The droplet diffusion model for micromixing

The concept of segregation number leads to a simple but plausible model of micromixing. Initially, bulk mixing of fluid occurs from hydrodynamic mechanisms and it is this type of mixing that determines the residence time distribution. Co-mingling of material on a molecular scale requires diffusion, and the droplet model provides a convenient representation of such micromixing. The model can be used to relate the degree of segregation to a single, physically meaningful parameter. The model is easily applied to the prediction of reaction yields including complex kinetic schemes where diffusivities and hence levels of micromixing vary between the different molecular species.     

AN EVALUATION OF MODELS OF MIXING AND CHEMICAL REACTION WITH A TURBULENCE ANALOGY

Five mechanistic models of mixing and chemical reaction having an analogy with isotropic turbulent mixing are evaluated. The turbulence analogies, based on matching variance decay laws of models and turbulence theory, provide a physical basis for the models and a means of estimating their micromixing parameters apriori. Experimental data for single second order liquid phase reactions provide strong support for the analogies. However, it is demonstrated that in spite of their success for single reactions, the models may predict grossly different selectivities in the case of competing reactions in a plug flow reactor. This emphasizes the importance of certain structural features of the models which are independent of the existence of a turbulence analogy, such as: (i) reacting regions which are rich in each of the reactants of a two feedstream reactor, and (ii) unmixed regions in the reaction mixture. The importance of obtaining data for competing reactions in a highly segregated plug flow reactor for the purpose of model discrimination is made apparent.     

NETmix®, a new type of static mixer: Modeling,simulation, macromixing,and micromixing characterization

NETmix® is a new technology for static mixing based on a network of chambers connected by channels. The NETmix® model is the basis of a flow simulator coupled with chemical reaction used to characterize macro and micromixing in structured porous media. The chambers are modeled as perfectly mixing zones and the channels as plug flow perfect segregation zones. A segregation parameter is introduced as the ratio between the channels volume and the whole network volume. Different kinetics and reactants injection schemes can be implemented. Results show that the number of rows in the flow direction and the segregation parameter control both macro and micromixing, but the degree of micromixing is also controlled by the reactants injection scheme. The NETmix® model enables the systematic study of micromixing and macromixing for different network structures and reaction schemes, enabling the design of network structures to ensure the desired yield and selectivity. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Non-isothermal micromixing in turbulent liquids: Theory and experiment

Partial segregation of reagents occurs when reaction rates exceed mixing rates and frequently causes product distributions to be mixing-dependent. A simultaneous temperature segregation, whereby the temperature in a reaction zone differs from that in its surroundings, has rarely been considered when mixing reagents in the liquid phase. The Prandtl number is usually sufficiently small that engulfment, not thermal conduction, determines the local temperature. The engulfment model of micromixing can then be extended by a heat balance to specify this temperature. To evaluate this model, a new pair of fast competitive reactions (neutralisation and acetal hydrolysis) has been characterised thermochemically and kinetically. A Mettler RC1 calorimeter was operated under isothermal and adiabatic conditions with various stirrer speeds and HCl was slowly added to a mixture of NaOH and 2,2-dimethoxypropane. Measured hydrolysis yields compared quite well with the extended engulfment model, although temperature segregation was of minor importance. It was also unimportant in other reaction systems (simultaneous neutralisation and ester hydrolysis; diazo coupling) employed earlier to study micromixing. Suggestions for further work are made.     

Interaction between micro- and macro-mixing during reactions in agitated tanks

The present investigation focusses on the interactions between micro-and macro-mixing in a stirred tank reactor, operated in the semi-batch mode. With long feed times only micromixing controls reaction, but below a critical feed time macroscopic gradients also become important. Experiments generated a coherent data set which can be used as a design guide and also for model validation. A competitive, consecutive azocoupling reaction was carried out, whereby imperfect mixing produces finite values of X_S (yield of secondary product) which can be conveniently used as a mixing index. The influences of feed location, feed rate, stirrer speed, concentrations and vessel size on selectivity were studied. The micromixing model of Baldyga and Bourne (1989) was extended to include interactions between macro-and micro-mixing and should be valid for feed times below the critical value, although not so short as the macromixing time in the vessel. Model predictions were compared with the experimental results.     

