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.     

Numerical investigation of blade shape in static mixing

The mixing performance of the KMX and SMX static mixers have been compared using 3D high-resolution computational fluid dynamics (CFD) simulations. Although these mixers have a similar design composed of layers of blades, their blade shape is different: curved for the KMX and flat for the SMX. The flow of a Newtonian fluid in steady laminar regime has been considered as the benchmark of the study. The simulation was first validated by assessing the pressure drop vs. the number of mixer elements and the results were found to be in good agreement with experimental data. To evaluate the mixing quality, cross-section stream function, extensional efficiency, mean shear rate, residence time, intensity of segregation, stretching, and Lyapunov exponent have been selected. Analysis of the flow pattern and mixing parameters shows differences between the mixers and it appears that the curved blade is more efficient than the flat blade design at the expense of a slightly higher pressure drop. In practice, the KMX mixer should provide a higher mixing rate at high viscosity ratio than the SMX mixer. © 2004 American Institute of Chemical Engineers AIChE J, 51: 44–58, 2005     

Pressure drop in a split‐and‐recombine caterpillar micromixer in case of newtonian and non‐newtonian fluids

Microreactors are very promising tools for the design of future chemical processes. For example, emulsions of very narrow size distribution are obtained at much lower energy consumption than the one spent with usual processes. Micromixers play thereby an eminent role. The goal of this study is to better understand the hydrodynamic properties of a split‐and‐recombine Caterpillar micromixer (CPMM) specially with regard to handling viscoelastic fluids, a topic hardly addressed so far in the context of micromixers in general, although industrial fluids like detergent, cosmetic, or food emulsions are non‐Newtonian. Friction factor was measured in a CPMM for both Newtonian and non‐Newtonian fluids. For Newtonian fluids, the friction factor in the laminar regime is f/2 = 24/Re. The laminar regime exists up to Reynolds numbers of 15. For shear‐thinning fluids like Carbopol 940 or viscoelastic fluids like Poly Acryl Amide (PAAm) aqueous solutions, the friction factor scales identically within statistical errors up to a generalized Reynolds number of 10 and 0.01, respectively. Above that limit, there is an excess pressure drop for the viscoelastic PAAm solution. This excess pressure drop multiplies the friction factor by more than a decade over a decade of Reynolds numbers. The origin of this excess pressure drop is the high elongational flow present in the Caterpillar static mixer applied to a highly viscoelastic fluid. This result can be extended to almost all static mixers, because their flows are generally highly elongational. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2679–2685, 2013     

Use of an areal distribution of mixing intensity to describe blending of non‐newtonian fluids in a kenics KM static mixer using PLIF

The performance of KM static mixers has been assessed for the blending of Newtonian and time‐independent non‐Newtonian fluids using planar laser induced fluorescence (PLIF). A stream of dye is injected at the mixer inlet and the distribution of dye at the mixer outlet is analyzed from images obtained across the pipe cross section. The effect of number of mixing elements, fluid rheology, and apparent viscosity ratio for two‐fluid blending have been investigated at constant mixture superficial velocity of 0.3 m s^?1. Aqueous solutions of glycerol and Carbopol 940 are used as the working fluids, the latter possessing Herschel–Bulkley rheology. The PLIF images have been analyzed to determine log variance and maximum striation thickness to represent the intensity and scale of segregation, respectively. Conflicting trends are revealed in the experiments, leading to the development of an areal‐based distribution of mixing intensity. For two‐fluid blending, the addition of a high viscosity stream into the lower viscosity main flow causes very poor mixing performance, with unmixed spots of this component observable in the PLIF image. © 2013 The Authors AIChE Journal published by Wiley Periodicals, Inc. on behalf of American Institute of Chemical Engineers AIChE J, 60: 332–342, 2014     

