Phenomenological Kinetic Model Research Articles

Amphoteric chitosan derivatives for the removal of basic and reactive dyes from aqueous solutions

The present study describes the use of [2-(methacryloyloxy)ethyl]dimethyl-(3-sulfopropyl) ammonium hydroxide and 2-acrylamido-2-methyl-1-propanesulfonic acid as grafting agents to chitosan (CS) natural polymer were examined. Two chitosan derivatives were synthesized in this study, and then added in single-component aqueous solutions in order to study the removal of Methylene Blue (MB) and Remazol Brilliant Blue R (RBBR) dyes, by adsorption, in a more innovative way. The characterization of the chitosan derivatives was achieved via X-Ray Diffraction (XRD), Scanning Electron Microscopy (SEM) and Fourier Transform Infrared Spectroscopy (FTIR). Adsorption efficiency of the chitosan derivatives was tested at several pH values (2–12) and for adsorbent’s dosage between 10 and 50 mg per 30 mL effluent. The rising of temperature from 25 to 65 °C led to increased adsorption capacity. Equilibrium data were fitted to both the more common Langmuir and Freundlich isotherm models, as well as the Sips isotherm model. Pseudo 1st and 2nd kinetic order equations and a relatively simple phenomenological kinetic model for adsorption kinetics, were studied as well as the thermodynamic parameters were calculated. The adsorption capacity for CS grafted with [2-(methacryloyloxy)ethyl]dimethyl-(3-sulfopropyl) ammonium hydroxide (CS-SBMA) was 238.1 and 244.5 mg/g for MB and RBBR removal, respectively, at 25 °C, while for CS grafted with 2-acrylamido-2-methyl-1-propanesulfonic acid (CS-AMPS) the adsorption capacity was 219.5 and 203.9 mg/g for MB and RBBR removal, respectively, at 25 °C.

Kinetic modelling of the cellular metabolic responses underpinning in vitro glycolysis assays.

This study aims to demonstrate the benefits of augmenting commercially available, real-time, in vitro glycolysis assays with phenomenological rate equation-based kinetic models, describing the contributions of the underpinning metabolic pathways. To this end, a commercially available glycolysis assay, sensitive to changes in extracellular acidification (extracellular pH), was used to derive the glycolysis pathway kinetics. The pathway was numerically modelled using a series of ordinary differential rate equations, to simulate the obtained experimental results. The sensitivity of the model to the key equation parameters was also explored. The cellular glycolysis pathway kinetics were determined for three different cell-lines, under nonmodulated and modulated conditions. Over the timescale studied, the assay demonstrated a two-phase metabolic response, representing the differential kinetics of glycolysis pathway rate as a function of time, and this behaviour was faithfully reproduced by the model simulations. The model enabled quantitative comparison of the pathway kinetics of three cell lines, and also the modulating effect of two known drugs. Moreover, the modelling tool allows the subtle differences between different cell lines to be better elucidated and also allows augmentation of the assay sensitivity. A simplistic numerical model can faithfully reproduce the differential pathway kinetics for three different cell lines, with and without pathway-modulating drugs, and furthermore provides insights into the cellular metabolism by elucidating the underlying mechanisms leading to the pathway end-product. This study demonstrates that augmenting a relatively simple, real-time, in vitro assay with a model of the underpinning metabolic pathway provides considerable insights into the observed differences in cellular systems.

Investigating The Kinetics of Anionic Polymerization of Butadiene in Presence of 1,2‐diethoxypropane Using Online Near‐Infrared Spectroscopy

AbstractOnline near‐infrared spectroscopy technique is employed to investigate the kinetics of the anionic polymerization of butadiene with n‐butyllithium initiator in the presence of the microstructure modifier 1,2‐diethoxypropane (DEP) in cyclohexane solvent. A phenomenological kinetic model is developed to describe the anionic polymerization process in the presence of DEP, and its influence on the microstructure of polybutadiene under different conditions is determined.

