Characteristic Mixing Time Research Articles

Narrow polydispersity P(AN-MA) copolymers synthesized in continuous flow as potential carbon fiber precursors

In this work, poly (acrylonitrile-methyl acrylate) [P(AN-MA)] copolymers with controllable molecular weights and narrow polydispersity were successfully synthesized in continuous flow without pre-deoxygenation. A dual-reactor method was designed to prepared P(AN-MA) with higher molecular weight and achieve a high yield from 62.57 % to 70.16 %. To facilitate industrial production of P(AN-MA), pre-mixing stage was added in continuous flow for replacing the ultrasonic mixing process. The characteristic mixing time is 27.80 min and the length of Polyfluoroalkoxy (PFA) tube exceeds 74.625 m for thoroughly mixing. Higher molecular weight P(AN-MA) copolymers possess poorer preoxidation properties such as higher initiation temperature, more concentrated heat release and larger activation energy of cyclization reaction as well as lower extent of stabilization and poorer thermal stability against high-temperature treatment. Moreover, 192 g P(AN-MA) was continuously prepared by the dual-reactor method for 105 min without suffering from notable pressure increase.

Analysis of C2HF5 concentration and calculation of characteristic mixing time behind obstacle

C2HF5 is not only a refrigerant but also a highly efficient fire extinguishing agent. The effect of obstacle on the concentration distribution of extinguishing agent is important in the design for a firefighting strategy. Based on the extinguishing agent concentration analyzer using the differential pressure principle, the fire extinguishing agent concentration under the influence of different wind speeds, blockage ratios, and obstacle types is measured. The fire extinguishing agent is brought into the recirculation zone by the mutual entrainment of the primary eddy and the secondary eddy. The concentration of fire extinguishing agent decreases with the increase of wind speed. The increase of blocking ratio makes the concentration of extinguishing agent decrease in the recirculation zone. In the recirculation zone, when the blockage ratio is small, the concentration of fire extinguishing agent in the baffle and the 45° backward facing step at different wind speeds is approximately equal. With the increase of blockage ratio, the concentration of fire extinguishing agent in the baffle is greater than 45° backward facing step in the recirculation zone. Through experimental analysis, the feasibility of discrete calculation of characteristic mixing time is proved. The characteristic mixing time of different obstacles is not equal under cold spraying condition. The calculation formula of characteristic mixing time of the baffle and 45° backward facing step is obtained by fitting analysis, the characteristic mixing time coefficients are 34.4 for the baffle and 30.7 for the 45° backward facing step.

Flame detachment of jet fires at windward and leeward sides in crossflow: Experiment and a Damköhler number based model

Flame detachment of jet fires are important in practical application such as elevated flares, where flame detachment is used to minimize damage on nozzle and the attendant fire safety problem. In this work, detachment behavior of a jet flame under crossflow was studied, especially focused on the difference in critical crossflow speeds for flame detachments at the windward and leeward sides of the nozzle exit, such problem has not been quantified previously. Experiments were conducted in a wind tunnel using propane as the fuel by adopting jet nozzles with inner diameters of 3, 5, 8, and 10 mm and an outer diameter of 15 mm; together with inner diameters of 13 and 15 mm and an outer diameter of 20 mm. The results showed that the critical crossflow speeds for flame detachments both at the windward and leeward sides decreased as the jet velocity increased. The critical crossflow speed for flame detachment at the windward side was weakly dependent on nozzle diameter, while that at the leeward side increased with the increase in nozzle diameter. A model was proposed to characterize this difference on the basis of a Damköhler number, which is defined as the ratio of the characteristic mixing time to chemical reaction time. A satisfactory correlation was achieved for the difference in critical crossflow speeds for flame detachments at the windward and leeward sides as a function of fuel jet velocity and nozzle dimensions of inner diameter and wall thickness.

