Classical Kinetic Model Research Articles

Efficient Elimination of Inorganic/Organic Pollutants by Fe3O4/biochar@sodium Alginate Gel Beads.

The magnetic composite gel bead (Fe3O4-C@SA GB) adsorbent was prepared by sodium alginate (SA) crosslinking with pitaya peel-derived porous carbons (PPDPCs) and magnetic iron oxide nanoparticles (Fe3O4 NPs). The adsorption effects of Fe3O4-C@SA GBs on heavy metal ions (HMIs) and 17 β-estradiol (E2) in water are evaluated by classical kinetic models and isotherm models. The pseudo-second-order kinetic model shows that Fe3O4-C@SA GBs have maximum adsorption capacities of 9.62, 7.50, and 13.61 mg/g for Cu (II), Cd (II), and Pb (II), respectively. Meanwhile, the highest adsorption performance of the synthesized gel beads to E2 is of ca. 276.3 mg/g. In addition, the Fe3O4-C@SA GBs can still maintain a high level of adsorption efficiency after five adsorption cycles, displaying economic efficiency and reusability. Hence, this work provides useful insights into the efficient adsorption elimination of pollutants in sewage and the corresponding adsorption mechanisms.

Influence of sodium hydrogen carbonate, ammonium dihydrogen phosphate, and lignin-based explosion inhibitors on the sensitivity of coal dust explosion

In order to prevent coal dust explosions, this study developed a targeted environmentally friendly and efficient lignin-based explosion inhibitor. The effects of NaHCO3, NH4H2PO4, and lignin-based explosion inhibitors on the sensitivity parameters of coal dust explosions were investigated using a 20 L spherical vessel and a Hartmann tube for comparison. Furthermore, the explosion inhibition mechanisms of the three inhibitors were elucidated through SEM, conductivity, In Situ FTIR, TGA-DTG/DSC, and other testing methods. The results indicate that from the perspective of explosion sensitivity, ZA-L-NP exhibits better explosion inhibition effects than NaHCO3 and NH4H2PO4. The zeolite carrier of the composite explosion inhibitor has a fine porous structure, with some materials filling the pores of the zeolite, resulting in a rough surface of ZA-L-NP. The use of ZA-L-NP for explosion suppression has a minimal impact on the turbulent combustion rate of coal dust. Its poor conductivity provides an advantage in inhibiting coal dust explosions. All three inhibitors exhibit significant inhibitory effects on the OH functional groups in coal dust, with inhibition effects decreasing in the order of ZA-L-NP, NH4H2PO4, and NaHCO3. Using classical kinetic models, the activation energy (E) and pre-exponential factor (A) of coal dust with and without added explosion inhibitors were calculated. Analysis was conducted from the perspective of kinetic parameters such as mass residual, maximum burning rate, average burning rate, flammability discrimination index, and comprehensive combustion characteristic index. It was found that the zeolite and modified lignin (L-NP) in ZA-L-NP synergistically increased the activation energy of coal dust. The research results can provide theoretical basis for the effective prevention of coal dust explosions.

Time-Dependent Multi-Particle Model Describing the Hydrogen Absorption of Nanocrystalline Magnesium Powders: A Case Study

Classical kinetic models describing the hydrogen absorption of nanocrystalline metallic hydrides generally do not involve any parameter related to the change in the crystallite size during the hydrogenation at constant temperature. In the present investigation, ball-milled nanocrystalline Mg powders exhibiting lognormal crystallite size distribution have been subjected to hydrogen absorption in a Sievert-type apparatus. Partially absorbed states were achieved by interrupting the hydrogenation cycle at different hydrogen content, i.e., when 15%, 50%, and 90% of Mg powder transformed to MgH2. The evolution of the characteristic size of the nucleating MgH2 phase was determined from X-ray diffraction analysis. Considering the crystallite size distribution of the as-milled powder agglomerate as well as the growth during the isothermal hydrogenation process, a time-dependent multi-particle reaction function ∝CV¯t;R(t) was developed. It was shown unambiguously for this case study that the measured hydrogen absorption curve of the ball-milled Mg powder shows the best correlation with this model when it is compared to classical kinetic functions or the previously developed multi-particle reaction function excluding the change in the average crystallite size during hydrogenation.