High removal performance of reactive blue 5G dye from industrial dyeing wastewater using biochar in a fixed-bed adsorption system: Approaches and insights based on modeling, isotherms, and thermodynamics study

In an eco-friendly context, an adsorption study was performed in a fixed-bed column system to remove organic pollutants from dyeing wastewater, testing preliminary theoretical models and reactive blue 5G (RB5G) dye as a reference pollutant and tilapia bone-based biochar as an alternative adsorbent. Adsorption approaches in removing RB5G dye molecules from synthetic solutions were performed to understand better based on a reliable mathematical representation and provide insights and strategies into treating dyeing wastewater. Initial dye concentration, pH, temperature, and stirring velocity were used as process variables to search for maximal capacity in batch mode. Thermodynamic analysis and a series of phenomenological kinetic models were applied to understand and interpret the mechanisms and develop a predictive model for a fixed-bed column adsorption system, trying to minimize the total organic carbon (TOC) in dyeing wastewater. An intraparticle mass transfer resistance model and the Langmuir-BET isotherm better represented kinetic and equilibrium data, respectively. In the Langmuir-BET model context, the first monolayer has systematically changed its predicted Langmuir adsorption capacity from 18 mg g−1 to 31 mg g−1 being favored by the increase in temperature of 30 to 60 °C, respectively, with the lowest Gibbs free energies for the multilayer formation ruled by weak physical interaction. Theoretical values of the breakpoint, full saturation time, and useful column height were well predicted related to their experimental ones, including the better fitting of all adsorption curve patterns in a fixed-bed adsorption column system with an adsorption capacity of 30.4 mg g−1 (at 50 °C) for an inlet of 200 mg L−1 RB5G solution resembling almost the same value found in batch mode (30.9 mg g−1). After treating the dyeing wastewater characterized by 75 mg L−1 RB5G dye, the adsorption capacity of 23.3 mg g−1 was attained with a 12% loss in comparison with the expected one for a synthetic RB5G solution due to adsorptive competition with other organic pollutants. Finally, a final TOC value near 5.0 mg L−1, the maximum allowed for the Brazilian environmental council, was attained with an almost zero RB5G concentration after a 5-h breakpoint.

Kinetic simulation of hydrogen production reaction parameters based on TiO2 photocatalyst

Hydrogen is a clean, efficient, and renewable energy source with significant potential to reduce greenhouse gases. Solar photocatalytic water splitting is a promising and sustainable route to produce hydrogen. Currently, the strategies to improve the efficiency of photocatalytic hydrogen production are mainly focused on the development of sustainable photocatalysts. However, the extent to which multiple working conditions affect photocatalytic hydrogen production efficiency is not yet clear. This paper established a TiO2-based photocatalytic phenomenological kinetic model and then validated it using experimental data to clarify the impact of the combined effects of various reaction conditions on the efficiency of photocatalytic hydrogen production. The effects of photocatalyst dosage, reaction temperature, sacrificial agent concentration, and other decisive parameters on TiO2-based photocatalytic hydrogen evolution performance were analyzed under light intensity of 365 nm. The optimization results revealed that the maximum STH efficiency of 5.30 % was observed, at the reaction temperature of 348.15 K and 0.25 g/L photocatalyst concentration. The model provides insights into the combined effects of different factors on photocatalytic efficiency. The identified optimal reaction conditions relationships are helpful to provide guidance for efficient designing of solar photocatalytic hydrogen evolution systems.

A phenomenological kinetic flotation model: Distinct Time-Variant floatability distributions for the pulp and froth materials

A simple and easy-to-use phenomenological kinetic flotation model, strongly connected with the physics of the process, is proposed in this paper. The model explicitly contains the cell volume, aeration rate, volumetric hold-up, mean bubble size, and particle density as input variables. It can be employed to characterize the floatability distributions of the particles in the pulp and the froth separately any time during the flotation process. Two new time-dependent kinetic parameters, the bubble loading factor φ(t) and the maximum cell mass transfer capacity Ṁmax(t) also appear in the model expression. φ(t) is a measure of the degree of crowding of the bubble surfaces and accounts for the deviations from the first-order rate equation. Ṁmax(t) describes the maximum amount of mass that can be transported to the froth phase by the bubble population in the cell. Screen fractionation of each froth product collected at different time intervals during a single kinetic flotation test is sufficient to generate the data required by the model for analysis. Application of the model to this data yields directly time-dependent functions for the floatability of the particles reporting to froth Kf(t) or remaining in the cell Kp(t) for each size fraction separately, without the need for any empirical parameters. The test of the model was carried out using published kinetic flotation data from the literature.

Evaporation of As and Sn from Liquid Iron: Experiments and a Kinetic Model during Top-Blown Oxygen Steelmaking Process.

