Fully resolved numerical simulation of reactive mixing in a T-shaped micromixer using parabolized species equations

This paper introduces and exploits a hybrid numerical approach for fully resolved numerical simulations of reactive mixing in T-shaped microreactors and thereby enables a computational analysis of how chemical reactions interact with convective and diffusive transport. The approach exploits the fast redirection of the flow inside the mixing channel, resulting in a flow field with positive axial flow component everywhere after a short entry zone. This allows handling the axial flow direction as a pseudo-time variable, so that the evolution of the concentration profile can be computed consecutively on successive cross sections, following the main axial flow direction. With this approach the finest length scales, given by the Batchelor length scale, can be resolved for such a reactive mixing process inside a T-microreactor at stationary flow conditions. This allows for a detailed analysis of the mixing state as well as important characteristics of the reactive mixing process like yield and selectivity. The concrete numerical simulations yield local diffusion times inside the reactor, reveal the influence of the strength of the secondary flow on the progress of the chemical reaction and show how local selectivities result from the species transport.     

Numerical simulation of mixing process in T-shaped and DT-shaped micromixers

Recently, numerous studies have been done on the micro- and nano-scale equipment because of their importance and wide range of application. Micromixers are among the equipment in which two or more fluids are mixed and have applications in the processes, such as chemical synthesis. In this research, a numerical investigation using finite volume approach is done on mixing two incompressible fluids in 3D mixers with T- and double-T-(DT) shaped geometries in the range of Reynolds numbers 75–400. One of the important parameters for the quantitative analysis of the mixing performance of micromixers is the mixing index. So, the effects of different geometries, Reynolds number and channel length on this parameter are studied. The results show that, at different Reynolds numbers, the mixing index of fluids in the DT-shaped channel with 90° is less than the corresponding one in T-shaped mixers because changing the flow regime occurs at higher Reynolds numbers in the DT-shaped channels. The amount of mixing index increases by decreasing the angle of branches in the DT-shaped channel. It is observed that the mixing index of fluids increases along the channel, which tends to a constant value far away from the inlet.     

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.     

Engineering study of continuous supercritical hydrothermal method using a T-shaped mixer: Experimental synthesis of NiO nanoparticles and CFD simulation

In the synthesis of metal oxide fine particles by continuous supercritical hydrothermal method, rapid mixing of starting solution with supercritical water is a key factor for producing nanoparticles that have a narrow size distribution. In this paper, continuous hydrothermal synthesis of NiO nanoparticles from Ni(NO₃)₂ aqueous solution at 400 °C and 30 MPa was carried out with T-shaped mixers and the effect of inner diameter, flow rate, and mixing directions on the particle size was examined. The computational fluid dynamics (CFD) simulation of the mixers was performed to evaluate the heating rate of the starting solution. When the inner diameter of the T-shaped mixer was decreased from 2.3 to 0.3 mm and the flow rate was increased from 30 to 60 g/min, the produced NiO particle size decreased remarkably from 54.3 to 20.1 nm. This trend of the decrease in particle size could be described as a function of the heating rate. The experimental and CFD results showed the detail regions of local heating that correlated with the NiO nanoparticle size.     

Experimental characterization and multi-scale modeling of mixing in static mixers

Mixing in static mixers is studied using a set of competitive-parallel chemical reactions and computational fluid dynamics (CFD) in a wide range of operating conditions. Two kinds of mixers, a wide angle Y-mixer and a two jet vortex mixer, referred to as Roughton mixer, are compared in terms of reaction yields and mixing times. It is found that the Roughton mixer achieves a better mixing performance compared to the Y-mixer. The effect of flow rate ratio on mixing in the Roughton mixer has been studied as well and it is shown that the mixing efficiency is not affected by the flow rate ratio. Moreover, experimental results and model predictions are in good agreement for all mixer geometries and operating conditions. CFD is used to calculate absolute mixing times based on the residence time in the segregated zone and it is shown that mixing times of less than 1 ms can be achieved in the Roughton mixer. In addition, CFD provides insight in local concentrations and reaction rates and serves as a valuable tool to improve or to scale-up mixers.     

Experimental Investigations on the Mixing Behaviour of Impingement Mixers for Polyurethane Production

By means of experimental investigations on the mixing behaviour of impingement mixers it was possible to determine the influence of geometrical parameters, material properties and operating parameters on the mixing quality. Our investigations show that identical mixing behaviours can be observed with geometrically similar mixers and under dynamically similar flow conditions. The characterisation of the mixing quality as a function of the above parameters was done by a tomographic measuring technique.     

Statische Mischer und ihre Anwendung

Static mixers and their applications . Static mixers are generally made up of similar, fixed mixing units installed at right angles to each other in series along a tube or a channel. The energy of mixing is extracted from the flow. Twelve different units are presented. The mixing effect in static mixers under conditions of laminar flow is accomplished either by specially designed feed systems, by cutting and twisting, by displacement and distortion, or by separation and expansion. Depending upon the mixer, very different lengths are required to achieve the same degree of homogeneity. Compared with an empty tube, the pressure drop in static mixers is some 7-to 200-fold greater for laminar flow and 100- to 600-fold greater for turbulent flow. Static mixers are employed in all areas of chemical engineering for homogenization, for reduction of the resisdence-time spectrum, and for heat exchange. Since maintenance and wear are negligible, since incorporation frequently requires no extra space, and since they can be used over wide ranges of viscosity, static mixers are being increasingly employed in continuous processes.     

