within a specified mixing time.     

Development of mixing time correlation for a double jet mixer

BACKGROUND: Jet mixing is one of the simplest methods to achieve mixing. There have been a number of experimental studies concerned with jet mixing; some of these studies report empirical correlations. The existing correlations are not useful where there are significant deviations from the idealized conditions. Most correlations reported in the literature deal with liquid flow with single or multiple jets, whereas the effect of radial angle on mixing time was not studied. This present study investigates the effect of operating parameters on experimental mixing time in a double jet mixer. Nozzle configuration for jet1 was fixed based on earlier studies (2/3rd position, nozzle angle 45° and nozzle diameter 10 mm). Mixing times were estimated for different jet2 configurations of jet angle (30°, 45° and 60°), radial angles (60°, 120°, 180°), jet diameter (5 mm and 3 mm) and located at different tank heights (2/3rd and 1/3rd from the bottom of the tank). RESULTS: A mixing time correlation was developed in terms of all the parameters using dimensional analysis. The constants and powers of the parameters involved in the correlation developed were estimated using a least square method to calculate the straight line that best fitted the mixing time data obtained during the experiments. The effects of change in angle of inclination of jet2 (θ₂), radial angle of jet2 with respect to jet1 (Φ₂) and diameter of jet2 (d₂) on mixing time were analyzed and compared with the experimental mixing time. CONCLUSION: The correlation developed based on the dimensional analysis and least square method predicts the mixing time for a double jet mixing tank. Copyright © 2009 Society of Chemical Industry