Mixing and chemical reactions: A contrast between fast and slow reactions

The effect of fluid mixing on chemical reactions is analyzed by means of a model which treats simultaneously the complex interactions of mechanical mix diffusion and reaction. The model assumes that reactants diffuse from adjacent sheets of fluid undergoing a stretching motion, contact one another and This stretching motion causes deformation of the intermaterial surface and is designated mechanical mixing. A history of striation thickness s(t) contains all information about fluid mechanical mixing. Numerical methods were employed to solve the simultaneous partial differential equations of the model for mixing and single-step irreversible reactions. A criterion is established for limits of reaction control of bimolecular reactions by mixing, including diffusion, and by chemical kinetics in terms of a single dimensionless group φ  kC_B0S²/D_A. The present model can be applied to reactions in both laminar and turbulent flows.     

Modelling of mass transfer coupling with crystallization kinetics in microscale

Microstructure technologies have attracted interests in chemistry, chemical engineering, and biotechnology. To investigate the mass transfer of ions and crystallization of crystals in microscale and then to explain the formation mechanism of the porous structure materials, a microscale mathematical model for mass transfer processes coupling with local reactions is proposed in which the chemical potential gradient Δμ is used as the driving force to avoid the discontinuity of the kinetics equations in the micro-channels. Meanwhile, the dissolution kinetics of KCl at 298.15 K is measured to determine the dissolution rate constant k_d and the average area of crystals Ac. The investigation for the fractional crystallization process of carnallite shows that the calculated mixing time versus channel width agree with the Einstein diffusion equation, which validates that the model can be used to describe the ion diffusion very well. Meanwhile, to have an accurate Δμ of KCl, in the channel width of or narrower than 2.0×10^?6 m, it is enough to consider the diffusion only, while in the channel width of or wider than 2.0×10^?5 m, diffusion should be coupled with reaction. The investigation also shows the vital of the consideration of the ionic activity coefficient for the investigated systems in micron scales. Moreover, the new formation mechanism of the porous structures in the inorganic material fabrication will be proposed from the process simulation for the synthesis of porous KCl, which will provide a reference for the porous structure formation in the advanced inorganic material synthesis.     

Influence of morphology on the transport properties of polystyrene/polybutadiene blends. 1. Experimental studies

Experimental and quantitative image analysis studies are presented to investigate the influence of morphology on the transport of small gaseous penetrants (CO₂, O₂, N₂) in randomly interspersed blends of polystyrene (A) and polybutadiene (B) ranging in volume fractions, ф_B, from 0.08 to 0.90. The overall transport process, for the blends, appears non-Fickian even though both pure phases A and B exhibit Fickian behaviour. An explanation of this phenomenon, based solely on morphological effects, is presented. A conclusion of the study is that the different methods usually taken as equivalent, to compute the effective diffusion coefficient from sorption data, can give significantly different results. An examination of the morphology is performed by means of digital image analysis on transmission electron microscopy, TEM, micrographs. A significant finding is that, for this system, the maximum intermaterial area density occurs for ф_B around 0.15.     

Synthesis,characterization and correlation with the catalytic activity of efficient mesoporous niobia and mesoporous niobia–zirconia mixed oxide catalyst system

Mesoporous mixed oxide has always remained as a subject of interest due to diffusion relaxation and generation of new surface potential and acidity by mixing of different stoichiometries of metal oxide. To deliver more insight on niobia based catalyst, herein, we have synthesized mesoporous niobia and five different mole ratios of niobia–zirconia mixed oxide. The catalysts were characterized by XRD, N₂-physisorption, FTIR, UV–Vis and NH₃-TPD techniques. Less distorted NbO₆ octahedra and NbOH or Nb–OH–Zr are found to act as Bronsted center responsible for reaction. The results established the role of Kung model to generate acidic sites in mesoporous mixed oxide.     

