Two-parameter Kinetic Model Research Articles

Modeling of spatial spread of COVID-19 pandemic waves in Russia using a kinetic-advection model

Objectives. COVID-19 has a number of specific characteristics that distinguish it from past pandemics. In addition to the high infection rate, the high spread rate is due to the increased mobility of contemporary populations. The aim of the present work is to construct a mathematical model for the spread of the pandemic and identify patterns under the assumption that Moscow comprises the main source of viral infection in Russia. For this purpose, a twoparameter kinetic model describing the spatial spread of the epidemic is developed. The parameters are determined using theoretical constructions alongside statistical vehicle movement and population density data from various countries, additionally taking into account the development of the first wave on the examples of Russia, Italy and Chile with verification of values obtained from subsequent epidemic waves. This paper studies the development of epidemic events in Russia, starting from the third and including the most recent fifth and sixth waves. Our twoparameter model is based on a kinetic equation. The investigated possibility of predicting the spatial spread of the virus according to the time lag of reaching the peak of infections in Russia as a whole as compared to Moscow is connected with geographical features: in Russia, as in some other countries, the main source of infection can be identified. Moscow represents such a source in Russia due to serving as the largest transport hub in the country.Methods. Mathematical modeling and data analysis methods are used.Results. A predicted time lag between peaks of daily infections in Russia and Moscow is confirmed. Identified invariant parameters for COVID-19 epidemic waves can be used to predict the spread of the disease. The checks were carried out for the wave sequence for which predictions were made about the development of infection for Russia and when the recession following peak would occur. These forecasts for all waves were confirmed from the third to the last sixth waves to confirm the found pattern, which can be important for predicting future events.Conclusions. The confirmed forecasts for the timing and rate of the recession can be used to make good predictions about the fifth and sixth waves of infection of the Omicron variant of the COVID-19 virus. Earlier predictions were confirmed by the statistical data.

Effect of pumping and atomisation on the stability of oil/water emulsions

This work evaluated the effects of a peristaltic pump and a two-fluid pneumatic nozzle on the stability parameters of oil/water emulsions. Droplet size (DS), polydispersity index (PDI), Turbiscan® stability index (TSI), and wall material thicknesses were measured in emulsions with three different initial stabilities (most stable or ME, intermediate stable or IE, and less stable or LE) at different stages during their transport to the atomisation nozzle. Results indicated that pumping and atomisation gave place to more homogeneous emulsions in respect to the original one, having smaller sizes (0.98–1.29 μm), thicker shells (0.21–0.29 μm), and better stability as indicated by TSI (1.20–2.40), which kinetics were successfully fitted to a two-parameter kinetic model (R 2 = 0.99; RMSE <0.245). LE emulsion increased the most its stability because of its passage through the pump and nozzle due to greater instability differences in TSI. It was noted that, for all emulsions after their passage through the pump and nozzle, changes in stability were driven by coalescence. This study can contribute to determining operating conditions for encapsulating by spray drying. • Pumping and atomisation gave place to emulsions with smaller sizes, thicker shells, and improved stability. • Turbiscan stability index kinetics were well fitted to a two-parameter model. • The less stable emulsion increased the most its stability with pumping and atomisation. • Emulsion particles with higher stability had thicker shells.

A complete two-parameter kinetic model to describe the thermal pretreatment of biomasses

This study proposes a generalized approach to investigate the kinetics of thermal degradation of biomasses. The main purpose of this study aims to exploit the potentialities of the “model-free” methods in setting up an innovative computational procedure to completely describe the kinetics of thermal degradation processes involving organic materials and in particular biomasses. The proposed kinetic model enhances the features of the consolidated “isoconversional” procedures, conventionally limited only to activation energy determination, by introducing a new kinetic parameter (φα) in replacement of both the Arrhenius pre-exponential factor A and the f(a) reaction function. The usefulness of the model is achieved by implementing a suitable computational procedure based on an explicit Euler scheme easy executable. The achieved result provides an effective “two-parameter” kinetic model replacing, therefore, the conventional kinetic triplet modelling scheme. The novelty of the proposed approach is that it can be applied to study the thermal degradation of biomasses when submitted to different thermal pathways, isothermal or not and, furthermore, it can work as well in a predictive manner. Considering the limited amount of the required experimental data and the simplified form of the representative kinetic equation, this model looks particularly attractive to be generalized and extended to describe the kinetics of thermal processes involving whichever kind of organic and biologic substrates.

Development of a Reliable Kinetic Model for Ladle Refining

Kinetic modeling of ladle refining can be used by steel plants to improve steelmaking and to produce cleaner steels. It can also help researchers to understand the process better. There have been several recent attempts to develop a kinetic model that can predict changes in steel, slag, and inclusion compositions with time. Often the models require parameters that can be difficult to measure under plant conditions, and model limitations have not been discussed in detail. In this study, a two-parameter kinetic model has been developed to predict changes in steel, slag, and inclusion compositions during ladle refining; the two parameters are the mass-transfer coefficient in steel and the inclusion flotation rate constant. The model was based on FactSage macro-processing. Examples of results show that the model can be used to diagnose effects of steel and slag sampling practices and to estimate alloy dissolution time. The model results demonstrate that the presence of solids in slag can significantly reduce the rate of steel–slag reaction while maintaining a high inclusion flotation rate. Some limitations of the model are discussed: the overprediction of calcium transfer to alumina inclusions and the absence of information on inclusions originating from entrained slag.