Facile synthesis of CoFe2O4-graphene oxide nanocomposite by high-gravity reactor for removal of Pb(II)

Heavy metals pose a serious threat to human health due to high toxicity and non-biodegradability, and the selection of adsorbent is crucial for the adsorption separation technology. In this paper, based on the problem of non-uniform micromixing in traditional stirred tank reactor (STIR) in the preparation of adsorbent, an impinging stream-rotating packed bed (IS-RPB) using the high gravity technology is proposed to quickly prepare CoFe2O4-graphene oxide nanocomposite (CoFe2O4-GO-RPB) in less than 1 min. Compared with STIR, IS-RPB has the advantages of good micromixing effect, short characteristic mixing time and easy formation of uniform supersaturated environment. The reactivity of CoFe2O4-GO-RPB was evaluated through the adsorption performance towards Pb(II), and the adsorption capacity was 459.8 mg·g−1 at the initial concentration of Pb(II) of 1000 mg·mL−1 and pH of 6. The adsorption behavior of CoFe2O4-GO over Pb(II) was preferably described by Langmuir isotherm model and Elovich model, and the analysis of XPS and FT-IR confirmed that Pb(II) was adsorbed by the action of electrostatic adsorption, ion exchange and complexation. Herein, a facile way of rapid preparation of CoFe2O4-GO with excellent reactivity is provided, and the preparation method of high-gravity co-precipitation will enrich the application of CoFe2O4-GO for hazardous heavy metal remediation from wastewater.

A generalized partially stirred reactor model for turbulent closure

A generalized Partially-Stirred Reactor (PaSR) model is presented in this work based on the inclusion of multiple chemical times. The PaSR model has shown promising results at modelling turbulence-chemistry interaction in Large-Eddy Simulations (LES) and Reynolds-Averaged Navier-Stokes (RANS), providing an extension of the well-known Eddy Dissipation Concept (EDC). PaSR model divides the computational domain into reactive and non-reactive parts. The factor defining this partition is expressed as a function of the system characteristic chemical and mixing times. However, the estimation of these factors, particularly the chemical one, is often oversimplified. The approach proposed in this study seeks to include in the PaSR model the whole set of chemical times involved in the reactive system. Besides, the concept of fine structures, first introduced in the EDC and often adopted also in the PaSR model to characterize the evolution of chemistry in the reactive part of the fluid, is here abandoned in favour of direct manipulation of species production rates. The mean source term is formulated according to the new generalized model through a modal decomposition of the Jacobian matrix. The method is validated a priori with DNS data of a syngas non-premixed jet flame, whose filtered data represent the validation benchmark. A good agreement is found between the new PaSR model and the filtered data for all species at different filter widths. Comparison with the single time scale based model clearly shows the limitations of the old standard approach and the necessity of including the whole spectrum of chemical times for a more comprehensive description of turbulence-chemistry interaction. A thorough analysis with the time scale participation index reveals the complexity of reaction rates contributions to the development of a specific time scale, underlying the importance of developing a model able to inherit all kinetic pathways in the turbulent closure.

Numerical research of characteristic mixing times of isothermal three-component steam-gas systems

Multicomponent diffusion in gases is characterized by a number of effects that are not observed in binary diffusion. Analysis of existing works shows that convective instability may occur in some systems with significantly different diffusion coefficients with certain geometric and thermophysical characteristics. Stability analysis allows determining the spectrum of parameters at which a transition from a diffusive state to a convective is possible. However, this approach does not allow the researchers to investigate the dynamics of the process. Therefore, this work aims to describe emergence and evolution of convective flows in threecomponent systems and assess the influence of the initial composition on the occurrence of concentration gravitational convection. The main part of the work presents a mathematical model describing the occurrence of convective flows based on the splitting scheme according to physical parameters. Numerical data on the concentration fields of the gas with the highest molecular weight at various time points is obtained. It is established that curvature of the isoconcentration lines of the diffusing components can be associated with instability of the mechanical equilibrium of the system. Degree of curvature is determined by the initial concentration of components of the mixture. The obtained data can be used to determine the main characteristics of mass transfer used in calculations related to combined heat and mass transfer in a wide range of thermophysical parameters.