Mixing and fast chemical reaction—IX: Comparison between models and experiments

Theoretical considerations given in earlier parts indicate that mixing on the molecular scale (micromixing) takes place by molecular diffusion into small, turbulence-free fluid elements, which are being gradually distorted by uniform shear. This mechanism, when applied to fast, consecutive, competitive chemical reactions, predicts that the product composition will be a function of the variables given in eqn (3). A pair of diazo coupling reactions has been employed to test these predictions. The additional experimental results contained in this part refer to three impeller types (Rushto turbine, marine propeller and axial flow turbine), nine feed locations and three volumetric feed ratios. Semi-batch operation was modelled by extending the earlier batch reactor model and also used experimentally. Taking reasonable estimates of the model parameters from the fluid mechanics literature, satisfactory predictions of the experimental results were obtained.     

Mixing and fast chemical reaction—VI: Extension of the reaction zone

Work reported earlier[1, 3] as well as here indicates that mixing at the molecular scale (micromixing) takes place by molecular diffusion in fluid elements, which are simultaneously undergoing laminar deformations. Whereas simple shear was considered before, the present analysis describes diffusion and reaction in regions deformed by extensional flow. After outlining various simple types of extension, results in the literature[4,7] are quoted, which were obtained from observations on the diffusion of heat spots in turbulent air. These indicated stretching motions in two directions with a corresponding shrinkage in the third. Direct application of these findings to diffusion in the direction of shrinkage leads to predictions of th product distribution from competitive, consecutive reactions. Without fitting any parameters, these predictions agree quite well with the distributions of two dyestuffs produced by two diazo coupling reactions. Insufficient fluid mechanical information is available to enablea more accurate comparison; matters requiring further study are listed.     

Mixing effects in the bromination of resorcin

The product distribution from the bromination of resorcin (m-dihydroxybenzene) is influenced by mixing in an experimentally convenient range of concentration and mixing intensity at room temperature. The degree of bromination is insensitive to mixing, a fact which can be explained chemically. Similarly explicable is the high sensitivity of the composition of the isomeric dibromoresorcins; the % 2,4-dibromoresorcin formed has been used to characterise mixing in semi-continuous and continuous stirred tank reactor operation. In the latter case the influences of the concentration and flow rate of the feed, turbine speed and feed positions near the turbine were investigated. Although full reaction kinetics are not available, these reactions are fast and sensitive enough to study micromixing.     

Characterisation and comparison of the micromixing efficiency in torus and batch stirred reactors

The mixing at a molecular scale (micromixing) plays an important role on selectivity, yield and quality of final products of a large range of competing fast chemical reactions. In this study, we have compared, by the use of iodide–iodate reaction tests, the micromixing in two reactors, the first one is the standard batch stirred reactor and the second is the torus reactor. Various conditions of agitation and feed locations were used for this study. A comparative analysis of the micromixedness ratio (α) in the two reactors was carried out on the basis of the local rate of specific energy dissipation.     

Mesomixing scale controlling and its effect on micromixing performance

To direct highly efficient microdevice design, the mixing performance of different mixing methods was investigated. Three different microstructured mixers representing three kinds of mixing methods were utilized in this work. The mesomixing scale was adjusted through different ways in these mixers and the micromixing performance was characterized by a parallel competing reaction. A dimensionless parameter of mesomixing scale with different forms in these mixers was defined by considering contacting surface and mixing volume, and its relation with the segregation index which characterized the micromixing performance was investigated. All results indicate the enhancement of the micromixing performance with the decrease of the mesomixing scale. The mixing potential of different mixing method was discussed and it shows that the droplet cross-flow mixing method has the highest mixing potential. A linear relationship between the dimensionless parameter of mesomixing scale and the segregation index has been obtained. The results could provide much better understanding of how mesomixing scales affect the micromixing performance, which are very helpful for designing new micromixing devices and optimizing the geometric structures and operation conditions.     

