Multiparameter Equations Research Articles

Kinetic and Mechanistic Study of the Oxidation of Some Para-substituted Benzhydrols by Cetyltrimethylammonium Bromochromate using Spectrophotometric Technique

Objectives: This study investigates the oxidation of para-substituted benzhydrols by cetyltrimethylammonium bromochromate (CTMABC) in dimethylsulfoxide (DMSO), aiming to elucidate the reaction kinetics and solvent effects. Methods: The oxidation was carried out under pseudo-first-order conditions, showing first-order kinetics for both CTMABC and benzhydrols. The role of hydrogen ions in catalysis was examined, and the reaction was analyzed in 19 different organic solvents. Solvent effects were quantified using Kamlet’s and Swain’s multi-parametric equations. Findings: The reaction produced the corresponding benzophenones and demonstrated a first-order dependence on both reactants. The presence of hydrogen ions accelerated the reaction. Solvent studies indicated that solute-solvent interactions significantly influenced reactivity. Novelty: This research provides a comprehensive kinetic and mechanistic understanding of benzhydrol oxidation, utilizing a novel multi-parametric approach to analyze solvent impacts, offering new insights into solute-solvent interactions in oxidation processes. Keywords: Kinetics, Mechanism, Cetyltrimethylammonium bromochromate, Benzhydrol, Solvent effect

Biomechanical Analysis of Camellia oleifera Branches for Optimized Vibratory Harvesting

To investigate the biomechanical properties of Camellia oleifera branches under two loading speeds within a specific diameter range, three-point bending tests were conducted using a universal material–testing machine. The tests were performed at loading speeds of 10 mm/min and 20 mm/min on branches with diameters ranging from 5 mm to 40 mm. This study aims to provide insights into the design of a manipulator gripper used in a vibrating harvester for Camellia oleifera fruit. Four main varieties of Camellia oleifera were tested to determine their elastic modulus. The nonlinear least squares method, based on the hyperbolic tangent function, was employed to fit the bending load–deflection curves of the branches. This process constructed multi-parameter transcendental equations involving elastic modulus, diameter, and loading speed. Results indicated that the branches of four Camellia oleifera varieties exhibited significant differences in their biomechanical properties, with their modulus of elasticity ranging from 459.01 MPa to 983.33 MPa. This suggests variability in the bending performance among different varieties. For instance, Huaxin branches demonstrated the highest rigidity, while Huashuo branches were softer in general. For the proposed empirical fitting equations, when the fitting parameter k is 168 ± 20 and the parameter c is 3.102 ± 0.421, the bending load–deflection relationship of the branches can be predicted more accurately. This study provides a theoretical basis for enhancing the efficiency of mechanized vibratory picking of Camellia oleifera and optimising the design of the gripper.

Extrapolating into no man’s land enables accurate estimation of surface properties with multiparameter equations of state

Thermodynamic properties of homogeneous fluids in the metastable and unstable regions are needed to describe confined fluids, interfaces, nucleating embryos and estimate critical mass flow rates. The most accurate equations of state (EoS) called multiparameter EoS, have a second, non-physical Maxwell loop that renders predictions unreliable in these regions. We elaborate how information from the stable region can be used to reconstruct the metastable and unstable regions. For a simple interaction potential, comparison to results from molecular simulations reveals that isochoric expansion of the pressure from stable states reproduces simulation results in the metastable regions. By constructing a dome that extends above the critical point, we obtain an extrapolated pressure from multiparameter EoS that is free of second Maxwell loops. A reconstructed EoS is developed next, by integrating the extrapolated pressure from a stable state to obtain the Helmholtz energy. The consistency of the reconstructed EoS is gauged by computing phase equilibrium densities, pressures, and enthalpies of evaporation, which are in reasonable agreement with experimental values. Combined with density gradient theory, the reconstructed EoS yields surface tensions of water, carbon dioxide, ammonia, hydrogen and propane that deviate, on average, 4.4%, 1.6%, 6.0%, 0.7% and 5.4% from experimental values respectively. The results reveal a potential to develop more accurate extrapolation protocols, which can be leveraged to obtain prediction of metastable properties, surface properties or used as constraints in fitting multiparameter EoS.