A SIMULATION OF A MOTIONLESS MIXER

Continuous laminar mixing in segmented twisted-tape motionless mixers is considered. A solution to the steady isothermal creeping flow of a Newtonian fluid in a twisted-tape mixer has been obtained via two-dimensional numerical procedures. The developed flow within a section of the mixer has been solved in a helical coordinate system by an iterative scheme. The resulting solution is rigorously correct in the absence of entrance and exit flows at the junction between sections. An algorithm is presented for the modelling of these junction flows via two-dimensional procedures. Simulated cross-sectional mixing patterns have been generated for comparison with experimental results

The performance of twisted-tape mixers is simulated for various designs, beginning with the particular geometry of the Kcnics Static Mixer, and for different operating conditions Results suggest that the rate of mixing as a function of the total twist per section is optimized with respect to pressure drop when sections contain 80 degrees of twist. The capability for rational improvement in other design and operating parameters is illustrated. The mechanisms of laminar mixing are discussed and quantified; of primary importance is the tendency for interfacial area to assume an orientation within each section which is favorable to mixing in subsequent sections.     

The effects of power characteristics on the heat transfer process in various types of motionless mixing devices

The main objective of this paper is to present the measurement results of the pressure drop and the heat transfer coefficient in the various types of static mixers. The experimental investigations are provided for the explanation of the influence of hydrodynamic conditions on the heat transfer enhancement for different static mixers. Based on the analysis of the experimental database and theoretical considerations, original formulas are proposed for the determination of the power consumption and the heat transfer in various types of motionless mixing devices. In this paper a new criterion is also defined which takes into consideration both the heat transfer process and hydrodynamic conditions. This criterion may be successfully applied to the selection of a static mixer for the heat transfer problems.     

Numerical analysis of mixing in block‐head mixing screws

The research reported here used 3D non‐Newtonian flow simulations to investigate the pumping and mixing capability of block‐head mixers. Block‐head mixers are distributive mixing screws that are widely used to homogenize the polymer melt and eliminate thermal gradients. The polymer‐processing industry employs a variety of block‐head mixers, with little consensus on design and distribution of screw flights and mixing blocks. This analysis addresses this issue based on a computational design study in which the influence of three geometrical parameters was examined: (1) the number of flights at a mixing block, (2) the number of blocks along the screw, and (3) the stagger angle between the blocks. To examine the flow behavior of the mixing screws, the pressure consumption and energy dissipation is evaluated. Distributive mixing is analyzed using residence time distribution functions, kinematic stretching parameters, and the scale of segregation. Dispersive mixing is assessed by means of the mixing index and the shear stress. The results of this design study increase the understanding of block‐head mixers and contribute to the design and optimization of such geometries. The findings can further be applied to mixing screws of similar geometry, including pin‐type and knob mixers. POLYM. ENG. SCI., 59:E88–E104, 2019. © 2018 The Authors. Polymer Engineering & Science published by Wiley Periodicals, Inc. on behalf of Society of Plastics Engineers.     

Characterization of mixing in an optimized designed T-T mixer with cylindrical elements

Passive micromixers are preferred over active mixers for many microfluidic applications due to their relative ease in integration into complex systems and operational flexibility. They also incur very low cost of manufacturing. However, the degree of mixing is comparatively low in passive mixers than active mixers due to the absence of disturbance in the flow by external forces and the inherent laminar nature of microchannel flows. Various designs of complex channel structures and three-dimensional geometries have been investigated in the past to obtain an efficient mixing in passive mixers. But the studies on mixing enhancement with simple planar geometries of passive mixers have been few and limited. The present work aims to investigate the possibility of mixing enhancement by employing simple planar type designs, such as T-mixer and T-T mixer with cylindrical elements placed in the mixing channel. The mixing performance has been evaluated in the Reynolds number range of 6 to 700. Numerical results have shown that T-T mixer with cylindrical elements performed significantly well and obtained very good mixing quality over basic T-mixer for the entire range of Reynolds number (6 to 700). The device has also shown better mixing as compared to basic T-T mixer and T-mixer with cylindrical elements. A larger pair of vortices formed in the stagnation area due to the presence of a cylindrical element in the junction. Cylindrical elements downstream caused significant enhancement in mixing due to splitting and recombining action. The size of the cylindrical element in the T-T mixer has been optimized to obtain better mixing performance of the device. Remarkable improvement in mixing quality by T-T mixer with cylindrical elements has been obtained at the expense of small rise in pressure drop as compared to other passive designs considered in this study. Therefore, the current design of T-T mixer with cylindrical elements can act as an effective and simple passive mixing device for various micromixing applications.     