Moment methods for kinetic traffic flow and a class of macroscopic traffic models

Starting from a nonlocal version of a classical kinetic traffic model, we derive a class of second-order macroscopic traffic flow models using appropriate moment closure approaches. Under mild assumptions on the closure, we prove that the resulting macroscopic equations fulfill a set of conditions including hyperbolicity, physically reasonable invariant domains and physically reasonable bounds on the speed with which the waves propagate. Finally, numerical results for various situations are presented, illustrating the analytical findings and comparing kinetic and macroscopic solutions.

Enhanced flotation separation of aluminum electrolysis anode slag via microemulsification of diesel collector

Aiming at the defects such as poor dispersion and high consumption of conventional diesel collector in the flotation process of aluminum electrolysis anode carbon slag (CS), a microemulsion diesel collector was prepared, and its performance and mechanism in CS flotation were investigated by means of flotation experiments as well as modern analysis methods (surface tension, laser particle size, zeta potential, FTIR, etc.). A complex of sorbitan monooleate (Span 80) and cetyltrimethylammonium bromide (CTAB) was used as the primary surfactant, and the optimal formulation of the microemulsion collector was HLB of 8, co-surfactant of n-butanol, Km of 1.7, and oil-surfactant-water mass ratio of 27.80:27.8:44.40, and the droplet size of the obtained microemulsion collector was 62.22 nm. The flotation results showed that a carbon recovery of 74.48 % was obtained at a microemulsion collector dosage of 400 g/t, which resulted in a collector saving of 66.67 % with similar flotation indexes. The flotation process of microemulsion diesel for CS is in accordance with the classical first-level kinetic model, and its flotation rate is faster than that of conventional diesel. Analysis test results showed that microemulsification resulted in smaller droplet size and better dispersion of diesel collector in water, which enhanced its adhesion to carbon particles even at low reagent dosage. At the same time, the microemulsion diesel reduces the electronegativity of the CS particles and enhances the coverage of oxygenated functional groups on the carbon surface, thus enhancing the hydrophobicity of the carbon particles and improving its flotation recovery performance. This research can provide new theoretical basis and technical support for efficient waste disposal and resource recovery for CS.

Temperature inversion in a gravitationally bound plasma: Case of the solar corona

The temperature of the solar atmosphere increases from thousands to millions of degrees moving from the lower layer (chromosphere) to the outermost one (corona), while the density drops accordingly. The mechanism behind this phenomenon, known as a temperature inversion, is still unknown. In this work, we model a coronal loop as a collisionless plasma confined in a semicircular tube that is subject to the Sun’s gravity and in thermal contact with a fully collisional chromosphere behaving as a thermostat at the loop’s feet. By using kinetic N-particle simulations and analytical calculations, we show that rapid, intermittent, and short-lived heating events in the chromosphere drive the coronal plasma towards a non-equilibrium stationary state. The latter is characterized by suprathermal tails in the particles’ velocity distribution functions, exhibiting temperature and density profiles strikingly similar to those observed in the atmosphere of the Sun. These results suggest that a million-Kelvin solar corona can be produced without the local deposition of heat in the upper layer of the atmosphere that is typically assumed by standard approaches. We find that suprathermal distribution functions in the corona are self-consistently produced instead of postulated a priori, in contrast to classical kinetic models based on a velocity filtration mechanism.

A simulation study of the optimal experimental designs for a two-compartment kinetic model

The optimal design of nonlinear experiments is based on an optimality criterion that maximizes the Fisher information of an assumed model. In practice, however, we can be less certain about the actual performance or statistical efficiencies of the obtained designs that are jointly affected by the nonlinear model structure, the prior assumption, and the parameter estimation, all of which can make an optimal design underperform. For a realistic numerical evaluation of the designs, we implement a Monte Carlo simulation and parametric bootstrapping approach. In particular, we are interested in a classical second-order kinetic model, the structure of which is however unstable and vulnerable to random noises, as shown in our demonstration. As a result, the corresponding optimal designs are found to be inefficient, even so when the parameter prior is uninformative. Reasonable and robust model and prior assumptions are crucial for careful planning of future optimal design of experiments.