Nonlinear evolution characteristics and seepage mechanical model of fluids in broken rock mass based on the bifurcation theory

With the deep extension of coal mining in China, fault water inrush has become one of the major disasters threatening the safety production of coal mine. Based on the control equations of steady state and non-Darcy seepage in fractured rock mass, the multi-parameter nonlinear dynamic seepage equations of fractured rock mass are established in this paper. Based on the nonlinear dynamics theory, the function of the state variable in the system is derived, and the influence of the gradual change of non-Darcy flow factors on the structural stability of seepage system is studied. The research achievements show that there are three branches in the equilibrium state of the seepage system. Specifically, the stability of the equilibrium state changes abruptly near the limit parameter. The seepage dynamic system of fractured rock mass has the delayed bifurcation, and the coal mine disaster such as fault water inrush occurs easily at the bifurcation point. The research results are of great significance to enrich the theory of fault water inrush in coal mine, and to reveal the disastrous mechanism of fault water inrush and guide its prevention and control technology in coal mine, which can provide the theoretical reference for predicting the water seepage stability in fractured rock mass.

Superancillary Equations for the Multiparameter Equations of State in REFPROP 10.0

Superancillary equations have been developed for the recommended (by NIST) multiparameter equations of state (EOS) for all 147 pure fluids in NIST REFPROP 10.0. These superancillary equations represent the orthobaric densities and saturation pressure of the EOS as a function of temperature by Chebyshev expansions to an accuracy better than the iterative calculations in REFPROP and are hundreds to thousands of times faster to evaluate than a full iterative solution of Maxwell’s criteria. The C++ code required to develop and test the superancillary equations is provided as open-source material. The methodology is straightforwardly extensible to new multiparameter EOS, establishing a new paradigm for the evaluation of vapor–liquid equilibria for pure fluids.

Experimental and Computational Kinetic Assessment of Ruthenium (III) Catalyzed Oxidation of Paracetamol by Hexacyanoferrate(III): A Mechanistic Pathway

AbstractThe ruthenium (III) catalyzed redox reaction of paracetamol with hexacyanoferrate (III) in an acidic medium has been investigated. The reaction shows fractional order dependence respecting paracetamol and first‐order dependence respecting the oxidant and ruthenium (III). It is enhanced by medium according to the equation kobs=a+b[H+]. The activation and thermodynamic parameters of the reaction have been estimated using the Arrhenius and Eyring equations. The oxidation product of paracetamol has been identified as quinone oxime through spectral analysis. Furthermore, the reaction has been examined in nine various organic solvents, and the solvents effect has been investigated by Taft's and Swain's multiparametric equations. The rate constants have been found to correlate well with Kamlet‐Taft's solvatochromic parameters (α, β, π*). The reaction constants have been found to be negative, suggesting that the reactivity is influenced mainly by the solute‐solvent interactions. On the basis of kinetic results, a plausible reaction mechanism has been proposed. The proposed mechanism is reinforced by additional evidence from density functional theory (DFT) computations conducted at b3lyp/6‐311*G (d,p) level, which demonstrate that the activation energy barriers align with the reactivity trend observed in the kinetics experiments. Therefore, these computational results provide further support for the proposed mechanism.

Inverse source problems for multi-parameter space-time fractional differential equations with bi-fractional Laplacian operators

<p>Two inverse source problems for a space-time fractional differential equation involving bi-fractional Laplacian operators in the spatial variable and Caputo time-fractional derivatives of different orders between 1 and 2 are studied. In the first inverse source problem, the space-dependent term along with the diffusion concentration is recovered, while in the second inverse source problem, the time-dependent term along with the diffusion concentration is identified. Both inverse source problems are ill-posed in the sense of Hadamard. The existence and uniqueness of solutions for both inverse source problems are investigated. Finally, several examples are presented to illustrate the obtained results for the inverse source problems.</p>

Энтропийная космология на основе модифицированной энтропии Шарма-Миттала на космологическом горизонте Вселенной

In the framework of entropic cosmology, several scenarios of the evolution of the Friedman-Robertson-Walker (FRW) Universe are considered, based on a new modification of the non-additive Sharma-Mittal and Renyi entropy measures on the cosmological horizon. This is done by replacing in the original logarithmic formulas for these entropies, the Tsallis entropy by the Barrow entropy associated with the modification of the horizon surface due to quantum gravitational effects. Several versions of the generalised multi-parametric FRW equations have been constructed, which can serve as an effective theoretical basis for describing the accelerating phase of the expansion of the late Universe. In the considered model there is no mutual interaction between the black components of the cosmos. The proposed approach, based on the use of non-additive extensive entropic measures on the cosmological horizon, meets the well-known requirements for thermodynamic modelling of the dynamical evolution of the Universe without involving the concept of hypothetical dark energy, but using the antigravity effect of entropic forces. The obtained results show that the generalised entropic formalism can open new possibilities for a deeper insight into the nature of spacetime and its fractal properties.