旋转填充床内微观混合的数值模拟

旋转填充床作为新型的高效反应传质设备,广泛应用于快速反应过程,如制备纳米粉体材料.对旋转填充床内微观混合进行研究,有助于进一步认识旋转填充床内高度分散液体微元在填料丝网中的流动行为和分散混合机制,为旋转填充床内液液反应混合制备纳米材料提供理论基础.基于公开文献报道的实验观测结果,通过合理假设,建立了旋转填充床内微元流动的物理模型.在该物理模型的基础上,结合此前提出的湍流混合与反应模型,模拟计算了液体微元经过实验条件下50层丝网填料最终流出填料空间的浓度分布.由浓度分布得到的微观混合特征指数与实验值进行了对比,吻合良好.     

Mixing and fast chemical reaction—VII Deforming reaction zone model for the CSTR

Earlier work on batch reactors indicated that the final stage of homogenisation to the molecular scale (micromixing) occurs by molecular diffusion in deforming fluid elements. The product distribution of, for example, consecutive, competitive reactions is sensitive to concentration gradients at the molecular scale (segregation). Such reactions may be used as reactive tracers to throw light on the behaviour of small fluid elements. Moreover an understanding of micromixing allows the selectivity of fast, multiple reactions to be better controlled. This paper describes two ways of applying the unsteady-state equations for diffusion and reaction within a shrinking fluid element to determine the steady-state concentrations in a CSTR. The iterative model is more economical in computer time than the dynamic model and applies to fast reactions (i.e. when the time for diffusion and reaction is a small fraction of the mean residence time). It described well the measured effects on the product distribution of varying the volumetric feed rati the stoichiometric ratio and of changing the operating mode from semicontinuous to continuous. When the initial size of the deformable fluid element is identified with the Kolmogoroff microscale and a reasonable estimate of shear rate is introduced, a highly satisfactory prediction of experimental resu knowing the kinematic viscosity and the power consumption of the stirrer, becomes possible.     

Micromixing effects on complex reactions in a CSTR

Micromixing effects on consecutive-competing second order reactions in an ideally macromixed CSTR are investigated by the use of the Two Environment Model of Ng and Rippin for mixed feed, and the model of Spielman and Levenspiel for unmixed feed.General plots are obtained for various values of reaction and mixing parameters. Yield of the desired product is found to show a maximum at intermediate states of micromixing for unmixed feed conditions. For mixed feed condition, micromixing effects are found to be very small.     

MICROMIXING EFFECTS ON BARIUM SULFATE PRECIPITATION IN AN MSMPR REACTOR

The Effects of non-ideal and nonhomogeneous mixing on barium sulfate precipitation in an MSMPR reactor were observed experimentally and analyzed theoretically. To generate nonhomogeneous mixing the unmixed feed streams were fed to the reactor at the same location (joint feeding mode) or a plug flow reactor was connected to the MSMPR reactor. These nonhomogeneous mixing conditions resulted in significant reductions in particle size and increases in particle numbers. These non ideal mixing effects were dependent on the impeller speed, feed stream velocity and residence time in the connected plug flow reactor and are believed to result from elevated supersaturation levels in a premixing zone which are controlled by turbulent micromixing

To model the effect of nonhomogeneous mixing (premixing) in the MSM PR reactor a plug flow-stirred lank reactor series model was developed. The plug flow reactor represents the premixing region of the MSMPR reactor in which turbulent micromixing is important, and the stirred tank reactor describes the homogeneous mixing region of the MSMPR reactor where particle growth is important. The model predicts that the premixing effect is strongly dependent on micromixing of the feeds in the premixing region, and thus, as the turbulent mixing intensity in this region is increased, the particle size in the product suspension is reduced and the particle population is increased. These predictions of the model arc in good agreement with the experimental data. An interesting prediction of the model is that as the impeller speed increases, the precipitation of barium sulfate in an MSMPR reactor deviates increasingly from the precipitation in a perfectly mixed (ideal) reactor.     

