Mixing and micromixing times in the forced vortex region of unbaffled mixing devices

Unbaffied mixing devices are characterized by a very particular hydrodynamics. A well defined depression in the liquid surface is formed, resulting from the combined vortex established in the liquid. The combined vortex is composed of one central Forced Vortex Region (FVR) and one annular free vortex region. Because the FVR behaves like a confined mixing zone, this region inside an unbaffled mixing device appears to be quite interesting to carry out certain chemical reactions. In this paper the influence of operating conditions on the mixing time of two reagent feed streams arriving continuously in the FVR of unbaffled mixing devices is investigated. Process parameters investigated are?: stirrer speed, reagent flow rates and feed pipe position. Mixing time correlations are established, which are useful for the scale‐up of this reactor.     

Assessment of gel formation in colloidal dispersions during mixing in turbulent jets

Onset of gel formation upon mixing between colloidal dispersions and coagulant solutions in turbulent jets was studied using a combination of computational fluid dynamics (CFD) and population balance equation (PBE). To describe the interaction between turbulence fluctuations and particle aggregation, a micromixing model based on presumed probability density function was implemented inside the CFD code. Furthermore, effect of the solid phase on the fluid flow was modeled through an effective viscosity of the mixture evaluated from PBE. The results are presented in the parameter space of the primary particle diameter and the solid volume fraction where strong interplay between mixing and aggregation mechanisms controls the gelation phenomena and consequently also the fluid dynamics. Simulation results are in good agreement with observations from gelation experiments of concentrated nanoparticle suspensions injected into coagulant solutions. © 2013 American Institute of Chemical Engineers AIChE J, 59: 4567–4581, 2013     

旋转填充床中微观混合模型与实验验证

根据旋转填充床中液体流动和混合特征,建立了一个新的复合式微观混合模型,并对串联竞争反应的标准体系进行了模拟和实验验证。结果表明,在旋转填充床内,当体积比α较小时（如α＝2）,微观混合影响很小,过程处于化学反应控制区;当α较大时（如α＝20）,过程处于微观混合作用区,提高转速使离集指数降低,流量增加对离集指数影响很小;考虑液体初始宏观分布不均匀对混合的影响,模型计算结果与实验结果吻合良好。     

Turbulence in stirred tanks: Anisotropic,approximate, and applied

Over the last ten years, many ways of characterizing the turbulence in stirred tanks have been proposed, and the importance of the local rate of dissipation of turbulent kinetic energy (?) to various processes has been clarified. In this paper, our understanding of the role of ? is examined for the blend time of miscible fluids, for drop break-up, for reactor design, for cell damage in bioreactors, for gas dispersion, for crystallization, and for flocculation and coagulation. The conceptual difficulties inherent in approximate measurements of ? are discussed with examples and background theory. Particular attention is paid to the various length and time scales present in the tank, the anisotropic nature of the flow field, and the effect of organized structures on turbulence measurements. Progress in the area over the last ten years is reviewed in the context of these limitations.     

Hydrodynamics and flow regimes in turbulent bed contactor with non‐Newtonian liquids

The flow regimes normally encountered in a turbulent bed contactor (TBC) are static, partially fluidised, completely fluidised and flooding regimes. Experiments were conducted in a TBC operating in Type I mode to identify the flow regimes with non‐Newtonian liquid. Flow regime transition velocities were obtained from the pressure drop and bed expansion measurements at various operating and geometric variables. The variables include apparent viscosity of the liquid, gas and liquid velocities, size and density of the particles, and static bed height. The effect of the above variables on delineation of flow regime transition was studied. Based on the experimental data, correlations were proposed for predicting the transition velocity from one regime to the other. The influence of the variables on regime transition velocities is more or less similar to that observed for Newtonian liquids. © 2011 Canadian Society for Chemical Engineering     

Flow patterns in a pilot plant-scale turbulent fluidized bed reactor: Concurrent application of tracers and fiber optic sensors

Hydrodynamics of a turbulent fluidized bed is studied by means of the concurrent application of fiber optic sensors and a helium tracer. It is observed that in the vicinity of the column wall there is a high bubble activity region. Low bubble activity and negative bubble velocities are reported for the dense phase near the column centre-line region. A temperature increase from 22 to 145°C results in a more homogeneous turbulent fluidized bed with smaller bubbles and more gas flowing through an expanded dense bed emulsion phase. Mass transfer coefficients between bubble-emulsion (k_be) and bubble-annulus (k_ba) are evaluated. The dominant mass transfer path was the one from the bubbles to the annular region with k_ba being several times greater than k_be.     