Numerical research of characteristic mixing times of isothermal three-component steam-gas systems

Multicomponent diffusion in gases is characterized by a number of effects that are not observed in binary diffusion. Analysis of existing works shows that convective instability may occur in some systems with significantly different diffusion coefficients with certain geometric and thermophysical characteristics. Stability analysis allows determining the spectrum of parameters at which a transition from a diffusive state to a convective is possible. However, this approach does not allow the researchers to investigate the dynamics of the process. Therefore, this work aims to describe emergence and evolution of convective flows in threecomponent systems and assess the influence of the initial composition on the occurrence of concentration gravitational convection. The main part of the work presents a mathematical model describing the occurrence of convective flows based on the splitting scheme according to physical parameters. Numerical data on the concentration fields of the gas with the highest molecular weight at various time points is obtained. It is established that curvature of the isoconcentration lines of the diffusing components can be associated with instability of the mechanical equilibrium of the system. Degree of curvature is determined by the initial concentration of components of the mixture. The obtained data can be used to determine the main characteristics of mass transfer used in calculations related to combined heat and mass transfer in a wide range of thermophysical parameters.

The partially stirred reactor model for combustion closure in large eddy simulations: Physical principles, sub-models for the cell reacting fraction, and open challenges

For their ability to account for finite-rate chemistry, reactor-based models are well suited Turbulence–Chemistry Interactions (TCI) Sub-Grid Scale (SGS) closures for Large Eddy Simulations (LES). The SGS closure in the Partially Stirred Reactor (PaSR) model relies on the determination of the reacting fraction of each computational cell, whose definition is based on estimates of the characteristic mixing and chemical time scales. Direct Numerical Simulations (DNS) of turbulent combustion can supply key information on TCI for the development, validation, and comparison of combustion models. In particular, a priori testing allows the direct validation of model assumptions. In the present work, an a priori assessment of the PaSR model is conducted. Its ability to reconstruct thermo-chemical quantities of interest is investigated along with model assumptions. Sub-grid quantities are extracted from the DNS to investigate the role of the cell reacting fraction. Various definitions are then proposed to estimate the characteristic chemical timescale in the PaSR model. Modeled chemical source terms and heat release rates are compared against the filtered quantities from DNS data of a two-dimensional, spatially developing, turbulent nonpremixed jet flame with detailed kinetics. The results demonstrate the importance of accounting for the fine structures quantities in the context of reactor-based models. A new formulation of the chemical timescale is proposed and provides improved overall predictions. Several issues are raised in the discussion, representing realistic prospects for further developments of the PaSR model as a SGS combustion closure for LES.

Single and two‐phase flows in a horizontal pipe with a Kenics static mixer: Effect of pressure drop on mixing

AbstractSingle and two‐phase flows pressure drops through a Kenics static mixer were investigated, for liquid and gas Reynolds numbers ranging from 8110 < ReL < 18 940 to 1730 < ReG < 8680, respectively. New friction factor correlations were established for single and two‐phase flows, showing better agreement than those available in the literature. Dissipated energy and characteristic time constants were estimated from experimental data. For instance, a dissipated energy with a maximum value of 510 W/kg was calculated in two‐phase flow with the drift‐flux model. The dispersed phase reduced the characteristic mixing times and its influence was more important than the continuous phase for all the characteristic mixing time investigated. Furthermore, the macroscopic characteristic mixing time was shown to be the governing mixing process for almost all gas and liquid flow rates explored.

