Numerical simulations of partially‐filled rubber mixing in a 2‐wing rotor‐equipped chamber

Partially filled internal batch mixers are used for mixing of rubber compounds in the polymer industry. The use of mixing in such mixers equipped with a rotor is critical to the process itself, and hence, understanding of mixing is important in terms of evaluating how various operating parameters such as rpm, fill factor, and ram pressure affect distribution and dispersion of materials. The objective of the current study is to gain valuable insights on the influence of fill factor, which is the volume of the material relative to the volume of the chamber. Two‐dimensional (2D) computational fluid dynamics (CFD) simulations of rubber mixing in a 2‐wing rotor‐equipped chamber are presented here, for the first time, for fully‐filled/100% and partially‐filled/75% chambers. The volume‐of‐fluid (VOF) technique is employed to capture the interface between the rubber and air in partially filled isothermal simulations. Flow patterns are visualized to analyze the material movement. Massless particles are injected and various statistics are calculated from their positions in order to compare dispersive and distributive mixing characteristics between the fully‐filled and partially‐filled cases. Specifically, quantities such as mixing index and the maximum shear stress distribution history of particles are analyzed to obtain information about dispersive mixing, while length of stretch and cluster distribution index, also calculated from particles, are presented to investigate distributive mixing capabilities. All the results consistently demonstrated the superior effectiveness of partially‐filled mixing chambers in terms of their dispersive and distributive mixing characteristics in comparison to fully‐filled chambers. © 2016 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2017 , 134, 44250.     

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.     

An elastic analog model for controlling the impingement point position in confined impinging jets

Confined impinging jets (CIJs) are highly efficient mixers. The scales of mixing in CIJs are controlled by the opposed jets interaction. A mechanistic model is described here, which accurately predicts the impinging position of the opposed jets for a large range of flow rate ratios. The impinging point position is shown to impact the dynamic properties of the flow and the achieved mixing quality. The opposed jets kinetic energy ratio is shown to have a critical impact on mixing, similar to the Reynolds number. A mixing chamber design relation is proposed and verified for the opposed injectors diameters ratio, , which enables to operate CIJs under optimum mixing conditions for large ranges of flow rate ratios, viscosity and density ratios between the opposed streams. Optimum values have asymptotes for large and small Reynolds number depending on the process stoichiometry, viscosity, and density ratios of the opposed jet streams. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2200–2212, 2016     

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.     

T型撞击流混合器内流动特性的PIV研究

采用粒子图像测速技术对入射管直径为3 mm、混合腔直径为16 mm的T型撞击流混合器内的流动特性进行了研究,考察了不同流速比和撞击轴线上方空间条件下混合腔内的速度和湍流动能分布. 结果表明,在相同入射管直径和流速下,撞击驻点位于混合腔中心处,无因次化的速度和湍流动能分布趋势基本一致. 高湍流动能区主要集中在撞击点附近区域,其无因次化数值是传统Rushton涡轮搅拌槽叶端处的3倍. 流速比对撞击驻点位置影响显著;减小撞击轴线上方空间可增加高湍流动能分布区域,利于物料混合.     

Countercurrent Droplet‐flow‐based mini extraction with pulsed feeding and without moving parts

A countercurrent arrangement of immiscible liquid‐liquid mini contactors based on droplets is described in this article. Mini mixers without any moving parts were used as the contactors. The single stage mini mixer consists of a top and bottom mixing chamber. Both of the mixing chambers have two recirculating channels on either side. In these mini mixers, a liquid was broken up into droplets that dispersed into other continuously flowing liquid, consequently achieving a mass transfer between the two liquids. To realize the countercurrent arrangement, the two liquids were alternately fed into the system from opposite ends by compressed air according to a periodic program. One period consists of the following stages: organic phase feeding stage, droplet aggregation stage I, aqueous phase feeding stage, and droplet aggregation stage II. This continuous countercurrent arrangement is without the defects of continuous countercurrent arrangements based on laminar flows and multiple‐stage countercurrent arrangements based on droplets. © 2016 American Institute of Chemical Engineers AIChE J, 62: 3685–3698, 2016     

Mixing Agglomeration in a High‐Shear Mixer with a Stirred Mixing Vessel

This paper deals with the agglomeration process in a high‐shear mixer. High‐shear mixers rotate with a very high mixing tool speed such that not only a mixing effect, but also a grinding effect is achieved. The parameter study reported here was carried out to determine the parameters influencing mixing agglomeration. The results will help the user to decide which parameters have to be considered for an optimum mixing agglomeration. This article will highlight some of the findings obtained from the comprehensive parameter study.     