High‐Throughput T‐Jets Mixers: An Innovative Scale‐Up Concept

The influence of geometrical and design parameters of T‐jets mixers on flow dynamics and mixing patterns is studied by means of two‐dimensional computational fluid dynamics simulations, planar laser‐induced fluorescence, and test chemical reactions. The ratios between injector width and mixing chamber width and between width and depth of the mixing chamber were evaluated as parameters. These ratios determine the flow regime in T‐jets mixers: high values of injector/chamber width ratio favor mixing and high depth values also increase the flow dynamics and thus mixing. A strategy for scale‐up of T‐jets mixers is devised, based on increasing a noncritical dimension (depth) while keeping other dimensions small.     

Einsatz und Auslegung statischer Mischer

Application and design of static mixers . Static mixers are units without, or only with fixed, internal fittings which effect the mixing of flowing materials with the aid of their kinetic energy. They are used for continuous homogenization and dispersion, for limitation of the residence time spectrum, and for raising heat and mass transfer in all areas of chemical engineering. Over 20 static mixers are presented, and compared with regard to pressure drop, mixing quality, energy consumption, and residence time and heat transfer behaviour. Important selection criteria are reported. Static mixers have the following advantages over dynamic mixers: use for a wide range of viscosities, narrow residence time spectrum, readily adaptable to existing pipe systems, frequently require no extra space (in-line mixers), negligible maintainance and wear, low investment and operating costs.     

Mischer mit mikrostrukturierten Folien für chemische Produktionsaufgaben

Mixers with Microstructured Foils for Chemical Production Purposes Since about 10 years the Institut für Mikrotechnik Mainz GmbH (IMM) is engaged with the application of microstructures for chemical micro process engineering. Their advantages – more efficient heat exchange and mass transport – lead to, among other things, an increase in yield and selectivity even while saving resources. The development of microstructured mixers thereby played a key role for carrying out advanced syntheses of fine chemicals as well as for the generation of dispersions, creams, foams, and emulsions. So far, microstructured mixers were mainly limited for laboratory‐scale or at best pilot plant‐scale – typical maximum flow rates were from 2 – 100 L/h for watery fluid systems. With the introduction of the StarLaminators StarLam300 and StarLam3000 this barrier could be lifted far beyond 300 L/h up to the m³/h domain. Both apparatus yield at high flow rates a mixing efficiency which reaches the high performance of today's low‐capacity (L/h) micro mixers. Therefore, continuity from the ”?real”? micro mixers over the herein described high‐throughput tools to conventionally manufactured static mixers with even higher flow rates is given.     

Static mixers: Mechanisms,applications, and characterization methods – A review

Static mixers and multifunctional heat exchangers/reactors (MHE/R) are qualified as efficient receptacles for processes including physical or chemical transformations accompanied by heat transfer due to their high productivity and reduced energy expenditures. The present work reviews recent conceptual and technological innovations in passive static mixers and continuous in-line reactors. Current industrial applications are discussed from a process intensification perspective, focusing on mixing and mass transfer performance. Typical experimental techniques employed to characterize and quantify the mixing process are explored. The work is complemented by a review of mixing fundamentals, knowledge of which allows the development of theoretical models crucial for the analysis of experimental data, like the chemical probe mixing assessment method. Considering the development of continuous flow equipment in numerous processes, advances in this field will certainly be of increasing interest to the scientific and industrial communities.     

Application of Polyimide-based Microfluidic Devices on Acid-catalyzed Hydrolysis of Dimethoxypropane

Microfluidic devices intensify transport phenomena and can improve chemical processes. New manufacturing processes and materials are perpetually developed due to constantly growing interest in process intensification. In this contribution, the authors present the design and application of polyimide-foil-based microfluidic mixing devices manufactured by reactive ion etching. As appropriate model reaction system, acid-catalyzed 2,2-dimethoxypropane (DMP) hydrolysis was chosen and investigated in three different mixing structure with varying flow rate. Energy dissipation rates were calculated to estimate mixing performances. The results show good mixing quality for Reynolds numbers between 10 and 100 and similar mixing times scales for all investigated microstructured mixers.     

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.     

不同三维微通道中被动混合特性的研究

Based on the transport phenomena theory, the passive mixing of water and ethanol in different three-dimensional microchannels is simulated numerically. The average variance of water volume fraction is used to index the mixing efficiency in the cases with different Reynolds number and different fabricated mixers. The results show that the efficiency of liquid mixing is progressively dependent on the convective transport as the Reynolds number increases. The efficiency of serpentine microchannel decreases with the increasing Reynolds number in the laminar regime. Altering the aspect ratio of channel inlet section has no significant effect on the mixing efficiency. Increasing the area of channel inlet section will cause the decrease of the mixing efficiency. The mixing in serpentine channels is the most efficient among three different mixers because of the existence of second flow introduced by its special structure.     