Digital simulation of load-bearing structures with movable cargo carts

The process of digital simulation of the design parameters of load-bearing structures when moving a cargo cart on them is developed on the example of a load-bearing beam of a crane (bridge. gantry, ...). This process includes three main stages. The first stage is the creation of appropriate mathematical multiparametric equations for automated simulation of: the values of reactions in the supports of the crane load-bearing beam; bending moments; transverse forces; displacements; beam deflection angles and maximum stresses at different positions of the cargo cart on the crane beam. The second stage is the creation of appropriate computer models in the Mathcad system using an effective functional programming language built into the system with a graphical representation of the simulation results depending on the location of the cargo cart on the load–bearing beam of the crane. The third stage is the animation simulation of the studied parameters, both for each parameter individually and all together.

An Analysis of the Critical Region of Multiparameter Equations of State.

In this work, two classes of defects with multiparameter equations of state are investigated. In the first, it is shown that the critical point provided by equation of state developers often does not exactly meet the criticality conditions based on the first two density derivatives of the pressure being zero at the critical point. Based on the more accurate locations of the critical points given in the first part, the scaling of the densities along the binodal and spinodal in the critical region are investigated, and we find that the vast majority of equations have reasonable behavior but a few do not.

A General Model for Thermodynamic Properties of Fluid Mixtures Based on Helmholtz Energy Formulations for the Components. Virial Expansion and Reduction to van der Waals Mixing Rules

Over the recent decades, Helmholtz energy formulations became available for a broad range of fluids. These multiparameter equations of state (R. Span, Springer 2000) allow computation of thermodynamic properties essentially within the experimental errorbars. Corresponding states-based model by Lemmon and Tillner-Roth (Fluid Phase Equilib 165:1, 1999) enabled construction of Helmholtz energy formulations for mixtures. However, we show that this model generates a non-physical dependence of virial coefficients on composition, which can be strong when the components are dissimilar. We propose a new mixture model that overcomes this deficiency. It has two main ingredients: (i) Quadratic mixing of “Helmholtz volumities”. This quantity with units of molar volume is introduced as a ratio of the molar residual Helmholtz energy to a product of gas constant, thermodynamic temperature, and molar density. It reduces to the second virial coefficient in the zero-density limit. Helmholtz volumities are considered for components and “cross-components”, hypothetical fluids representing the binary interactions. (ii) Replacing the variables—reduced reciprocal temperatures and reduced densities—with temperature and density scaling functions. Different scaling functions can be used for different components and cross-components, thus providing a highly flexible framework for representing the properties of mixtures. The scaling functions must be expandable into Taylor series in terms of molar concentrations in the zero-density limit. For the proposed mixture model, we develop formulas for computing virial coefficients up to the fourth order. Furthermore, we show that when the proposed mixture model is applied to a cubic equation of state, the conventional van der Waals mixing rules can be retrieved. These findings allow to consider the new model as a viable alternative to the corresponding states method of modeling thermodynamic properties of fluid mixtures.

Oxidation Kinetics of some Unsaturated Acids by Tributylammonium Chlorochromate: A mechanistic Study

The oxidation of maleic, fumaric, crotonic and cinnamic acids by tributylammonium chlorochromate (TBACC) in dimethylsulphoxide (DMSO) leads to the formation of corresponding epoxide. The reaction is of first order with respect to TBACC. A Michaelis-Menten type of kinetics are observed w.r.t. the acids. Due to non-aqueous nature of the solvents, toluene-p-sulphonic acid (TsOH) was used as the source of hydrogen ions. The reaction is catalysed by hydrogen ions. The hydrogen-ion dependence has the form: kobs = a + b [H+]. The oxidation of these acids was studied in nineteen different organic solvents. The solvent effect was analyzed by Kamlet’s and Swain’s multiparametric equations. Solvent effect indicated the importance of the cation-solvating power of the solvent. A mechanism involving a three-centre transition state has been postulated.

Flutter of carbon-based nanohybrid composite panels

Recently, carbon-based composite aerospace and mechanical structures have considerable attention due to their great material and mechanical properties. Carbon nanotubes (CNTs) or graphene platelets (GPLs) reinforcements for different matrices are common for the design of modern multilayer structures. In the present paper, the supersonic flutter of nanohybrid composite multilayer panels is examined and discussed. The nanohybrid multilayer panel is made of different technologically justified configurations of polymer layers reinforced by CNTs and GPLs The effective material properties of each CNTs and GPLs layer are determined according to two well-established homogenization techniques: the Mori–Tanaka scheme and the modified Halpin–Tsai model, respectively. Reddy’s third-order shear deformation theory is applied to avoid determining shear correction factors for different distributions of material properties. Hamilton’s principle and the first-order piston theory are applied to formulate aeroelastic coupled equations of motion of the panel. The numerical meshless method is employed to discretize dynamic equations and find generalized multi-parametric characteristic equations functionally dependent on the parameters of the structure with different boundary conditions. The accuracy of the obtained solution and results is examined by comparing the determined natural frequency and critical aerodynamic pressure with those obtained in previous studies. Then, a comprehensive parametric study is carried out to show the effects of hybridization of different distribution patterns of CNTs and GPLs, weight fractions, total layer number, and aspect ratio of hybrid composite panels on the flutter bounds. Results show that the present method provides a highly effective general numerical model for flutter analysis of hybrid nanocomposite panels with different boundary conditions for all thickness categories including thick plates. Moreover, an optimization nanoparticles distribution for the flutter of the nanohybrid composite panel has been obtained.