Mixed potential measurements in the elucidation of corrosion mechanisms—II. Some measurements

The behaviour of the mixed potential as a function of oxidant concentration and agitation is examined for a variety of corrosion reactions. Using the theory developed in a previous paper, this information is used to elucidate the mechanism of each reaction.The dissolution of mercury, copper and silver in the presence of ferric ions was studied. For the Fe(III)-CuSO₄^2? system, it was shown that the anodic dissolution half-reaction was activation controlled and the cathodic half-reaction was diffusion controlled. Changing the anion to Cl^? made both half-reactions diffusion controlled. For the Fe(III)AgNO₃^? system, the anodic half-reaction is diffusion controlled the ferric reduction being activation controlled. In the attack of ferric ions on mercury in nitrate solution, both half-reactions are activation controlled.The metal oxidation reaction in which silver is oxidized to silver iodide by the triiodide ion was considered. It was shown that the ir drop in the AgI layers had a negligible effect on the corrosion potential.An examination of the behaviour of the corrosion potential in the Cu(II)Zn metal displacement reaction enabled estimates to be made of the anodic area at various times during the reaction. It was shown that in the first stage of the reaction the anodic area is fairly constant and equal to the geometric area of the zinc. As the second stage is entered, the anodic area suddenly drops to about 3 per cent of the geometric area, at which level it remains constant.     

Magnetic-field assisted mixing of liquids using magnetic nanoparticles

Size and magnetic properties of magnetic nanoparticles (MNPs) in fluids allow special remote control of fluid flow using appropriate externally applied magnetic fields, especially when submicronic mixing is critical, inter alia, for catalytic reactions, separation and drug delivery. This work explores MNPs as nanoscale devices to control mixing at microscale by submitting the system of interest to a rotating magnetic field (RMF). Magnetic nanoparticles are harnessed by RMF and converted into nanostirrers thereby generating MNP-pinned localized agitation in the liquid phase. Using this technique, self-diffusion coefficient of water in a static diffusion cell was intensified up to 200 folds. Also, axial dispersion of capillary Poiseuille flows under RMF underwent a reduction prompted by MNP-mediated intensification of lateral mixing relative to that in absence of magnetic field. Finally a multiphase flow case concerned gas–liquid mass transfer from oxygen Taylor bubbles to the liquid in capillaries where dilute MNP solutions led to measurable enhancement of k_La under RMF.     

Viscous fluid mixing in a tilted tank by periodic shear

A tilted-partially filled rotating tank is studied, both experimentally and theoretically at small Reynolds and capillary numbers, to study mixing viscous fluid by periodic shear. The maximum mixed cross-sectional area, A_max(α)=A(Δt_max(α)), and mixing rate, 1/Δt_max(α), are estimated as a function of the flow parameters, which are the tilt angle, α, and free surface height, H₀. A nonlinear flow model is found by expanding linear solid body rotation about a curved rotation axis that is needed to satisfy the zero shear stress and no normal velocity component for the flow in the vicinity of the free surface. A linear analysis of the nonlinear solution reveals an underlying periodic shear that is responsible for fluid mixing. The analysis suggests that the rate of mixing per unit area is a maximum near α=52π/180. Laser fluorescence experiments are performed to examine the mixing patterns via experimental Poincaré mapping [Fountain, G.O., Khakhar, D.V., Ottino, J.M., 1998. Visualization of three-dimensional chaos. Science 281, 683-686.]. Steady-state images of the mixed cross-sectional area are compared with the theory as a function of the flow parameters.     

Investigation of alternating-flow mixing in microchannels

A number of different approaches to mixing liquids in microscale systems can be found in the literature. In the case of miscible liquids it is desirable to produce mixtures with residual non-uniformity in composition that is below some specified level. Yet very little quantitative information is available concerning the conditions required to produce a given level of mixture uniformity. A theoretical approach to this problem is described. Computational fluid dynamics and simple scaling are used to develop a quantitative understanding of the alternating flow method of mixing using pressure driven flow. In this approach, external flow control is used to produce alternating injection into a single microchannel of two or more solutions to be mixed. The resulting streamwise slugs of solution then mix by the stretching of the slugs into thin striations resulting from shear strain. The most challenging condition for mixing is where the Reynolds number is approaching zero and inertia effects are negligible, a common situation in microchannel flows, particularly where relatively high-viscosity liquids, for example ionic liquids, are involved. The scaling theory demonstrates that an initial time period of rapid mixing of fluid outside the core of the flow, scaling as Pe^-2/3, is followed by a far slower process of mixing in the core region, scaling as Pe^-1/2. An approximate correlation for the deviation from the perfectly mixed state as a function of time is found. This correlation applies over the range of Peclet number, slug length and solution mixture ratio that are of interest. The mixture uniformity produced is shown to be limited by the initial uniformity of each solution over the channel section resulting from the injection process.     