Lightnin内插件强化混合器内湍流混合及反应特性

采用计算流体力学组分输运模型和SST k-ω湍流模型,在Re=3000～9000范围内研究Lightnin静态混合器内萘酚(组分A)与对氨基苯磺酸(组分B)偶合氮化串联竞争反应,分析化学反应场中各组分浓度分布规律、湍流流动及微观混合特性。Lightnin内插件能够推进管内主反应的高效进行,副产物S较少且其浓度在0.0004～0.03 mol/L,而主产物R的浓度较副产物S高两个数量级。湍流强度随着雷诺数的增大呈现明显上升趋势,Re=3000时z/l=2处的湍流强度峰值(达到2.95)是出口处的2.02倍。湍流耗散率ε随径向位置的增加而减小,w_A=0.5～0.6时浓度对ε的影响微弱,而w_A=0.7～0.9时ε的轴向和径向分布随着浓度的增大逐渐减小,w_A=0.6～0.9时z/l=10处的ε相比于w_A=0.5时依次减小2.43%,8.86%,19.80%,42.25%。Re=6000～9000时径流数呈周期规律分布,偶数旋流元件内形成小峰值,奇数元件内则内凹。组分A与组分B在摩尔比一定的条件下,Re=40...     

Globally optimal synthesis of heat exchanger networks. Part III: Non-isothermal mixing in minimal and non-minimal networks

In this work, the enumeration algorithms presented in Parts I and II for the globally optimal synthesis of minimal and non-minimal heat exchanger networks are extended to consider non-isothermal mixing. New mathematical models, including non-isothermal mixing constraints, are proposed to target the bounds of energy consumption and the binding exchanger minimum approximation temperature. These models are solved using the algorithms, which involve solving systems of equations instead of mathematical programming. Three global optimization strategies are proposed to optimize each enumerated structure, involving the use of a global solver directly, or the use of a Golden Search based on energy consumption and a flowrate optimization model considering non-isothermal mixing. The flowrate optimization model is reformulated as a convex problem, which is solved by using nonlinear programming or a mathematical programming-free methodology, that is, solving Karush–Kuhn–Tucker equations. A new Global Optimum Search Algorithm is developed and examples are tested comparing different optimization strategies.     

The use of mixing-sensitive chemical reactions to study mixing in dispersed fibre systems: Adsorption of reactants and product dyes on the dispersed phase

Mixing-sensitive chemical reactions conducted under controlled conditions can be used to qualitatively and quantitatively assess mixing in aqueous systems. These reactions are typically competitive reactions where the distribution of products is used to quantify mixing. This technique is valuable for studying both mixing and local energy dissipation in dispersed systems where the opacity of the suspension prevents the use of other techniques. However, correct interpretation of the test results requires that adsorption of reactants and product dyes on the dispersed phase be known. The adsorption of the reactants and product dyes formed in the mixing-sensitive azo coupling between mixtures of 1- and 2- naphthol and diazotized sulfanilic acid was measured in aqueous suspensions of nylon, polyethylene, fibreglass and kraft pulp fibres. The polyethylene fibre did not adsorb the reactants or product dyes. The nylon, fibreglass and kraft fibres adsorbed both reactants and product dyes, with adsorption described by Langmuir isotherms. Accounting for the adsorption of dye on the dispersed phase allowed correct interpretation of mixing in the aqueous phase of the dispersions. This technique is evaluated for mixing assessment in suspensions of nylon fibre and fully bleached kraft (FBK) pulp in a medium-intensity mixer.     

Hydrodynamics in a jet bubbling reactor: Experimental research and mathematical modeling

The radial distribution of liquid velocity in the axial direction of a jet bubbling reactor has been measured by experimentation. Three different typical flow structures controlled by liquid jet, gas bubbling, and liquid jet coupled with bubbling are observed. A tank in series model is established on this basis. Calculated values in each region are in good agreement with measured values in jet, bubbling, and wall effect controlled areas. Axial flow rate, radial exchange rate, and jet controlled volume η are analyzed from energy input aspect under different u_g and u_j. Simulation results indicate that under the synergetic action of the liquid jet and gas bubbling effect, jet controlled area exhibits a “spindle” structure, and its size decreases with the increase of u_g. When gas input power occupies about 67% of total energy consumption, the best synergy of liquid jet and gas bubbling is obtained. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1814–1827, 2018     

Mixing study in an inductive plasma reactor: Comparison between model calculations and experimental results

This study compares the predictions of a multicomponent reactive model of inductive plasma reactor mixing and experimental data obtained with the enthalpy probe technique. Central injection of two different gases, helium and nitrogen, into the core of an inductive (h.f.) plasma discharge permits us to analyze the influence of the nature of the central gas on the reactor's mixing patterns. This work highlights diffusion in a multicomponent situation. The model considers the dissociation of H₂, present in the sheath gas.     