面激光诱导荧光技术用于快速液液微观混合研究

建立了面激光诱导荧光技术研究液液微观混合过程的实验方法,在无干扰流场条件下,研究了毫米尺度流道内、错流接触的两股液膜的时空混合行为,以可视化的手段揭示了液液微观混合过程的二维瞬态浓度场,发现了液膜快速错流接触后形成的有序波形涡结构,涡的尺度大小为1～2 mm,涡的发展过程是影响两股流体混合的主要因素.同时建立了混合过程的定量表征方法,用混合液膜中组分的离析度（intensity of segregation, IOS）定量描述了混合过程所达到的程度,获得了不同液膜流速下液液混合过程IOS值随着液体流动方向的变化趋势图,并分析了两股液膜之间的速率比以及混合液膜的Reynolds数对混合过程的影响.     

The influence of viscosity on micromixing in turbulent flows

Viscosity has a negligible effect, if any, on macromixing parameters (e.g. velocity distribution and blending time when turbulent flow is fully developed). It does, however, influence micromixing parameters (e.g. Batchelor concentration microscale (νD²/ε)^1/4 and time constant for decay of fine-scale concentration fluctuations). The product distribution of two rapid, competitive, consecutive reactions (diazo coupling between 1-naphthol and diazotized sulphanilic acid) is sensitive to reagent concentration gradients on the molecular scale. It is shown that if all the independent micromixing parameters are kept constant, except the viscosity, the product distribution changes. The viscosity was varied by dissolving less than 0.5wt.% carboxymethyl cellulose (Hercules, type 7MF) in the aqueous reagent solutions. The viscosity then depends upon many factors (CMC concentration, temperature, shear rate, pH, chemical composition of the solution and mixing sequence during make-up of the solution), and CMC is not an ideal additive. Nothing better seems to be available. At least the spectrophotometric analytical method and the rate constants are unaffected by low CMC concentrations (0.5 wt.%). Three reactors (rotor---stator high intensity mixer, flow in a pipe, stirred tank) were operated in the turbulent flow regime. Increasing the viscosity caused more secondary product to be formed. This effect was described quantitatively by our earlier micromixing model.     

Makro- und Mikromischen im Rührkessel

Macro- and micromixing in stirred tanks. Macromixing time, based on turbulence theory, is calculated theoretically as a function of the specific power input, the kinematic viscosity, the Schmidt number, and the degree of segregation. A comparison of the micromixing time with data for macromixing found in literature reveals that the micromixing time governs the reaction for very small vessel diameters. If the vessel diameter is greater than the critical size than the turbulent macromixing time controls the mixing process. The micromixing time θ_mikro is calculated by means of the experimental results of the turbulent velocity distributions in different stirred vessels for several geometrical arrangements of stirred tanks and different positions of feed input. The calculated data for turbulent mixing times are only valid for geometrically optimized stirred vessels. The necessary mixing time may increase or, if a chemical reaction of 2nd order takes place, the desired yield of the product may decrease considerably if the geometrical conditions are not taken into account.     

Production of commercial dyes via impingement-sheet mixing: Part I. Testing of a device suitable for industrial application

Impingement-sheet mixing is a proven technique for the rapid mixing of liquids on the laboratory scale. In this paper a practical mixer design for use on the industrial scale is presented. The industrial impingement-sheet mixer was tested at flow rate ratios typical of commercial applications and, compared with earlier laboratory results, only a slight loss in mixing speed was noted. At flow rates of the order of liters/minute and pressure drops up to 1.5 bar, the micromixing times of the industrial impingement-sheet mixer are of the order of tens of milliseconds for reactant stoichiometric ratios near 1.00. If one of the reactants is present in at least a 10% excess, then the micromixing time of the limiting reagent is reduced to several milliseconds.