Calculation of the limit pore ranges of the reaction of porous carbon materials with CO2

In the production of activated carbon materials reaction temperature is important for the course of the chemical reaction. The higher the reaction temperature the faster the increase of the reaction rate as against the diffusion rate. In the range of small carbon burn-off reactions the decrease in k_meff values can be ascribed to a reduction of the surface area available for the reaction. Depending on the pore size distribution the surface area can be determined from the walls of the cylindrical tubes. With the help of the pore efficiency value determined from the k_meff values, the limit pore ranges for C0₂ diffusion can be calculated.     

A novel approach for describing mixing effects in homogeneous reactors

The Liapunov–Schmidt technique of classical bifurcation theory is used to spatially average the convection–diffusion–reaction (CDR) equations over smaller time/length scales to obtain low-dimensional two-mode models for describing mixing effects due to local diffusion, velocity gradients and reactions. For the cases of isothermal homogeneous tubular, loop/recycle and tank reactors, the two-mode models are described by a pair of coupled balance equations for the mixing-cup (C_m) and spatial average (〈C〉) concentrations. The global equation describes the variation of C_m with residence time (or position) in the reactor, while the local equation expresses the coupling between local diffusion, velocity gradients and reaction at the local scales, in terms of the difference between C_m and 〈C〉. It is shown that the two-mode models have many similarities with the classical two-phase models of heterogeneous catalytic reactors with the concept of transfer between phases being replaced by that of exchange between the two-modes. It is also shown that when the local Damköhler number (ratio of local diffusion to reaction time) is small, the solution of two-mode models approaches the exact solution of full CDR equations, while for fast reactions the two-mode models retain all the qualitative features of the latter. Examples are provided to illustrate the usefulness of these two-mode models in predicting micromixing effects on homogeneous reactions.     

Thermodynamic studies of Hydrobromic acid in acetonewater mixtures (10, 30 and 50 wt-%) from electromotive force measurements

The emf of the cell: Pd,H₂(g)/HBr(m), x wt-% acetonewater mixture/AgBr,Ag was measured with x = 10, 30 and 50 at temperatures 15, 25 and 35°C in the molality range for HBr from 0.003 to 0.1 mol kg^?1. From these data the standard potentials for Ag|AgBr electrode are obtained, and used in calculations of: (a) the standard thermodynamic quantities for the cell reaction and the reaction of HBr formation, (b) the mean activity coefficients of HBr, (c) the primary medium effect, and (d) the standard thermodynamic quantities for transfer of HBr from water to the acetonewater mixed solvents. On the basis of the values obtained under (d), the spontaneity of transfer the process for HBr is discussed, the acid—base properties of mixed solvents and their structure.     

Predictions of CO and NOx emissions from steam cracking furnaces using GRI2.11 detailed reaction mechanism – A CFD investigation

This investigation develops a three-dimensional Computational Fluid Dynamics (CFD) model to simulate the turbulent diffusion flame on the fire-side of the radiation section of a thermal cracking test furnace coupled with a non-premixed low NO_x floor burner. When this type of burners which uses the internal Flue Gas Recirculation (FGR) technique is coupled with large scale furnaces, both the turbulent mixing and chemical reaction rates are comparable and hence this should be considered in the model. Different combustion models are used to simulate the turbulence–chemistry interactions for this flame. The CFD model, based on the Eddy Dissipation Concept (EDC) combustion model coupled with the detailed GRI2.11 reaction mechanism, gives the most reasonable predictions compared with the available experimental data or empirical correlations for the diffusion flame in the thermal cracking test furnace, especially for the flame length and the CO and NO_x emissions.     

Structural and electrical properties of 0.56Pb(Ni1/3Nb2/3)O3-0.10Pb(Zn1/3Nb2/3)O3-0.34PbTiO3 ceramics prepared by different ceramic processings