Investigation into the influence of droplet size on the stability of diesel emulsions based on multiple light scattering

Diesel oil emulsification is a common method to enhance the coal slime flotation, but difficult to apply industrially due to its unstable characteristics. In this paper, based on the multiple light scattering technique and the statistical Box-Behnken design (BBD) tests, the effect of the process parameters such as shear speed (A), shear time (B), and the mass ratio of SDBS to Span80 (C) on turbiscan stability index (TSI) value was systematically studied, and the relationship between emulsion stability and emulsion droplet size was also explored. The results showed that the destabilization of emulsified diesel (ED) was related to gravity migration and an increase in droplet size and was well fitted by the classical first-order kinetic model with R2 > 0.99. The significant order in which the three factors negatively affect the TSI value is, shear speed (A) > the mass ratio of SDBS to Span80 (C) > shear time (B), with shear speed ranging from 1000 to 16000 rpm, with shear time from 10 to 15 min, and with ratio of Span 80/SDBS from 0.45 to 1.48, respectively. Analysis of variance (ANOVA) revealed a high R2 value of the regression model equation (R2 = 0.9857) and fitted to a second-order polynomial equation using multiple regression analysis. The representative particle size (D50) has a positive linear correlation with the TSI value, indicating the smaller the particle size, the more stable the ED. The theoretical analysis using the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory and Stokes-Richardson-Zaki model demonstrated that the smaller ED droplets have the greater energy barrier to overcome before coalescing and lower rising velocity to move to the upper oil phase, and hence better stability.

Predicting micropollutant fate during wastewater treatment using refined classical kinetic model based on quantitative monitoring in multi-metropolitan regions of South Korea

This study aimed to implement an extensive prediction model for the fate of micropollutants (MPs) in wastewater treatment plants (WWTPs). Five WWTPs equipped with seven different biological treatment processes were monitored from 2020 to 2022 with three to four sampling events in each year, and 27 datasets for 20 MPs were collected. Among these datasets, 12 were used to investigate the behavior and fate of MPs in WWTPs in South Korea. Metformin, acetaminophen, caffeine, naproxen, and ibuprofen were the MPs with the highest influent concentrations (ranging from 3,933.3–187,637.0 ng L−1) at all WWTPs. More than 90% of MPs were removed by biological treatment processes in all WWTPs. The Kruskal-Wallis test verified that their efficacy did not differ statistically (p-value > 0.05). Meanwhile, to refine the performance of the prediction model, this study optimized the biodegradation rate constants (kbio) of each MP according to the variation of seasonal water temperature. As a result, compared to the original prediction model, the mean difference between the actual data and predicted results (MEAN) decreased by 6.77%, while the Nash-Sutcliffe efficiency (NSE) increased by 0.226. The final MEAN and NSE for the refined prediction model were calculated to be 5.09% and 0.964, respectively. The prediction model made accurate predictions, even for MPs exhibiting behaviors different from other cases, such as estriol and atrazine. Consequently, the optimization strategy proposed in this study was determined to be effective because the overall removal efficiencies of MPs were successfully predicted even with limited reference datasets.

Towards a better understanding of granular flows

Understanding the transport of particles immersed in a carrier fluid (bedload transport) is still an exciting challenge. Among the different types of gas–solid flows, when the dynamics of solid particles is essentially dominated by collisions between them, kinetic theory can be considered as a reliable tool to derive continuum approaches from a fundamental point of view. In a recent paper, Chassagne et al. (J. Fluid Mech., vol. 964, 2023, A27) proposed a two-fluid model based on modifications to a classical kinetic theory model (Garzó & Dufty, Phys. Rev. E, vol. 59, 1999, pp. 5895–5911). First, in contrast to the classical model, the model proposed by Chassagne et al. takes into account the interparticle friction not only in the radial distribution function but also through an effective restitution coefficient in the rate of dissipation term of granular temperature. As a second modification, at the top of the bed where the volume fraction is quite small, the model accounts for the saltation regime in the continuum framework. The theoretical results derived from the model agree with discrete simulations for moderate and high densities and they are also consistent with experiments. Thus, the model proposed by Chassagne et al. (J. Fluid Mech., vol. 964, 2023, A27) helps provide a better understanding of the combined impact of friction and inelasticity on the macroscopic properties of granular flows.