The Mixing Efficiency of an Eccentric‐Disc Kneading Zone in Intermeshing Co‐ and Counter‐Rotating Twin‐Screw Extruders

The distributive mixing efficiency of a twin‐screw extruder kneading zone consisting of eccentric disc elements was measured using an online video technique. Both co‐ and counter‐rotation were examined. Viscous Newtonian silicone oil was used as model liquid and black iron oxide pigment served as tracer substance. Under isoviscous, creeping flow and non‐diffusive conditions and for a fixed flow rate ratio of the colored and uncolored feed streams, the intensity of segregation S is only a function of the kinematic parameter Λ (the ratio of the imposed extruder throughput and the throughput at zero axial pressure gradient). The measured dependency of S on Λ is in qualitative agreement with the results of Pawlowski for a single screw extruder. The data was also plotted against the dimensionless speed of rotation, i.e. the product of the screw speed and the average residence time within the mixing section. This brings the abscissa ranges for mixers with different conveying capacity closer together, and differences in mixing efficiency between the tested configurations can be better interpreted. The energetic efficiency of the mixers investigated is compared by applying the concept of specific action. This helps to decide which mixer geometry and operating conditions produce a given homogeneity with the lowest amount of work done by viscous forces.     

Eignung von kontinuierlich durchströmten Mischern zum Homogenisieren

Suitability of continuous flow mixers for homogenization. The homogenizing characteristics, calculation of power consumption, and the scope of continuous flow mixers are reported. An attempt is made to summarize the present state of knowledge in this area. Some experimental results are presented which have been obtained in the homogenization of gases or liquids in pipes and containers in which mixing was achieved by jets, built in flow-directing fittings, stirrers or a combination of these. The investigations extend from the laminar to the turbulent range of flow. A comparison of energy requirements for the various apparatus affords important data for the choice and design of continuous flow mixers.     

Depletion of cross‐stream diffusion in the presence of viscoelasticity

An effort to analyze the viscoelasticity effects on transverse transport of neutral solutes between two miscible streams in an electrokinetic T‐sensor is presented. The analysis is based on an approximate analytical solution for the depthwise averaged concentration, assuming a channel of large width to depth ratio for which a one‐dimensional profile is sufficient for describing the velocity field. We show that the solution derived is surprisingly accurate even for very small channel aspect ratios and the maximum error reduces to only about 1% when the aspect ratio is 5. The developed model reveals that the mixing length for a viscoelastic fluid may be by far larger than that for a Newtonian fluid. Moreover, the Taylor dispersion coefficient for electroosmotic flow of viscoelastic fluids, which its determination is a main part of the analysis, is found to be an increasing function of both the elasticity level and the EDL thickness. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4533–4541, 2015     

Numerical Investigation of Flow Patterns and Concentration Profiles in Y‐Mixers

The fluid flow patterns and associated concentration fields in Y‐mixers are investigated using lattice Boltzmann method‐based models. The focus lies on the impact of the mixing angle on the flow and concentration fields, with the mixing angle varying between acute (θ = 10°) and obtuse (θ = 130°) angles. Residence time distributions are determined to study the effect of the angles on the mixing and velocity patterns, in particular, different flow regimes, i.e., stratified laminar, vortex, and engulfment flow. The results from the simulations are validated with literature data and found to be in good agreement. Maximum mixing occurs in the 100° obtuse‐angle Y‐mixer, attributed to the extensive engulfment of flows in the mixing channel.     

Morphological study of two‐phase polymer blends during compounding in a novel compounder on the basis of elongational flows

A new laboratory‐scale mixing device based on an original concept was built and tested. This device has important technical features such as tightness to liquids and gases, the possibility of direct specimen molding after mixing, and easy handling of reactive systems. In comparison with existing laboratory mixers, the flow in this mixer is characterized by a high contribution from elongational flow. Morphological data on model polystyrene/poly(methyl methacrylate) blend systems have proved the high distributive and dispersive mixing efficiency in comparison with a classical rotational batch mixer. The influence of different experimental parameters such as the flow rate, mixing time, mixing element geometry, and viscosity ratio of blends is characterized and discussed. Much finer dispersions have been obtained with this new device versus those obtained with a conventional mixer with equivalent specific energy input. © 2010 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Mixing performance comparison of milliscale continuous high‐shear mixers

Mixing performance of two continuous flow millilitre‐scale reactors (volumes 9.5 mL and 2.5 mL) equipped with rotor‐stator mixers was studied. Cumulative residence time distributions (RTD) were determined experimentally using a step response method. Distributions were measured for both reactors by varying impeller speed and feed flow rate. The mixing effect was determined by measured RTDs. Computational fluid dynamics (CFD) were used to verify that the residence time distribution in the measurement outlet agreed with the outlet flow. The mixing power of both reactors was determined using a calorimetric method. The reactor inlet flow rate was found to affect mixing performance at 1–13 s residence times but the effect of impeller speed could not be noted. Both milliscale reactors are close to an ideal continuous stirred‐tank reactor (CSTR) at the studied impeller speed and flow rate ranges. The specific interfacial area was found to depend on the reactor inlet flow rate at constant impeller speed for the case of copper solvent extraction.