The ternary system of 0.56Pb(Ni_1/3Nb_2/3)O₃-0.10Pb(Zn_1/3Nb_2/3)O₃-0.34PbTiO₃ (0.56PNN-0.10PZN-0.34PT) ceramics were prepared by conventional solid-state reaction method via straight mixed oxide method, columbite precursor method and B-site oxide mixing route. X-ray diffraction (XRD) measurement demonstrated that both the tetragonal and rhombohedral phases coexist in the B-site oxide mixing route prepared ceramics accompanied by the largest content of perovskite phase of 95.18%. The 0.56PNN-0.10PZN-0.34PT ceramics prepared by the straight mixed oxide method and the B-site oxide mixing route exhibit rather homogeneous microstructure. As a comparison, in the columbite precursor method prepared ceramics nebulous granules and octahedral or other polyhedral morphology grains are observed. All the sintered ceramics exhibit diffused ferroelectric phase transition where the dielectric response peaks are broad, diffused and strongly frequency dependent. However, the temperature of dielectric maximum (T_m) increases greatly from 398.0 K of the 0.56PNN-0.10PZN-0.34PT ceramics prepared by the B-site oxide mixing route to 423.3 K of the ones prepared by the straight mixed oxide method. Saturated and symmetric P-E hysteresis loops are observed in all the sintered ceramics, where the B-site oxide mixing route prepared ceramics exhibit large value of remanent polarization (P_r) of 17.13 μC/cm² and the least value of coercive field (E_c) of 11.99 kV/cm. Piezoelectric constant (d₃₃) exhibits the largest value of 449 pC/N for the ceramics prepared by the B-site oxide mixing route. Such results are related to the phase composition, density and porosity of the ceramics.     

Non-oxidative methane conversion into aromatics on mechanically mixed Mo/HZSM-5 catalysts

The catalyst prepared by the physical mixing of powder MoO₃ and HZSM-5 exhibits a better performance for methane conversion at high Mo loading compared with those prepared by the impregnation method. The specific surface area is larger for physically mixed samples than that for impregnated samples with the same Mo loading. The preferential orientation of MoO₃ crystallite is along the (0 k 0) axis, while the (0 2 1) plane is exposed preferentially by MoO₃ to impregnated HZSM-5. Both hcp β-Mo₂C and fcc α-Mo₂C can be formed on physically mixed samples, while only hcp β-Mo₂C is found on the impregnated samples under the same reaction condition.     

Hydrogen generation and separation using Gd0.2Ce0.8O1.9−δ–Gd0.08Sr0.88Ti0.95Al0.05O3±δ mixed ionic and electronic conducting membranes

Decomposition of steam under a chemical driving force at moderate temperatures offers a simple and economical way to generate hydrogen. A significant amount of hydrogen can be generated and separated by splitting steam and removing the oxygen using Gd_0.2Ce_0.8O_1.9−δ (GDC)–Gd_0.08Sr_0.88Ti_0.95Al_0.05O_3±δ (GSTA) mixed oxygen ionic and electronic conducting membranes. Hydrogen generation experiments for the self-supported thick membranes and porous supported thin membranes were conducted at different oxygen partial pressure gradients across the membrane established using H₂–H₂O mixture gas. Experimental results indicate that the hydrogen generation from steam using GDC–GSTA MIEC membranes at elevated temperatures is mainly controlled by the bulk diffusion of oxygen for the self-supported thick membranes, while the permeation process for the porous supported thin membranes is mixed controlled, i.e. the hydrogen generation/oxygen permeation process is controlled by the surface exchange reactions and bulk diffusion of oxygen through the MIEC membrane. A mathematical model for the calculation of the area specific hydrogen generation rate is proposed in this paper based on the measured oxygen partial pressures, gas compositions, and gas flow rates of the inlet and outlet gases on feed side of the membrane, as well as the permeation area of the membrane.     

Principle of corresponding states of liquid solutions—excess enthalpy and the pseudocriticals

A new generalized enthalpy function of low pressure saturated liquids is developed to permit the accurate calculation of heats of mixing from the known pseudo quantities of a mixture system. A procedure is developed, with the aid of the new enthalpy function, by which ω′ and T′_c of binary mixtures are determined from experimental heat of mixing data of their liquid solutions at multiple temperatures. The procedure is applied to twenty-seven binary hydrocarbon systems for which data were found in the literature. The pseudo quantities are established over the entire composition range to reveal their functional forms.     