Evaporation kinetics of tramp elements (M = As and Sn) in liquid iron were investigated by high-temperature gas–liquid reaction experiments and a phenomenological kinetic model. Residual content of As or Sn in the liquid iron ([pct M]) during the evaporation was measured in the temperature range of 1680 C to 1760 C. [pct As] and [pct Sn] decreased faster as the reaction temperature and [pct C] increased. Assuming first-order reaction kinetics, the apparent rate constants () were obtained at each reaction temperature and [pct C]. [pct M] in a liquid iron during the top-blown oxygen steelmaking process was simulated, with an emphasis on enlarging the reaction surface area by forming a large number of liquid iron droplets. The surface area and the droplet generation rate were obtained based on the oxygen-blowing condition. The whole surface area increased up to ∼163 times the initial liquid iron (bath) surface area, due to the generation of the droplets. Using the obtained in the present study, the evaporation of M during the top-blown oxygen steelmaking process for 200 tonnes of liquid iron was simulated. For a condition of [pct M] = 0.005 (M = As and Sn), As and Sn could be removed from the liquid iron, which was seen to be much improved by the consideration of the droplet generation. However, additional actions are required to improve the evaporation rate, as the evaporation rate in the BOF process was not fast enough to be practically considered.

Phase transitions in high-purity zirconium under dynamic compression

We present results from ramp compression experiments on high-purity Zr that show the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}, \ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$, as well as reverse $\ensuremath{\beta}\ensuremath{\rightarrow}\ensuremath{\omega}$ phase transitions. Simulations with a multiphase equation of state and phenomenological kinetic model match the experimental wave profiles well. While the dynamic $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition occurs $\ensuremath{\sim}9\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$ above the equilibrium phase boundary, the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$ transition occurs within 0.9 GPa of equilibrium. We estimate that the dynamic compression path intersects the equilibrium $\ensuremath{\omega}\text{\ensuremath{-}}\ensuremath{\beta}$ line at $P=29.2\phantom{\rule{0.16em}{0ex}}\mathrm{GPa}$, and $T=490\phantom{\rule{0.16em}{0ex}}\mathrm{K}$. The thermodynamic path in the interior of the sample lies $\ensuremath{\sim}100\phantom{\rule{0.16em}{0ex}}\mathrm{K}$ above the isentrope at the point of the $\ensuremath{\omega}\ensuremath{\rightarrow}\ensuremath{\beta}$ transition. Approximately half of this dissipative temperature rise is due to plastic work, and half is due to the nonequilibrium $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition. The inferred rate of the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition is several orders of magnitude higher than that measured in dynamic diamond anvil cell (DDAC) experiments in an overlapping pressure range. We discuss a model for the influence of shear stress on the nucleation rate. We find that the shear stress ${s}_{ji}$ has the same effect on the nucleation rate as a pressure increase $\ensuremath{\delta}P=c{\ensuremath{\epsilon}}_{ij}{s}_{ji}/(\mathrm{\ensuremath{\Delta}}V/V),$ where $c$ is a geometric constant $\ensuremath{\sim}1$ and ${\ensuremath{\epsilon}}_{ij}$ are the transformation shear strains. The small fractional volume change $\mathrm{\ensuremath{\Delta}}V/V\ensuremath{\approx}0.1$ at the $\ensuremath{\alpha}\ensuremath{\rightarrow}\ensuremath{\omega}$ transition amplifies the effect of shear stress, and we estimate that for this case $\ensuremath{\delta}P$ is in the range of several GPa. Correcting our transition rate to a hydrostatic rate brings it approximately into line with the DDAC results, suggesting that shear stress plays a significant role in the transformation rate.

Interpretation of induction time and particle recovery in a microstructured counter-current flow column

Low-grade coal is in abundance, which is used in most thermal power plants, cement units, metallurgical plants, etc., and creates environmental pollution because of the generation of large amounts of fine solid particles and gaseous pollutants. Therefore, it is of utmost importance to clean coal before use. The present work reports the particle recovery and bubble-particle induction times based on the demineralization of coal particles using the column flotation beneficiation technique in a microstructured flotation column. The effect of operating variables on particle recovery, flotation rate constant, efficiency index, ash content, combustible recovery, and induction time is studied. Induction time is enunciated using the phenomenological kinetic model, which is based on the consecutive sub-processes comprising bubble-particle collision, attachment, and detachment. The results showed a shorter induction time and a higher rate constant at higher particle recovery. The flotation system was optimized by varying the collector as well as surfactant doses, and the maximum efficiency index was found to be 47.70%, with 91.88% combustible recovery and 12.53% ash content in the concentrate at 0.020 m/s feed and 0.082 m/s gas velocity. The induction time was observed to vary from 8.68 to 16.6 ms.