Effect of Differences in the Primary Structure of the A-Chain on the Aggregation of Insulin Fragments.

Bovine and human insulin have similar primary structures. In this article, the region of the insulin A-chain of bovine and human insulin where the amino acid composition is different was studied. Bovine insulin fragment (BIF) and human insulin fragment (HIF) were synthesized in solid-phase peptide synthesis. The effects of pH, temperature, urea, ionic strength, and stirring on the formation of fibrils were studied using a fractional factorial resolution III experimental design. Fibrillation was monitored by fluorescence and infrared spectroscopy and optical microscopy. Both fragments formed fibrils at pH 1.6 and a temperature of 60 °C. The lag time and apparent aggregation growth rate constant were determined using a two-parameter kinetic model. It was found that the bovine insulin fragment has a shorter lag time than the human insulin one, whereas the exponential phase rate was faster for HIF than for BIF. An increase in β-sheets content with time was observed in both fragments. The increase in β-sheets was preceded by an initial decrease in α-helices followed by an intermediate increase during the transition from the lag phase to elongation phase. Temperature and ionic strength are among the most important experimental factors during the lag phase, whereas ionic strength is replaced by pH during the elongation phase for both the fragments. Congo red binding confirmed the presence of ringlike oligomer structures rich in antiparallel β-sheets, which tend to form fibrils rich in parallel β-sheets.

Experimental correlation for the formation rate of CO2 hydrate with THF (tetrahydrofuran) for cooling application

The CO2 hydrate formation experiments with THF (tetrahydrofuran) are performed in a stirred semi-bath reactor. The experimental data on CO2 hydrate formation are obtained at constant pressure and temperature with the low driving force conditions. The experimental temperature is above 279 K, which is high enough to prevent the formation of only THF hydrate. The Gibbs free energy difference by the pressure variation is chosen as the driving force. The experimental results confirm that the THF drastically reduces the required CO2 hydrate formation pressure. A two-parameter kinetic model based on the Chen-Guo model is developed to predict the CO2 hydrate formation rate and to correlate the experimental data. It is found that the experimental correlation based on the present estimation model fits well with the experimental results and can predict the CO2 hydrate formation rate satisfyingly for cooling application.

Two-Parameter Kinetic Model Based on a Time-Dependent Activity Coefficient Accurately Describes Enzymatic Cellulose Digestion

Lignocellulosic biomass is a potential source of renewable, low-carbon-footprint liquid fuels. Biomass recalcitrance and enzyme cost are key challenges associated with the large-scale production of cellulosic fuel. Kinetic modeling of enzymatic cellulose digestion has been complicated by the heterogeneous nature of the substrate and by the fact that a true steady state cannot be attained. We present a two-parameter kinetic model based on the Michaelis-Menten scheme ( Michaelis, L., and Menten, M. L. ( 1913 ) Biochem. Z. , 49 , 333 - 369 ) with a time-dependent activity coefficient analogous to fractal-like kinetics formulated by Kopelman ( Kopelman, R. ( 1988 ) Science 241 , 1620 - 1626 ). We provide a mathematical derivation and experimental support to show that one of the parameters is a total activity coefficient and the other is an intrinsic constant that reflects the ability of the cellulases to overcome substrate recalcitrance. The model is applicable to individual cellulases and their mixtures at low-to-medium enzyme loads. Using biomass degrading enzymes from cellulolytic bacterium Thermobifida fusca , we show that the model can be used for mechanistic studies of enzymatic cellulose digestion. We also demonstrate that it applies to the crude supernatant of the widely studied cellulolytic fungus Trichoderma reesei ; thus it can be used to compare cellulases from different organisms. The two parameters may serve a similar role to Vmax, KM, and kcat in classical kinetics. A similar approach may be applicable to other enzymes with heterogeneous substrates and where a steady state is not achievable.

The growth kinetics of hydrate film on the surface of gas bubble suspended in water or aqueous surfactant solution

A novel experimental method to study the hydrate formation kinetics on the gas/water interface was presented and, using this method, the two-dimensional growth kinetic data of hydrate film on the surface of quiescent methane gas bubble suspended in pure water, natural water and natural water added with different contents of sodium dodecyl sulfate (SDS) were measured and compared. The experimental results showed that the presence of the low dose of ions in natural water appreciably inhibited the hydrate formation; the presence of SDS promoted the hydrate growth when its concentration was lower than 1000 mg/L while it inhibited the hydrate formation beyond this region, the concentration of SDS corresponding to the most efficient promotion was determined to be 500 mg/L or so; the presence of low-dose ions in the natural water has little negative influence upon the promotion efficiency of SDS. A two-parameter kinetic model was developed to correlate the growth rates of hydrate films in different aqueous solutions consistently, where the dimensionless Gibbs free energy difference of hydrate formation reaction was chosen as driving force. Good agreement between calculated results and experimental data was achieved and only one parameter was found to be SDS concentration dependent. The mechanism that the presence of SDS affects the hydrate formation rate was discussed based on the experimental and theoretical results with some new insights. Additionally, the three-dimensional growth of hydrate shell covering the gas bubble was studied morphologically and a series of interesting phenomena were observed and discussed.