Mixing efficiency affects the morphology and compactness of chitosan/tripolyphosphate nanoparticles

Due to the rapid reaction kinetics, the morphology of chitosan/tripolyphosphate nanoparticles was difficult to control. We mixed chitosan and tripolyphosphate through a multi-inlet vortex mixer at different mixing efficiency and characteristic mixing time (τmix). Below a critical τmix, the aggregation of primary chitosan/TPP particles can be ceased. The corresponding aggregation time of primary particles (τagg) was dependent on the ionic strength, the degree of deacetylation and molecular weight of chitosan. Moreover, the particle compactness was estimated from the hydrodynamic diameter and the turbidity using a model based on the Mie theory. Slow and nonhomogeneous mixing led to more compact nanoparticles, while rapid and homogeneous mixing produced nanoparticles with a higher swelling ratio. Besides, the ionic strength and polymer concentration could affect the internal structure of nanoparticles. This study revealed the significance of mixing on the internal structure of chitosan/TPP nanoparticles, which could guide the preparation of other ionically-crosslinked polysaccharide colloids.

Numerical investigation of glycerol/diesel emulsion combustion in compression ignition conditions using Stochastic Reactor Model

In this work, we numerically investigate the potential of glycerol as a diesel fuel additive to reduce soot emissions. Many different fuel additives offer environmental benefits, since there is a surplus supply of glycerol as a by-product of biodiesel production, it is considered as a promising available candidate. The combustion process of glycerol in a direct injection compression ignition engine has been previously investigated experimentally for a 10 % (vol) glycerol emulsion. Based on the experimental set-up, a zero-dimensional Stochastic Reactor Model (SRM) is constructed to conduct numerical analysis with a detailed chemical mechanism for the combustion of hydrocarbon and oxygenated fuels. Applied models are presented and discussed with a focus on the characteristic mixing time scale of micromixing closure which is calculated using a 0D k-ε. The model constants are optimized to the analysed engine with the aid of a genetic algorithm and the sensitivity analysis is presented. For both fuels, emissions of major species are reproduced well but NOx results are slightly overestimated. Emissions of carbon monoxide are predicted well for the reference diesel fuel, but the SRM does not capture the trend of increased CO with glycerol emulsion. The stochastic nature of the model is used to represent the mixture inhomogeneity, and the results are analysed using equivalence ratio–temperature plots to identify soot promoting conditions. The evolution of selected soot precursor and oxidizers is analysed, showing the capability of glycerol to reduce the former and increase the latter with a moderate effect. Soot formation and decomposition rates are presented, with very similar behaviour for both fuels. A shorter combustion phasing for the glycerol emulsion was observed and identified as the main contributory factor that led to the soot reduction while the chemical effect i.e oxygen content of the glycerol was present but not the dominant factor. The soot model results do not provide any evidence for the origin of experimentally observed small-sized particles, but it is discussed that the emissions results indicate the presence of low volatile compounds that could condense in the exhaust system.

Scaling Relation of the Scalar Diffusion in a Rotating Mixer

Scalar mixing is under the joint control of convection and diffusion. The ratio of the dissipative scale of velocity field to that of the scalar field depends on the Schmidt number. In the high Schmidt number limit, the scalar scale is much smaller than that of the momentum, which then requires either special treatment or ad hoc models for the scalar quantity in numerical simulations. In order to avoid model uncertainty or unnecessary numerical complexity, the direct numerical simulation is performed for studying the scalar mixing process in a confined rotating mixer tank. It has been found that in the range of negligible numerical diffusivity, the characteristic scalar mixing time is inversely proportional to the scalar diffusivity. Analysis based on the dimensional argument justifies such scaling relation as well, from which the unaccepted computational time of the mixing process in the high Schmidt number limit can be efficiently determined, without the use of ad hoc models. This scaling idea is also of practical meaningfulness for other similar problems.