Residence time distributions of power law fluids in motionless mixers

Motionless mixers, which are also known as static mixers, can often be modeled as open, circular tubes with parabolic velocity distributions except at a few isolated planes where radial mixing occurs via an instantaneous coordinate transformation. The extension of this idea to the processing of non-Newtonian fluids is straightforward. The parabolic velocity distribution is replaced by whatever fully developed velocity profile is appropriate for the fluid. Experimental confirmation is given for the flow of carboxymethylcellulose solutions through motionless mixers of the Kenics variety. A previous observation that four Kenics elements are equivalent to one plane of complete radial mixing holds for these power law fluids as well as for Newtonian fluids.     

Design and assessment of a novel static mixer

This paper examines the performance of a novel static mixer comprising a circular tube fitted with eight alternating equi‐spaced semicircular rigid insert (baffles) as the mixer elements. Experiments were carried out to obtain the coefficient of variance (CoV) for the mixing of two streams of water and brine for Reynolds number between 60 and 700. Decreasing the baffles clearance ratio significantly reduces the CoV but at a cost of an increase in the pressure drop across the static mixer. The presence of the mixing elements (baffles) promotes a non‐laminar, turbulent‐like flow which considerably enhances the mixing. The static mixer described here represents a cost effective, easy to manufacture, low maintenance, and flexible alternative to the more sophisticated static mixers currently in use.     

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.     

Comparative analysis of different static mixers performance by CFD technique: An innovative mixer

The flow and mixing behavior of two miscible liquids has been studied in an innovative static mixer by using CFD,with Reynolds numbers ranging from 20 to 160. The performance of the new mixer is compared with those of Kenics, SMX, and Komax static mixers. The pressure drop ratio(Z-factor), coefficient of variation(CoV), and extensional efficiency(α) features have been used to evaluate power consumption, distributive mixing, and dispersive mixing performances, respectively, in all mixers. The model is firstly validated based on experimental data measured for the pressure drop ratio and the coefficient of variation. CFD results are consistent with measured data and those obtained by available correlations in the literature. The new mixer shows a superior mixing performance compared to the other mixers.     

Power Requirement for Mixing Shear‐Thinning Fluids with a Planetary Mixer

The optimal control of processes dealing with non‐Newtonian liquids requires the knowledge and control of the power demand of the mixing equipment. In this context, an extension of the Metzner and Otto concept to planetary mixers is proposed to adapt this concept to planetary mixers. The theoretical part of this work defines modified expressions of Reynolds and power numbers. These definitions introduce a characteristic velocity u_ch that is used to define the parameter K_s. A planetary mixer is employed to experimentally ascertain this guideline. Power consumption measurements carried out by mixing shear‐thinning fluids permit to determine the K_s factor. This factor varies only slightly with the flow behavior index and may be regarded as a defined constant for this geometry. Finally, experiments with an additional shear‐thickening fluid confirm the validity of this approach.     

Gas Dispersion in Rheologically‐Evolving Model Fluids by Hybrid Dual Mixing Systems

Gas dispersion experiments (0.18 ≤ Fr ≤ 0.71, 0.02 ≤ F1 ≤ 0.09) were carried out using a hybrid dual mixing system, which included a helical ribbon impeller and either a Smith or a Rushton turbine. Newtonian and non‐Newtonian model fluids were used as rheologically‐evolving fluids to evaluate changes in gas dispersion performance. A motionless helical ribbon agitator was used as a baffle in low‐viscosity Newtonian fluids. Both Smith and Rushton turbines produced a vortex, which was eliminated by the motionless helical ribbon impeller. Gas dispersion in low‐viscosity fluids was enhanced when the helical ribbon agitator and turbine of the dual hybrid mixing system was kept at a rotational speed ratio of 10 (N_T/N_HR = 10), which allowed dispersion at a lower Fr than the turbine alone. For moderate‐viscosity Newtonian fluids, gas dispersion was achieved at Fr ≤ 0.71 and F1 ≤ 0.05. Flow properties of non‐Newtonian fluids played an important role in gas dispersion; transition from dispersing to flooding stages was observed for the fluids that were more shear‐thinning (n ≤ 0.38).     