The effects of temperature, pH, and ammonia concentration on the inactivation of Ascaris eggs in sewage sludge

The reported inactivation of Ascaris eggs during alkaline sludge stabilization is highly variable. The objective of our research was to better understand the sources of this variability by quantifying the effects of temperature, pH, and ammonia concentration on the inactivation of indigenous Ascaris eggs in wastewater sludge. Primary sludge was supplemented with ammonia (0, 1000, and 5000 mg/l NH 3-N) and Ca(OH) 2 and incubated in sealed bottles across the range of temperatures (20, 30, 40, and 50 °C) and pH (7 and 12) that may be encountered during treatment. Changes in egg viability over time were fit to a two-parameter kinetic model (shoulder and first-order region); to compare treatment conditions, the time for 99% inactivation ( t 99) was also calculated. Each 10 °C increase in temperature caused a significant decrease in t 99 at every pH and ammonia concentration tested. At 50 °C, the effect of temperature was dominant, such that no effect of pH or ammonia was observed. At 30 and 40 °C, raising the pH from 7 to 12 decreased t 99, but at 20 °C no pH effect was seen over 80 d (very little inactivation occurred). At 20, 30, and 40 °C, the addition of ammonia dramatically decreased t 99. The effect of pH could not be completely separated from that of ammonia, as the unamended sludge samples contained 100–200 mg/l indigenous ammonia. Because temperature, pH, and ammonia all contributed to Ascaris egg inactivation, it is essential that these parameters are measured and accounted for when assessing the effectiveness of alkaline stabilization. Furthermore, inactivation by ammonia could be exploited to improve the effectiveness of alkaline sludge stabilization.

Kinetic model for the relationship between confined fission-track length shortening and fission-track age reduction in minerals

As a consequence of thermal treatment, fission tracks are shortened and a reduction of the surface density is expected, implying in a reduction of the fission-track age. Geometric considerations predict a linear relationship between track shortening and surface density reduction. However, experimental results for apatite, zircon and titanite found in literature, show a deviation from this relationship. Observation efficiency, crystallographic orientation, track segmentation and biases in length measurements have been invoked in order to explain the experiments, but do not succeeded in this aim. In this work, a model relating etching efficiency (via critical angle) with the amount of lattice defect (via mean track length) is proposed. It is assumed that the chemical etching obeys a rate law and that the observable means of densities and lengths are the net result from the mean actions of the orientation-dependent track and bulk etching velocities. The result is a two-parameter kinetic model described by the equation (ρ/ρ 0)=(l/l 0){1−[1+(kl 0(l/l 0)) n] −2}/{1−[1+(kl 0) n] −2}, where k and n are parameters related to the particular characteristics of the minerals. The model fits quite well the experimental data, showing that the general model principles (hypotheses and simplifications), provide a good general description of the processes causing the deviation detected by the experiments. The presented model does not discard, but embrace the previous attempts of explaining the relationship between fission-track lengths and densities.

Critique of Jar Testing for the Design of Coagulation-Flocculation Systems

Abstract The effects of clay type and concentration, jar shape, paddle shape, rapid mix time and flocculation velocity gradient on batch, bench-scale jar tests of turbidity were studied using a fractional factorial design. The two-parameter kinetic model for flocculation of Agraman, Kaufman and Bratby was used. This model provided a good fit of the data when they were log-transformed. The variables that had a statistically significant effect on the kinetics constants for floc agglomeration and breakup were the interaction of clay concentration and flocculation velocity gradient, plus clay type combined with rapid-mix time. The jar shape and the paddle shapes did not have significant effects. The kinetic constants measured in this analysis agreed with those reported previously by Agraman and Kaufman. The work assumes that turbidity is an acceptable measure of the number concentration. The results confirm the usefulness of the kinetic model and emphasize the importance of testing the goodness-of-fit of the model before analyzing the data.

Deuterium-hydride exchange in a single catalyst particle

The deuterium-neopentane exchange reaction on a single catalyst particle has been used to study the influence of intraparticle diffusion on product distribution. Experimental product distributions agree with those predicted by a two-parameter kinetic model. The parameters Φ and β representing diffusion limitation and desorption limitation, respectively, were varied independently by particle size reduction or catalyst pretreatment with oxygen. Thiele diffusion coefficients obtained from the deuterium-neopentane exchange experiments are about one-half of the Wicke-Kallenbach diffusion coefficients.