     

Enhancing liquid micromixing using low‐frequency rotating nanoparticles

Magnetic nanofluid actuation by rotating magnetic fields was proposed as a high‐performance tool for liquid mixing with enhanced micromixing features. A comparative study was conducted to evaluate the mixing index in T‐type mixers of magnetic and nonmagnetic fluids subject to static (SMF), oscillating (OMF), and rotating (RMF) magnetic fields. RMF excitation unveiled superior mixing indices with strong dependences to magnetic field frequency and content of magnetic nanoparticles. The impact of magnetic field types on micromixing was further examined at low and moderate Re numbers using the Villermaux–Dushman reaction and IEM micromixing model. The IEM‐inferred micromixing times were remarkably shorter by nearly four orders of magnitude in comparison with OMF and SMF excitations, and without magnetic field. The proposed mixing strategy is foreseen to complement innovative microfluidic devices with valuable mixing tools and methods for the diagnosis of the coupling between transport and intrinsic kinetics. © 2016 American Institute of Chemical Engineers AIChE J, 63: 337–346, 2017     

A particle‐scale index in the quantification of mixing of particles

Discrete element method (DEM) is a useful tool for obtaining details of mixing processes at a particle scale. It has been shown to satisfactorily describe the flow structure developed in bladed mixers. Here, the advantage is taken of the microstructure gained from DEM to evaluate how best to quantify the microstructure created by mixing. A particle‐scale mixing index (PSMI) is defined based on coordination numbers to represent the structure of a particle mixture. The mixture quality is then analyzed qualitatively and quantitatively in three different ways: a macroscopic mixing index based on the conventional approach, coordination number, and PSMI. Their effectiveness is examined based on DEM data generated for different particle loading arrangements and binary mixtures of particles with various volume fractions, size ratios, and density ratios. Unlike the two other methods, PSMI reveals in a straightforward manner whether a binary mixture of different particles is mixing or segregating over time, while being able to detect particle‐scale structural changes accompanying the mixing or segregation processes in all the mixtures investigated. Moreover, PSMI is promising in that it is not influenced by the size and number of samples, which afflict conventional mixing indexes. © 2011 American Institute of Chemical Engineers AIChE J, 2012     

CFD Investigation of the Mixing of Yield‐Pseudoplastic Fluids with Anchor Impellers

The study was carried out to simulate the 3D flow domain in the mixing of pseudoplastic fluids possessing yield stress with anchor impellers, using a computational fluid dynamics (CFD) package. The multiple reference frames (MRF) technique was employed to model the rotation of the impellers. The rheology of the fluid was approximated using the Herschel–Bulkley model. To validate the model, the CFD results for the power consumption were compared to the experimental data. After the flow fields were calculated, the simulations for tracer homogenization were performed to simulate the mixing time. The effects of impeller speed, fluid rheology, and impeller geometry on power consumption, mixing time, and flow pattern were explored. The optimum values of c/D (impeller clearance to tank diameter) and w/D (impeller blade width to tank diameter) ratios were determined on the basis of minimum mixing time.     

射流混合设备内混合时间的研究进展

介绍了有关射流混合设备内混合时间的实验研究进展,概述了计算流体力学（CFD）技术在射流混合设备内流场结构演化和混合效率评价中的应用,总结了不同研究者提出的混合时间关联式。分析影响射流混合效率的参数发现：混合时间随着混合槽直径的增加而增加,并与混合槽的高度呈正比;射流速度的增加可有效地降低混合时间;射流喷嘴的最佳直径与形状由混合槽的具体结构决定,但其最佳位置取决于混合槽高度与直径的比值;多股对置射流明显地提高混合效率。最后指出将CFD方法与压力波动信号（PFS）、PIV和PLIF等实验方法相结合可有效地推进射流强化混合机理研究和新型射流混合反应器的开发进程。     

The design and performance of a vane mixer based on extensional flow for polymer blends

A new laboratory‐scale mixing device called the “Vane Mixer” was designed, built, and tested. The vane mixer consists of three vane plasticizing and conveying unit. In comparison with the existing laboratory mixers, material flow in this vane mixer is characterized by a high contribution from extensional flow. As the mixer has mixing chamber of very simple geometry, the cleaning is very easy and the material lost is very small. The influences of mixing time and rotor speed on dispersed phase size were characterized and discussed. Morphology data on model immiscible polystyrene/high density polyethylene (PS/HDPE) blend have proved the high distributive and dispersive mixing efficiency. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015 , 132, 41551.     

Analysis of a Two‐Layer Nozzle‐and‐Diffuser Electroosmotic Micromixer

An electroosmotic micromixer with two‐layer microchannels of a nozzle‐and‐diffuser structure was proposed. Numerical analysis of the flow and mixing was performed using the three‐dimensional Poisson‐Boltzmann and Navier‐Stokes equations with a diffusion‐convection model for the species concentration. A parametric analysis of the microchannels was performed using three geometric parameters, i.e., length of the nozzle section, length of the diffusion section, and width of the nozzle end, to investigate the impact of each parameter on the mixing performance, which was quantified by a quantitative measure based on the mass variance. The numerical results were used to improve the design of the proposed micromixer, leading to a far better mixing performance with a much shorter channel length compared to an existing electroosmotic micromixer.