A frictional–collisional model for bedload transport based on kinetic theory of granular flows: discrete and continuum approaches

In this work, the modelling of collisional bedload transport is investigated with a focus on the continuum modelling of the granular flow. For this purpose, a frictional–collisional approach, combining a Coulomb model with the kinetic theory of granular flows, is developed. The methodology is based on a comparison with coupled fluid–discrete simulations that the classical kinetic theory model fails to reproduce. This inaccuracy may be explained by the assumptions of negligible interparticle friction and the absence of a saltation model in the continuum approach. In order to provide guidelines for the modelling, the fluctuating energy balance is computed in the discrete simulations and systematically compared with the kinetic theory laws. Interparticle friction is shown to affect the radial distribution function and to increase the energy dissipation, in agreement with previous observations. In addition, a saltation regime is identified, leading to departure from the viscosity and pseudo-thermal diffusivity laws of the kinetic theory in the dilute regime. Based on these observations, modifications to account for interparticle friction are included in the two-fluid model, and the kinetic theory is coupled with a saltation model. The results show that for inelastic frictional particles, interparticle friction controls energy dissipation, and the macroscopic behaviour of the granular flow does not depend on the microscopic particle properties. The proposed model reproduces the$\mu (I)$rheology in the dense regime of the granular flow. Finally, the model is evaluated with experiments, showing significant improvements concerning the granular flow modelling.

A Monte Carlo approach to study the effect of ions on the nucleation of sulfuric acid-water clusters.

The nucleation of sulfuric acid-water clusters is a significant contribution to the formation of aerosols as precursors of cloud condensation nuclei (CCN). Depending on the temperature, there is an interplay between the clustering of particles and their evaporation controlling the efficiency of cluster growth. For typical temperatures in the atmosphere, the evaporation of clusters is more efficient than the clustering of the first, small clusters, and thus their growth is dampened at its early stages. Since the evaporation rates of small clusters containing an ion are much smaller than for purely neutral sulfuric acid clusters, they can serve as a central body for the further attachment of molecules. We here present an innovative Monte Carlo model to study the growth of aqueous sulfuric acid clusters around central ions. Unlike classical thermodynamic nucleation theory or kinetic models, this model allows to trace individual particles and thus to determine properties for each individual particle. As a benchmarking case, we have performed simulations at a relative humidity of 50% with dipole and ion concentrations of and . We discuss the runtime of our simulations and present the velocity distribution of ionic clusters, the size distribution of the clusters as well as the formation rate of clusters with radii . Simulations give reasonable velocity and size distributions and there is a good agreement of the formation rates with previous results, including the relevance of ions for the initial growth of sulfuric acid-water clusters. Conclusively, we present a computational method which allows studying detailed particle properties during the growth of aerosols as a precursor of CCN.

Study of Carbonation-depth Prediction of Unsaturated Concrete Considering Carbonation-produced Water

Carbon dioxide can react with alkaline carbonate substances in cement-based materials, which harms the durability of the concrete structure. The carbonation reaction is a process of releasing water, resulting in an increase in pore water saturation, which was always neglected by previous studies. In this paper, a transient pore water saturation equation is proposed and introduced into the classical carbonation reaction kinetic model, which is simulated by finite-element software with a typical ordinary Portland cement. The model was verified by two classical empirical equations for carbonation-depth prediction. The simulation results indicated that the increment of pore water saturation originated by carbonation-produced water will weaken the CO2 diffusivity and enhance the carbonation resistance. Besides, the growth rate of carbonation depth is slightly faster without considering the produced water and with higher initial saturation, the difference will be more significant. If the influence of carbonation water is ignored, the predicted carbonation depth of unsaturated concrete may be less accurate. This study can provide some reference for theoretical and experimental studies on concrete carbonation. However, future work is still needed including more realistic effects in the model such as the mesoscale modeling of concrete and the integration of stress states. KEYWORDS: Ordinary Portland concrete, Carbonization reaction, Carbon-dioxide transport, Finite-element method, Pore saturation.