The Curing Kinetics of E-Glass Fiber/Epoxy Resin Prepreg and the Bending Properties of Its Products.

The curing kinetics can influence the final macroscopic properties, particularly the three-point bending of the fiber-reinforced composite materials. In this research, the curing kinetics of commercially available glass fiber/epoxy resin prepregs were studied by non-isothermal differential scanning calorimetry (DSC). The curing kinetic parameters were obtained by fitting and the apparent activation energy Ea of the prepreg, the pre-exponent factor, and the reaction order value obtained. A phenomenological nth-order curing reaction kinetic model was established according to Kissinger equation and Crane equation. Furthermore, the optimal curing temperature of the prepregs was obtained by the T-β extrapolation method. A vacuum hot pressing technique was applied to prepare composite laminates. The pre-curing, curing, and post-curing temperatures were 116, 130, and 153 °C respectively. In addition, three-point bending was used to test the specimens’ fracture behavior, and the surface morphology was analyzed. The results show that the differences in the mechanical properties of the samples are relatively small, indicating that the process settings are reasonable.

Pathways and Kinetics for Autocatalytic Reduction of CO2 into Formic Acid with Fe under Hydrothermal Conditions.

The utilization of CO2, as a cheap and abundant carbon source to produce useful chemicals or fuels, has been regarded as one of the promising ways to reduce CO2 emissions and minimize the green-house effect. Previous studies have demonstrated that CO2 (or HCO3–) can be efficiently reduced to formic acid with metal Fe under hydrothermal conditions without additional hydrogen and any catalyst. However, the pathways and kinetics of the autocatalytic CO2 reduction remain unknown. In the present work, the reaction kinetics were carefully investigated according to the proposed reaction pathways, and a phenomenological kinetic model was developed for the first time. The results showed that the hydrothermal conversion of HCO3– into formic acid with Fe can be expressed as the first-order reaction, and the activation energy of HCO3– is 28 kJ/mol under hydrothermal conditions.

A microwave irradiation-persulfate-formate system for achieving the detoxification and alkali-activated composite geopolymerization of the chromate-contaminated soil

A microwave (MA) irradiation-persulfate-formate system was constructed to detoxify Cr contamination and solidify the geopolymerization of the alkali-activated composite material. Three series of experiments were correspondingly conducted to evaluate the treatment for the chromate-contaminated soil. The changes in the molar ratios of formate to persulfate and the mass rates of fortifier to soil led to a significantly greater reduction of CrVI in the detoxification experiments. The increase of blast furnace slag from 50% to 80% in the composite cementitious materials (CCM) intensified the immobilization efficiencies of chromate and the compressive strengths of geopolymer blocks. MA irradiation potentially enhanced the binding of Ca cations to the aluminosilicate compounds. The degree of reaction in the phenomenological kinetics model mathematically verified the geopolymerization process. Ettringite was formed within the structure of the geopolymer in the coupling system. Sulfate radicals released from persulfate not only contributed to the detoxification process but also strengthened the immobilization process.

Mechanochemical Ignition of Self-propagating Reactions in Zn-S Powder Mixtures

The present work examines the mechanochemical reactivity of Zn-S powder mixtures subjected to mechanical processing by ball milling. Chemical composition, collision energy, powder charge inside the reactor, number of milling balls, Zn microstructure and temperature have been systematically varied to gain detailed information on the physical and chemical responses of reactant powders. It is shown that the mechanical activation of mixtures with intermediate Zn contents determines the ignition of self-sustaining high-temperature reactions that lead to the α and β ZnS line compounds and residual unreacted elements. Within the intermediate compositional range, ignition time decreases as the impact energy, the number of milling balls and the temperature increase and as the mass of powder decreases. In contrast, ignition times decrease as the hardness of Zn powder increases. Experimental findings are interpreted with the help of a phenomenological kinetic model.

Ion irradiation induced surface composition modulation in equiatomic binary alloys

Composition modulation by Ar bombardment on the Co0.5Cu0.5 alloy and the CoAl B2 phase was investigated on atomic scale by molecular dynamics simulation. The Ar bombardment on alloys at 300 K revealed that this bombardment induces a surface composition modulation in the layer-by-layer mode. In both the Co0.5Cu0.5 alloy and the CoAl B2 phase, the element of higher-sputtering yield is accumulated on the top surface layer, whereas it is depleted in lower layers, which is puzzling in the framework the conventional sputtering theory. A phenomenological kinetic model derived from the MD simulation results considering both the rearrangement and the sputtering of the substrate atoms successfully demonstrated that the rearrangement of the substrate atoms plays a significant role in the observed composition modulation.