Strain mode of general flow: Characterization and implications for flow pattern structures

Understanding the mixing capability of mixing devices based on their geometric shape is an important issue both for predicting mixing processes and for designing new mixers. The flow patterns in mixers are directly connected with the modes of the local strain rate, which is generally a combination of elongational flow and planar shear flow. We develop a measure to characterize the modes of the strain rate for general flow occurring in mixers. The spatial distribution of the volumetric strain rate (or non‐planar strain rate) in connection with the flow pattern plays an essential role in understanding distributive mixing. With our measure, flows with different types of screw elements in a twin‐screw extruder are numerically analyzed. The difference in flow pattern structure between conveying screws and kneading disks is successfully characterized by the distribution of the volumetric strain rate. The results suggest that the distribution of the strain rate mode offers an essential and convenient way for characterization of the relation between flow pattern structure and the mixer geometry. © 2016 American Institute of Chemical Engineers AIChE J, 62: 2563–2569, 2016     

Experimental characterization and multi-scale modeling of mixing in static mixers. Part 2. Effect of viscosity and scale-up

Static micro-mixers are used in precipitation processes to avoid mixing limitations. The mixing performance of these mixers, which are used in this study to mix two streams of different viscosity, is characterized using competitive-parallel chemical reactions and computational fluid dynamics (CFD). This work is an extension of a previous paper where mixing of fluids with equal viscosity has been studied [Lindenberg, C., Schöll, J., Vicum, L., Brozio, J., Mazzotti, M., 2008. Experimental characterization and multi-scale modeling of mixing in static mixers. Chemical Engineering Science 63, 4135-4149]. It is found that the mixing performance in terms of reaction yield and mixing time decreases slightly with increasing viscosity ratio in a two jet vortex mixer (Roughton mixer). In the Y-mixer the trend is the same at low flow rates, but it is the opposite at large flow rates due to a symmetry breaking phenomenon. The Roughton mixer is scaled-up using the CFD model and a linear relationship between scale-up factor and mixing time is observed. Finally, it is shown that mixing times can be described satisfactorily as a function of velocity, jet diameter and viscosity.     

Mixing efficiency of a multilamination micromixer with consecutive recirculation zones

Adding recirculation zones to a mixer for a microplant is proposed for enhanced mixing efficiency. A multilamination interdigital micromixer has been widely used in microchemical plants for precision or small scale chemical process. The mixing efficiency of this micromixer is relatively low as the mixing of two fluids is executed by the laminar diffusion process. To assist the mixing by fluid action, a series of recirculation zones were added to the mixing chamber. The effectiveness of the recirculation zones on mixing was estimated through a numerical simulation which indicated the dependence on Reynolds number. Mixing efficiency increased at Reynolds number that is relevant to the condition that is prevalent in a microchemical plant. The proposed micromixer was fabricated by the lithography process on the photosensitive glass wafers. The mixing qualities of the fabricated micromixer were measured by two methods; the flow visualization of dilution type experiments and the reactivity measurement. The measurement of color intensity of the mixed fluid followed the predictions by the simulation. For a Reynolds number greater than 400 that was relevant in mixers for microchemical plant, a mixing efficiency higher than 90% was obtained by adding the recirculation zones.     

Numerical and experimental investigations of mixing in T-shaped and cross-shaped micromixers

Mass transfer within the T-shaped and cross-shaped micromixers has been studied using CFD and confocal laser scanning microscopy methods. The concentration profiles, based on flow regimes, were used to compare the T- and cross-geometries. The cross-shaped micromixer tends to intensify the mixing and this is occurring for lower flow rates in comparison to the T shape. The improvement made by the cross geometry is attributed to the stronger vortex stretching and high shear rate, which reduces the liquid transfer length. The presence of a single outlet in the T-shaped micromixer induces a smaller degree of freedom for the fluid. A higher pressure drop is calculated in T-shaped micromixer than in cross-shaped micromixer.     

Influence of agitator design on powder flow

Design influences the flow within a powder mixer but quantitative guidance is lacking. Here the performance of mixers of different geometry was compared using positron emission particle tracking. One mixer had six long flat blades; the other carried short paddles. With the former, blade angle and number of axial compartments had little effect on agitation in the transaxial plan but axial dispersion was enhanced by longer axial compartments. A loop of circulation was found below the shaft. For the short paddle device, the transaxial agitation was more uniform, with a lower mean angular velocity and narrower ranges of velocities. The mixing elements inhibited the formation of the loop of circulation. In both cases, the axial flow had a cellular structure created by the radial supports for the blades but the short paddles mixer showed more chaotic behaviour, the axial dispersion coefficient being typically five times higher and increasing with fill rather than decreasing as seen with the six-blade device. A rationale for the design of powder mixers is thus emerging.     

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.