Demonstration of a minimum in the recovery of nanoparticles by flotation: Theory and experiment

The flotation of nano- and submicron particles does not follow the conventional collection theory based on the interception and collision mechanisms, which predicts extremely low collection efficiency for particles smaller than 10-μm. Brownian diffusion and colloidal forces strongly influence the collection of such particles by air bubbles in flotation. In this paper, a theoretical model is presented for predicting the collection efficiency of nanoparticles. The theory incorporates mass transfer by Brownian diffusion, microhydrodynamics of particles in the vicinity of a slip surface of rising air bubbles, and colloidal interactions that come into effect at small separation distances. The governing equation was solved numerically using the Crank-Nicolson method with variable step size. A finite difference scheme with mesh refinement in the vicinity of the air bubble surface was used to discretise the stiff partial differential equation for the particle concentration. The mesh refinement produced correct numerical solutions without oscillation in the particle concentration distribution, which otherwise occurred due to the stiffness of the differential equation and coarseness of the numerical mesh. Predictions from the model were compared with experimental results obtained with a small laboratory column cell, in which colloidal silica particles with diameters in the range were floated using fine bubbles of typical average diameter . The particle concentration in the pulp was about 1% by weight. Cetyltrimethyl ammonium bromide and Dowfroth 250 were used as the flotation collector and frother, respectively. Both the theory and experiment show significant effect of the electrical double-layer and non-DLVO hydrophobic attractive forces on the collection of nanoparticles by air bubbles. The theoretical and experimental results show the collection efficiency to have a minimum at a particle size in the order of . With larger particles, the interception and collision mechanisms predominate, while the diffusion and colloidal forces control the collection of particles with a size smaller than the transition size.     

Temperature Profile Analysis in Combustion Synthesis: I, Theory and Background

An analysis of the use of temperature profiles in the determination of the kinetic parameters of self-sustaining combustion synthesis is provided. Two mathematical approaches are discussed. In the first approach, the analysis focuses on the initial portion of the temperature profile and thus emphasizes the kinetics of the initial stages ( η ≲ 1.0) of this process. The second approach emphasizes both the initial and final stages of the process ( η ∼ 1.0). With the simultaneous measurements of the velocity of the combustion wave, temperature profile analysis provides values for the effective thermal diffusivity of the reactants.     

Flow-rate effects in flow-reversal reactors: experiments, simulations and approximations

Design and operation of a reactor with flow reversal requires accurate prediction of the domain of operating conditions, and especially the range of flow rates, where the ignited state exist. In this work we compare experimental observations of flow-rate effects during ethylene oxidation on Pt/Al₂O₃, with simulations of this reactor using a kinetic rate expression that was derived elsewhere and with approximate solutions based on instantaneous or very fast reactions. The oxidation of ethylene on supported Pt catalyst, that is employed here as a model reaction, is a complex reaction characterized by self-inhibition (expressed by Langmuir-Hinshelwood kinetics), by strong activation energy and by strong thermal effects that lead to a wide domain of steady-state multiplicity. The analysis of a flow- reversal reactor for such reactions can be approximated using the assumption of an instantaneous or fast reaction as the feed meets the catalyst layer. We suggest several approximations that capitalize on this property and apply them to the structure of our reactor, in which the catalytic bed is imbedded between two inert zones.Adequate agreement between the experimental results and simulations, using homogeneous or heterogeneous reactor model with no adjustable parameters, is demonstrated. The difference between the homogeneous and heterogeneous model predictions is usually small. The approximations show that the most important parameters for predicting the highest temperature are the inert zone properties (conductivity and length).     

Flow and temperature patterns in an inductively coupled plasma reactor: Experimental measurements and CFD simulations

Measurements of temperature patterns in an inductively coupled plasma (ICP) have been carried out experimentally. Plasma torch was operated at different RF powers in the range of 3–14 kW at near atmospheric pressure and over a wide range of sheath gas flow rate (3–25 lpm). Measurements were made at five different axial positions in ICP torch. The chordal intensities were converted into a radial intensity profile by Abel Inversion technique. Typical radial temperature profile shows an off‐axis temperature peak, which shifts toward the wall as the power increases. Temperatures in the range of 6000–14,000 K were recorded by this method. The temperature profiles in the plasma reactor were simulated using computational fluid dynamics (CFD). A good agreement was found between the CFD predictions of the flow and temperature pattern with those published in the literature as well as the temperature profiles measured in the present work. © 2014 American Institute of Chemical Engineers AIChE J, 60: 3647–3664, 2014     

Aqueous two‐phase micellar systems in an oscillatory flow micro‐reactor: study of perspectives and experimental performance

BACKGROUND: Aqueous two‐phase micellar systems (ATPMS) are micellar surfactant solutions with physical properties that make them very efficient for the extraction/concentration of biological products. In this work the main proposal that has been discussed is the possible applicability and importance of a novel oscillatory flow micro‐reactor (micro‐OFR) envisaged for parallel screening and/or development of industrial bioprocesses in ATPMS. Based on the technology of oscillatory flow mixing (OFM), this batch or continuous micro‐reactor has been presented as a new small‐scale alternative for biological or physical‐chemical applications. RESULTS: ATPMS experiments were carried out in different OFM conditions (times, temperatures, oscillation frequencies and amplitudes) for the extraction of glucose‐6‐phosphate dehydrogenase (G6PD) in Triton X‐114/buffer with Cibacron Blue as affinity ligand. CONCLUSION: The results suggest the potential use of OFR, considering this process a promising and new alternative for the purification or pre‐concentration of bioproducts. Despite the applied homogenization and extraction conditions have presented no improvements in the partitioning selectivity of the target enzyme, when at rest temperature they have influenced the partitioning behavior in Triton X‐114 ATPMS. Copyright © 2011 Society of Chemical Industry