Quantification of Solid Mixing in Bubbling Fluidized Beds via Two-Fluid Model Simulations

The influence of particle density and fluidization velocity on the mixing behavior of Geldart B particles was investigated in bubbling fluidized beds for various operating conditions using a two-fluid model approach. The simulation results proved that the predicted solid flow pattern for a wide range of Geldart B particles differs from particles of Geldart B/D classification at identical fluidization numbers. Quantitative analysis of the predicted solid velocity variances revealed that the solid axial dispersion rate is higher than the lateral one. In detail, a Peclet number of 1.54 and 3.92 was predicted for axial and lateral mixings, respectively. Also, the solid dispersion and diffusion coefficients were linearly correlated with the excess gas velocity for a range of particle properties. Finally, the characteristic global particle mixing times were computed. Thereby, the characteristic mixing time can be correlated with the particle Froude number, expanded bed height, and solid dispersion coefficient with high accuracy.

Mixing intensification under turbulent conditions in a high pressure microreactor

The turbulent mixing of two miscible fluids is investigated in a high pressure (HP) coflow microreactor operated at 100 bar. Ethanol and CO2 are selected as model solvents to mimic the final targeted application, i.e.: a supercritical antisolvent process at microscale (μSAS). We first demonstrate experimentally that turbulent mixing can be reached in a microchannel using HP microfluidics. A computational fluid dynamic (CFD) model, performed using direct numerical simulation (DNS) down to the Kolmogorov scale has been applied for the turbulent mixing simulations. The effects of the main operating parameters on the final mixing efficiency have been studied, namely: the temperature, the fluid flowrates, the microchannel dimensions and the capillary inner and outer diameters. According to a predefined intensity of segregation, the characteristic mixing times are determined and used for determining mixing efficiency. The ratio of the total mixing time to the diffusion time depends on the ratio of the kinetic energies (the outer fluid to the inner one). The obtained micromixing times have been related to the turbulent energy dissipation rate ∊, calculated directly from the velocity fluctuations. The mixing intensification is obtained with much lower characteristic mixing times in the microreactor (one order of magnitude) than previously reported. This fundamental study is an indispensable guidance for several processes, including the μSAS applications.

Solid Dissolution and Liquid Mixing in Turbulent Stirred Tanks

AbstractThe dissolution of salt particles in turbulent stirred vessels is investigated. A novel method for achieving the simultaneous identification of the liquid mixing time and the dissolution time of salt particles from the conductivity data collected by electrical resistance tomography is presented. The characteristic time of the liquid mixing during the dissolution is found to be either uninfluential or significant on the dissolution itself, depending on the salt particle diameter and the vessel size. The adoption of a combination of literature correlations, which are proved to adequately estimate the two times, is suggested as a simple tool for identifying the minimum particle size for optimizing the dissolution operation.

Investigating laminar mixing in high pressure microfluidic systems

In this study, the hydrodynamic behavior of coflowing fluids CO2 and ethanol has been investigated in a high-pressure microfluidic reactor working at supercritical conditions, in which the two fluids are completely miscible. The velocity field has been measured by Micro Particle Image Velocimetry (μPIV) for different temperatures between 20 and 50 °C at a fixed pressure of 100 bar. Meanwhile, we have developed a model to investigate numerically the mixing. By comparing the experimental results to a three-dimensional numerical simulation, the mixing model has been validated for the laminar coflow in the micromixer. In order to understand the mixing condition effects, several parameters have been investigated, namely: the Reynolds number, the temperature and the CO2/ethanol ratio. A mixing time constant is defined by using the segregation intensity curve and later used to characterize the mixing quality. The characteristic mixing time has been related to the laminar energy dissipation rate ∊, similarly to the stretching efficiency model in previous studies. The mixing quality is eventually analyzed in term of segregation index and mixing time.

Axial to transverse energy mixing dynamics in octupole-based magnetostatic antihydrogen traps

The nature of the trajectories of antihydrogen atoms confined in an octupole minimum-B trap is of great importance for upcoming spectroscopy, cooling, and gravity experiments. Of particular interest is the mixing time between the axial and transverse energies for the antiatoms. Here, using computer simulations, we establish that almost all trajectories are chaotic, and then quantify the characteristic mixing time between the axial and transverse energies. We find that there are two classes of trajectories: for trajectories whose axial energy is higher than about 20% of the total energy, the axial energy substantially mixes within about 10 s, whereas for trajectories whose axial energy is lower than about 10% of the total energy, the axial energy remains nearly constant for 1000 s or longer.