An extended methodology for automated calculations of non-Boltzmann kinetic sequences: H + C2H2 + X and combustion impact

It is generally assumed in phenomenological kinetic models that bimolecular reactions only occur between species whose rovibrational energy follows a Boltzmann (thermal) distribution. That is, any complexes initially formed in non-Boltzmann distributions are assumed to be thermalized by energy-transferring collisions prior to bimolecular reactions. Given the high mole fractions of reactive species, X, in combustion environments, reactive collisions of the complexes with X often occur on the same timescale as energy-transferring collisions – yielding sequences proceeding through non-Boltzmann intermediates across multiple potential energy surfaces. Recent studies have shown that such non-Boltzmann kinetic sequences can have substantial impact on the global reactivity in combustion systems. Simulations of these non-Boltzmann reaction sequences, which can be described in phenomenological kinetic models via chemically termolecular reactions, require that rovibrational excitation from one potential energy surface be carried over to the next. This paper presents an extended theoretical and computational methodology that couples multiple master equations and derives rate constants for phenomenological reactions describing the conversion of thermal reactants to thermal products for use in phenomenological kinetic schemes. The methodology is then implemented using in-house scripts for non-Boltzmann sequences involving C2H3* + X (with X = O2, H, and OH) where C2H3* is formed via H + C2H2 association – which were identified as having strong potential for influencing combustion predictions in a recent study. The results reveal that non-Boltzmann reaction sequences for X = O2 (the primary focus of this paper) significantly alters the total conversion rate from H + C2H2 to products and product branching fractions from those of thermal sequential pathways. Furthermore, the present results demonstrate that non-Boltzmann reaction sequences have significant impact – as high as an order of magnitude – on predicted ignition delay times. Similarly, they yield significantly different dependence of ignition delay times with temperature and O2 mole fraction – yielding signatures that are likely observable experimentally.

An Alternative Parameterization of Relative Permeability and Capillary Pressure Curves

SummaryThis paper presents a theoretically rigorous correlation of the performance of capillary pressure and relative permeability of naturally fractured sandstone and carbonate reservoirs involving saturation shocks and loading/unloading hysteresis under various stress and thermal conditions. The proposed modeling approach accounts for the combined effects of the porous-rock alteration by various processes, including deformation, transformation, deterioration, and collapse of pore structure, under prevailing temperature and stress conditions during loading and unloading processes, and their effect on the capillary pressure and relative permeability of naturally fractured reservoirs. A saturation shock causing a slope discontinuity in the capillary pressure and relative permeability is shown to occur during saturation change in some sandstone- and carbonate-reservoir formations at a critical saturation condition. This phenomenon can be triggered by alteration of fluid-percolation pathways as a result of the transition from open to closed natural or induced fractures and the deformation of pore structure. The effect of the saturation shock and loading/unloading hysteresis on the capillary pressure and relative permeability of reservoir-rock formations is formulated by means of a phenomenological kinetics model and its applicability is demonstrated by analyzing and correlating the available experimental data.In this paper, the proven comprehensive model developed from a kinetics equation is shown to lead to a theoretically meaningful, universal, and practical constitutive equation in the form of a modified power law. This kinetics equation expresses the probability of dependence of a petrophysical property of porous rocks on a variable, such as saturation for capillary pressure and relative permeability, based on the value of the property relative to its low- and high-end limit values. The applicability of the modified power-law equation is validated by means of the experimental data of the capillary pressure and relative permeability gathered by testing of representative samples from various sandstone and carbonate reservoirs. The phenomenological parameters of the core samples obtained from sandstone and carbonate reservoirs are determined for best match of the experimental data with the modified power-law equation. The value of the critical fluid saturation is determined by the observance of a slope discontinuity occurring in the measured experimental data of the variation of the capillary pressure and relative permeability with saturation. The scenarios presented in this study indicate that loading/unloading hysteresis and saturation shock have significant effects on the stress- and temperature-dependent capillary pressure and relative permeability of the porous reservoir-rock formations. The data-inferred physics-based model presented in this paper is proved to describe the stress- and temperature-dependent capillary pressure and relative permeability of sandstone and carbonate rocks with high accuracy while meeting the endpoint-limit conditions satisfactorily.

Extended Rate Constants Distribution (RCD) Model for Sorption in Heterogeneous Systems: 2. Importance of Diffusion Limitations for Sorption Kinetics on Cryogels in Batch.