Computational fluid dynamics study of the synthesis process for a PET radiotracer compound, [11C]raclopride on a microfluidic chip

Recent synthetic applications conducted on microfluidic chips have shown improved yields and shorter reaction times as compared to conventional methods. These have generated great interest in the microfluidic synthesis of radiotracer compounds with short lived radioisotopes, such as carbon-11 (t_1/2 – 20.4 min). For the purpose of microreactor design optimization and to predict synthetic behavior, we launched a study of the radiosynthesis of [¹¹C]raclopride on three different microchip designs by computational fluid dynamics, using COMSOL Multiphysics^®. COMSOL's Reaction Engineering Lab^® tool and convection and diffusion models were used first to investigate the “ideal” reactor and then to study reaction progress in the microchip geometry. Examining the concentration distribution within the microchannel geometry, it was clear that the microchannel length can predict passive mixing and higher product generation than microchannel length. Reducing the flow rate of reagents, premixing the reagents, and increasing reagent concentrations also increased product generation due to increased space times and molecular interactions. For the purpose of simulation, the yield is undesirably reduced by decreasing the diffusion coefficient and the reaction rate constant. This study provides the optimized parameters to redesign the microchip in order to increase the efficiency of micromixing within the microchannels and, therefore, increase the reaction yield.     

Sonochemically activated solid-state synthesis of BaTiO3 powders

We report the sonochemically activated solid-state synthesis of BaTiO₃ powders. Unlike conventional ball-mill mixing, coarse BaCO₃ and fine TiO₂ powders were sonochemically mixed in ethanol, requiring only 5 min for full mixing and activation. Significantly accelerated phase conversion to BaTiO₃ via a solid-state reaction was achieved by the sonochemical mixing, and the process exhibited almost Arrhenius-type activation behavior depending on the ultrasonic power. The sonochemical activation was attributed to the preferential fragmentation of BaCO₃ by the ultrasonic irradiation, which led to the particle size reduction and homogeneous mixing in the sonochemical mixtures. Based on the structural, dielectric, and ferroelectric characterizations, we suggest that the sonochemical mixing can replace the time-consuming ball-mill mixing for the solid-state synthesis of BaTiO₃ powders and can also be applied to develop a time-saving, contamination-free, and cost-effective process for various ceramic industries.     

Mass‐transfer rate enhancement for CO2 separation by ionic liquids: Theoretical study on the mechanism

To promote the development of ionic liquid (IL) immobilized sorbents and supported IL membranes (SILMs) for CO₂ separation, the kinetics of CO₂ absorption/desorption in IL immobilized sorbents was studied using a novel method based on nonequilibrium thermodynamics. It shows that the apparent chemical‐potential‐based mass‐transfer coefficients of CO₂ were in three regions with three‐order difference in magnitude for the IL‐film thicknesses in microscale, 100 nm‐scale, and 10 nm‐scale. Using a diffusion‐reaction theory, it is found that by tailoring the IL‐film thickness from microscale to nanoscale, the process was altered from diffusion‐control to reaction‐control, revealing the inherent mechanism for the dramatic rate enhancement. The extension to SILMs shows that the significant improvement of CO₂ flux can be obtained theoretically for the membranes with nanoscale IL‐films, which makes it feasible to implement CO₂ separation by ILs with low investment cost. © 2015 American Institute of Chemical Engineers AIChE J, 61: 4437–4444, 2015     

On the effect of the uncompensated solution resistance on the applicability of the galvanostatic relaxation techniques and comparison to steady-state techniques for electrode kinetic measurements

The effect of the uncompensated resistance between the reference and working electrodes was investigated on the applicability fields of the single and double pulse galvanostatic relaxation techniques for the determination of exchange current density. The applicability field is defined in terms of three characteristic times of the electrode system: τ_c, the time constant of the double layer capacitance—reaction resistance system; τ_d, the time constant of the diffusion impedence—reaction resistance system; and τ_r, the time constant of the double layer capacitance—uncompensated solution resistance system. Within the boundaries of this field, the exchange current density can be determined with a maximum error of ±20%. It was found that the techniques are limited by the uncompensated solution resistance to τ_r ? 0.2τ_c. An applicability diagram was also constructed for steady-state measurement techniques. In this case, the applicability field is defined in terms of k₀ (the apparent standard rate constant of the reaction), k_m (rate constant of diffusion), and τ_r and τ_c. A comparison reveals that, at small τ_c values, the relaxation techniques can be used for systems with larger k_o values than can the steady-state techniques, but at large τ_c the situation is reversed. The crossover point depends on the specific techniques compared; for example, for the double pulse galvanostatic technique with computer curve-fitting data evaluation compared to the rotating disc electrode steady-state technique, the crossover is τ_c τ~ 10^?2 s.