Characterization of mixing performance in a microreactor and its application to the synthesis of porous coordination polymer particles

Here we quantitatively evaluated the mixing performance of a tailor-made microreactor with central-collision type through the iodide/iodate chemical test reaction, and applied the microreactor to the synthesis of zeolitic imidazolate framework-8 (ZIF-8), which is a subclass of porous coordination polymers (PCPs) or metal organic frameworks (MOFs). The chemical test reaction demonstrated excellent mixing performance of the microreactor with a characteristic mixing time shorter than 1ms, which is approximately 100 times faster than those of a batch reactor and a millimeter-sized Y-shaped mixer. Taking advantage of the rapid and uniform mixing, the microreactor successfully produced ZIF-8 particles with high reproducibility by simply mixing aqueous solutions of zinc nitrate and 2-methylimidazole. The synthesis at room temperature resulted in ZIF-8 particles with chamfered cube shape, while a lower temperature of 5°C produced raspberry-type spherical particles. We confirmed that prepared ZIF-8 particles have BET surface area of ∼1500m2/g and exhibit the gate adsorption behavior caused by the structural transition of the ZIF-8 framework.

Blow-out of nonpremixed turbulent jet flames at sub-atmospheric pressures

Blow-out limits of nonpremixed turbulent jet flames in quiescent air at sub-atmospheric pressures (50–100kPa) were studied experimentally using propane fuel with nozzle diameters ranging 0.8–4mm. Results showed that the fuel jet velocity at blow-out limit increased with increasing ambient pressure and nozzle diameter. A Damköhler (Da) number based model was adopted, defined as the ratio of characteristic mixing time and characteristic reaction time, to include the effect of pressure considering the variations in laminar burning velocity and thermal diffusivity with pressure. The critical lift-off height at blow-out, representing a characteristic length scale for mixing, had a linear relationship with the theoretically predicted stoichiometric location along the jet axis, which had a weak dependence on ambient pressure. The characteristic mixing time (critical lift-off height divided by jet velocity) adjusted to the characteristic reaction time such that the critical Damköhler at blow-out conditions maintained a constant value when varying the ambient pressure.

Heterogeneous nucleation and surface conformal growth of silver nanocoatings on colloidal silica in a continuous flow static T-mixer

Abstract Dielectric-metal core-shell particles with morphologically tunable optical properties are highly promising candidates for applications ranging from theranostics, energy harvesting and storage to pigments and sensors. Most structures of interest have, until now, been produced in small volume wet chemical batch approaches which are difficult to scale. In extension to the growing interest in continuous flow process for the scalable synthesis of single phase nanomaterials, here we describe the formation of two-phase core-shell particles. Specifically, the coating of silver onto colloidal silica particles using a static T-mixer approach is presented. The coating is achieved in a single reaction step in which careful control of educt concentration and process conditions leads to nucleation and surface conformal growth of silver. Through two generations of reactor, good coating yield and process reproducibility are demonstrated. In particular, the ability to control the characteristic time of mixing, as verified by the Villermaux-Dushmann reaction, was shown to be crucial in narrowing the range of morphologies obtained in the product particles. Moreover we could tune, through process parameters, the degree of coating of the core particles, leading to patchy particles, Janus particles and even complete nanoshells. Since silver nanostructures have a strong structure-dependent plasmon resonance, we could verify the coating morphologies via optical spectroscopy and electrodynamic simulations. Optical measurements were also used in order to optimize, via trial and error, the continuous flow process parameters to produce a high coating yield. This opens up future potential for feedback-driven optimization of particle coating. Finally, we demonstrate that the silver coatings can be morphologically stabilized, opening up the possibility of effective formulation for applications.