Here we address the problem of what we can expect from investigations of sorption kinetics on cryogel beads in batch. Does macroporosity of beads indeed help eliminate diffusion limitations under static sorption conditions? Are sorption rate constants calculated using phenomenological kinetic models helpful for predicting sorption properties under dynamic conditions? Applying the rate constants distribution (RCD) model to kinetic curves of Cu(II) ions sorption on polyethyleneimine (PEI) cryogel and gel beads and fines, we have shown that diffusion limitations in highly swollen beads are very important and result in at least ten-fold underestimation of the sorption rate constants. To account for intraparticle diffusion, we have developed the RCD-diffusion model, which yields “intrinsic” kinetic parameters for the sorbents, even if diffusion limitations were important in kinetic experiments. We have shown that introduction of a new variable—characteristic diffusion time—to the RCD model significantly improved the reliability of sorption kinetic parameters and allowed prediction of the minimal residence time in column required for efficient uptake of the adsorbate under dynamic conditions. The minimal residence time determined from kinetic curves simulated using the RCD-diffusion model was in good agreement with experimental data on breakthrough curves of Cu(II) ion sorption on monolith PEI cryogel at different flow rates.

Transfer of stored electrons between TiO2 polymorphs during photocatalytic H2 production in methanol–water medium

Mechanical mixtures of platinum-loaded and bare anatase, rutile and brookite TiO2 polymorphs were studied in the photocatalytic production of hydrogen (PHER) in methanol-water slurries. Mixtures of TiO2 and Pt/TiO2 materials show non-additivity of catalytic properties as a function of the nature of titania polymorphs involved. Addition of bare rutile or brookite to Pt/anatase leads to a drop of the PHER rate. By contrast, addition of bare anatase improves PHER activity of both Pt/rutile and Pt/brookite. These observations are coherently explained by directional transfer of long-live stored electrons between the particles in suspensions. Hydrogen release in the dark after addition of Pt/TiO2 to pre-illuminated bare TiO2 give evidence that such transfer is fast and have a pronounced directionality. The accumulated electrons are preferentially transferred from anatase to rutile or to brookite. A simple mechanistic framework and a phenomenological kinetic model are proposed that correctly describe the observed variations of PHER rates.

Phenomenological kinetic model of the nano-bainitic steels to characterize the dynamics of the autocatalytic nucleation process

A kinetic model has been proposed in the present work, which formulates the dynamic nature of autocatalysis. The autocatalytic factor is quantified in the present work which involves interaction energy between bainite nucleus and stress field generated by existing bainite. This interaction energy provides the stored energy for autocatalytic nucleation and eventually reduces the nucleation barrier of bainite transformation. The change in Gibbs free energy due to carbon partitioning will also alter the autocatalytic nucleation with the bainite transformation. The model also evaluates the activation energy due to dislocation barrier, which is arising by solid solution strengthening of austenite. The slow kinetics at low transformation temperature is due to the larger activation energy of the dislocation barrier, which provides greater resistance to atomic displacement during transformation. The interaction energy between bainite nucleus and stress field generated by existing bainite was validated by determining the transformation shear strain exhibited in austenite which was found to be in the range as reported in the literature for displacive transformations.

Synthesis of Ibuprofen Monoglyceride in Solventless Medium with Novozym®435: Kinetic Analysis

This study investigates the enzymatic esterification of glycerol and ibuprofen in a solventless medium catalyzed by immobilized lipase B from Candida antarctica (Novozym®435). Fixing the concentration of this enzymatic solid preparation at 30 g·L−1, and operating at a constant stirring speed of 720 rpm, the temperature was changed between 50 and 80 °C, while the initial concentration of ibuprofen was studied from 20 to 100 g·L−1. Under these conditions, the resistance of external mass transport can be neglected, as confirmed by the Mears criterion (Me < 0.15). However, the mass transfer limitation inside the pores of the support has been evidenced. The values of the effectiveness factor (η) vary between 0.08 and 0.16 for the particle size range considered according to the Weisz–Prater criteria. Preliminary runs permit us to conclude that the enzyme was deactivated at medium to high temperatures and initial concentration values of ibuprofen. Several phenomenological kinetic models were proposed and fitted to all data available, using physical and statistical criteria to select the most adequate model. The best kinetic model was a reversible sigmoidal model with pseudo-first order with respect to dissolved ibuprofen and order 2 with respect to monoester ibuprofen, assuming the total first-order one-step deactivation of the enzyme, with partial first order for ibuprofen and enzyme activity.