PRESSURE DROP AND HOMOGENIZATION EFFICIENCY OF A MOTIONLESS MIXER

Pressure drop and homogenization efficiency of a motionless mixer of helical type have been studied experimentally. For evaluation of the drag coefficient the equation has been proposed which is valid within the range of Reynolds number from 10^?2 to 10⁴ The efficiency of the motionless mixer for mixing of two Newtonian liquids has been investigated by using a decolourization method. For the operating conditions studied in this work it appears that there is the worse performance of the mixer about the Reynolds number of 50. No influence of volume flow rate ratios (from 1 to 10) upon the performance of the mixer has been observed. A higher number of mixing elements must be applied for homogemzation of liquids with viscosity ratios above 100 as compared with that for viscosity ratio 1.     

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.     

Method of analyzing and quantifying the performance of mixing sections

In this article, the performance of three different mixing elements on color dispersion in high‐density polyethylene and linear low‐density polyethylene polymer stream during extrusion is studied. Two similarly designed Maddock mixers and a Stratablend II mixer are used as the last part of a general purpose single screw. Moreover, an inline melt camera is used for the quantification of mixing quality by visualization of grayscale of the color dispersion and thus mixing. The Stratablend II mixer produces the lowest and most uniform standard deviation. Both the Maddock mixers showed the same trend but higher values of standard deviation. All results are then compared with a full 3D finite element method simulation. Simulations clearly indicate that the Stratablend II mixer has the best mixing abilities and that these are mainly given by its unique design with high average value of shear stress. The role of elongational stress does not appear to have a high influence on mixing for these mixers. The results also suggest that the key factor for achieving better mixing is the frequency by which a large fraction of the material passes through the high shear stress regions of the mixer. POLYM. ENG. SCI., 2012. © 2012 Society of Plastics Engineers     

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.     

Measures of mixing in laminar flow

The general domain in which this work resides is that of mixing in creeping flows. Mixing, in this context, refers to the stretch of an interfacial line, or area in a strain field. The advancement of mixing technology is applied to the design of continuous mixers used in polymer processing. The geometric designs included single screw extruders, static motionless mixers, and co- and counter-rotating twin screw extruders. The co-rotating twin screw extruder was chosen to be studied in detail since it enjoys wide applications and, for which, little understanding of the contribution to mixing in the different screw geometries is known. In order to evaluate the rate of mixing for the non-uniform strain history flows, the method for measuring mixing had to be reexamined and broadened. An automated method has been developed which incorporates a digital camera and a computer to analyze the cross-sections of interest. Two measures of mixing—the correlation function and the distribution function—are developed to describe mixing in these regimes. These measures are applied successfully to the mixer geometries revealing subtle differences as to the nature of mixing in each.     

新型4∶1转子与传统剪切型转子混合效率对比研究

利用POLYFLOW软件分别对传统2:1剪切型转子和新型4:1剪切转子密炼机的速度场进行有限元模拟。通过将速度矢量对时间进行积分获得流场内大量材料质点的运动轨迹,对胶料的动态分布混合过程进行可视化分析。在获得大量粒子轨迹的基础上,利用POLYSTAT模块进行流场的统计分析,采用分离尺度、拉伸长度、瞬时效率、时间平均效率和混合指数对两种转子的混合效率进行评价分析。统计结果表明,新型4:1转子在保持传统转子强分散混合能力的基础上,分布混合能力大幅度提高。