Multi-fractal modeling of curcumin release mechanism from polymeric nanomicelles

The physicochemical properties of “smart” or stimuli-sensitive amphiphilic copolymers can be modeled as a function of their environment. In special, pH-sensitive copolymers have practical applications in the biomedical field as drug delivery systems. Interactions between the structural units of any polymer-drug system imply mutual constraints at various scale resolutions and the nonlinearity is accepted as one of the most fundamental properties. The release kinetics, as a function of pH, of a model active principle, i.e., Curcumin, from nanomicelles obtained from amphiphilic pH-sensitive poly(2-vinylpyridine)-b-poly(ethylene oxide) (P2VP-b-PEO) tailor-made diblock copolymers was firstly studied by using the Rietger-Peppas equation. The value of the exponential coefficient, n, is around 0.5, generally suggesting a diffusion process, slightly disturbed in some cases. Moreover, the evaluation of the polymer-drug system’s nonstationary dynamics was caried out through harmonic mapping from the usual space to the hyperbolic one. The kinetic model we developed, based on fractal theory, fits very well with the experimental data obtained for the release of Curcumin from the amphiphilic copolymer micelles in which it was encapsulated. This model is a variant of the classical kinetic models based on the formal kinetics of the process.

Bridging ribosomal synthesis to cell growth through the lens of kinetics

Understanding prokaryotic cell growth requires a multiscale modeling framework from the kinetics perspective. The detailed kinetics pathway of ribosomes exhibits features beyond the scope of the classical Hopfield kinetics model. The complexity of the molecular responses to various nutrient conditions poses additional challenge to elucidate the cell growth. Herein, a kinetics framework is developed to bridge ribosomal synthesis to cell growth. For the ribosomal synthesis kinetics, the competitive binding between cognate and near-cognate tRNAs for ribosomes can be modulated by Mg2+. This results in distinct patterns of the speed – accuracy relation comprising “trade-off” and “competition” regimes. Furthermore, the cell growth rate is optimized by varying the characteristics of ribosomal synthesis through cellular responses to different nutrient conditions. In this scenario, cellular responses to nutrient conditions manifest by two quadratic scaling relations: one for nutrient flux versus cell mass, the other for ribosomal number versus growth rate. Both are in quantitative agreement with experimental measurements.

The effect of different clay minerals on the flotation kinetics of chalcopyrite

This study investigated the effects of clay minerals (montmorillonite, illite, and kaolinite) on chalcopyrite recovery and flotation kinetic parameters. Classical first-order flotation kinetic model was applied as a function of froth height and amount of clay minerals to fit overall flotation results on chalcopyrite recovery against flotation time. Clay minerals enhanced chalcopyrite recovery by mechanical entrainment and slime coating of valuable chalcopyrite particles. Flotation tests have shown that the deleterious impact of clay minerals on the chalcopyrite flotation is enhanced as follows: montmorillonite>kaolinite>illite. Montmorillonite significantly raised viscosity and also considerably diminished chalcopyrite grade. Recovery and selectivity were lower for montmorillonite than kaolinite and illite. The adjunct of illite was of little effect on chalcopyrite flotation kinetics. The obtained flotation rate constants indicate that clay minerals are carried to the concentrate together with the chalcopyrite. The flotation rate constants increased with increasing the amount of all clay minerals. Slime minerals easily entered to concentrate by mechanical entrainment, and the inhibition effect of clay particles on chalcopyrite became more obvious with increasing flotation time. However, the negative effect of clay minerals is reduced with high froth height.

Mathematical Modeling and Experiments on Pyrolysis of Walnut Shells Using a Fixed-Bed Reactor

Pyrolysis is a low-emission and sustainable thermochemical technique used in the production of biofuels, which can be used as an alternative to fossil fuels. Understanding the kinetic characterization of biomass pyrolysis is essential for process upscaling and optimization. There is no accepted model that can predict pyrolysis kinetics over a wide range of pyrolysis conditions and biomass types. This study investigates whether or not the classical lumped kinetic model with a three-competitive reaction scheme can accurately predict the walnut shell pyrolysis product yields. The experimental data were obtained from walnut shell pyrolysis experiments at different temperatures (300–600 °C) using a fixed-bed reactor. The chosen reaction scheme was in good agreement with our experimental data for low temperatures, where the primary degradation of biomass occurred (300 and 400 °C). However, at higher temperatures, there was less agreement with the model, indicating that some other reactions may occur at such temperatures. Hence, further studies are needed to investigate the use of detailed reaction schemes to accurately predict the char, tar, and gas yields for all types of biomass pyrolysis.

Digital light processing additive manufacturing of thin dental porcelain veneers

Digital light processing (DLP) 3D printing technology was applied to manufacture thin dental porcelain veneers. The prepared thin dental porcelain veneers showed excellent translucency and appearance. The median and mean particle sizes of the printed glass powders were 10.11 µm and 12.03 µm, respectively, with a unimodal distribution. The green glass compacts were printed layer by layer, with an individual layer thickness of 50 µm. The results showed that, according to the thermal expansion coefficient (TEC) and the thermogravimetry/differential scanning calorimetry (TG/DSC), the debinding procedure of the green glass compacts was annealed at 320 °C for 120 min and 570 °C for 120 min, respectively. The results of the classical sintering kinetics models and SEM examination demonstrated that the glass compacts were sintered at 790 °C for 5 min. The flexural strength and the chemical solubility of the sintered glasses were 132.58 ± 25.83 MPa and 18 μg·cm−2, respectively. Both flexural strength and chemical solubility met ISO 6872 criteria.

Isothermal crystallization kinetics in bulk of olefin-based multiblock copolymers

Isothermal crystallization kinetics of ethylene/1-octene (C2/C8) multiblock copolymers synthesized by chain shuttling technology is investigated. The samples are a reactor blend of segmented chains characterized by alternating crystalline and amorphous blocks with C8 content of 0.5 and 20 mol%, respectively, and statistical distribution of block number/chain and block length. The analysis is carried out after complete removal of a fraction (5–12 wt%), namely consisting of C8-rich blocks, through Kumagawa extraction with boiling diethyl ether. The resultant diethyl ether-insoluble fractions have similar average content of C8 units (≈13–14 mol%) and of crystalline blocks (≈23–27 wt%) but different molecular mass (the number average molecular mass Mn is ≈ 60–70 kDa for the samples 1,2 and ≈38 and ≈21 kDa for the samples 3 and 4, respectively). An additional sample with Mn ≈ 93 kDa, but a greater average content of C8 units (≈15 mol%) and a smaller content of crystalline blocks (15 wt%) is also analyzed. The crystallization half time of the samples increases with increase of Mn and, for each sample, its logarithm increases linearly with a decrease of the undercooling by a factor of -0.155/°C, for the samples 1–4 and −0.031/°C, for the sample 5. Using the classic kinetic crystallization model by Lauritzen and Hoffman, values of energy barrier constant due to contributions from primary nucleation KN and crystal growth KG are extracted. The KN contribution is esteemed to amount to ≈34% of the total barrier assuming regime II for the sample 5 and regime III (or I) for the samples 1–4, to ≈34% for the sample 5 and 67% for the samples 1–4, assuming regime II for all the samples. In all the cases, regardless of the assumed regimes, the KN values of the sample 5 are lower than those of the samples 1–4. As a final remark, the implications of crystallization kinetics on the solid-state morphology are also discussed, considering that transmission electron microscopy (TEM) images present a partially mesophase separated morphology for the samples 1,2, and 5 and a classic lamellar morphology for the samples 3 and 4.

Kinetic Model of Moisture Loss and Polyphenol Degradation during Heat Pump Drying of Soursop Fruit (Annona muricata L.)

The aim of this study is to investigate the impact of time and temperature of the heat pump drying process of soursop slices at different levels on moisture content and total polyphenol content (TPC). Twelve types of classical kinetic models have been used in this work to describe the suitability of experimental data with models. The conformity is assessed based on statistical values (e.g., coefficient of determination (R2), Chi–square value (X2), etc.). The loss of moisture in the material is described in accordance with Fick’s diffusion law. Value of moisture rate (MR), and effective moisture diffusivities (Deff) have been identified. Experimental results show that MR value depends on the time and drying temperature, Deff increases when increasing the drying temperature from 20–50 °C with values of 1.24 × 10−9, 1.85 × 10−8, 7.69 × 10−8, and 5.54 × 10−7 m/s2. The Singh et al. model is the best option to describe the moisture of the sliced soursop drying process at 30 °C (R2 = 0.97815). The largest TPC decomposition occurs at a temperature of 50 °C. The ability to decompose TPC is proportional to the drying temperature. The TPC decomposition dynamic model follows a first–order reaction when drying at 20 °C with a determinant coefficient R2 = 0.9693.