NIMOC: A design and analysis tool for supersonic nozzles under non-ideal compressible flow conditions

A computational tool for non-ideal supersonic nozzle flows is developed to perform direct design of nozzle geometries and flow analysis of shock-free off-design conditions. So-called non-ideal flows are characterized by the departure of the fluid thermodynamics from the ideal-gas law, which is the case of supersonic expansions close to the critical point, either in the superheated vapour or in the supercritical region. Deviations from the ideal-gas model of remarkable significance are observed in connection with, but not limited to, fluids made of complex molecules. NIMOC (Non-Ideal Method Of Characteristics) implements a formulation of the Method Of Characteristics (MOC) valid for non-ideal flows: the classical formulation of the MOC is complemented with state-of-the-art nonlinear multiparameter Equations of State (EoS) implemented in external thermodynamic libraries. NIMOC implements a two-dimensional and axisymmetric formulation of the MOC, which is applied to the solution of the isentropic expansion through nozzles of different geometrical configurations: straight-axis symmetric and axisymmetric conventional wind-tunnel nozzles, straight-axis symmetric and axisymmetric minimum-length nozzles, and asymmetric nozzles with curved meanline. Results are presented, which demonstrate nozzle design and flow analysis in the presence of paradigmatic non-ideal flow phenomena. Verification of MOC computations is performed by means of inviscid Computational Fluid Dynamics (CFD) simulations and experimental data. Results are presented for selected geometrical configurations.

Residual Entropy Scaling for Long-Chain Linear Alkanes and Isomers of Alkanes

Using residual entropy scaling approaches, transport properties, such as viscosity and thermal conductivity, can be linked to a thermodynamic property, i.e., residual entropy. It has been demonstrated in the literature that these approaches can be successfully used to correlate transport properties in the gas phase as well as the liquid phase over large temperature and density ranges. Recently, Yang et al. [ J. Chem. Eng. Data 2021, 66(3), 1385–1398] proposed a residual entropy scaling approach for the viscosity of 39 refrigerants and their mixtures, and they extended this approach in a subsequent work to 124 fluids [ Int. J. Thermophys. 2022, 43(12), 183]. The method of Yang et al. requires a fluid-specific scaling factor for each fluid. Yang et al. proposed a method for estimating this parameter as being proportional to the residual entropy at the critical point. In this work, it is demonstrated that for hydrocarbons, the fluid-specific scaling factor can be better approximated as a linear function of the longest carbon chain. All linear and branched alkanes for which accurate multiparameter equations of state are available have been considered in this work. Furthermore, the performance of other predictive equations of state, i.e., the Peng–Robinson and Lee–Kesler–Plöcker equations of state, is evaluated.

Structure-reactivity relation in the oxidation of some aliphatic aldehydes by Tripropylammonium chlorochromate

The oxidation of six aliphatic aldehydes by tripropylammonium chlorochromate (TPACC) in dimethyl sulfoxide (DMSO) leads to the formation of corresponding carboxylic acids. The reaction is of first order each in TPACC. A Michaelis-Menten type of kinetics is observed with respect to the aldehydes. The reaction is catalysed by hydrogen ions. The hydrogen-ion dependence has the form: kobs = a + b[H+]. The oxidation of deuteriated acetaldehyde MeCDO exhibited a substantial primary kinetic isotope effect (kH/kD = 5.75 at 298 K). The oxidation of acetaldehyde has been studied in nineteen different organic solvents. The solvent effect has been analysed using Taft's and Swain's multiparametric equations. The rate constants correlate well with Taft’s * values, reaction constants being negative. A mechanism involving transfer of hydride ion has been suggested.

Study of microwave cooking of legumes with excess water: The case of chickpeas

In the context of the agro-ecological transition towards sustainable systems, legumes are a real opportunity in terms of agronomy and nutrition. The development of vegetable seed consumption is currently hampered by the problem of the long hydration and cooking stages of current processes. Low CO2 emission processes, such as microwave treatment, are preferred. The efficiency of these processes relies on the transformation of the energy contained in an electromagnetic wave into heat within materials with dielectric losses. The objective of the presented work is to study the evolution of the characteristics of leguminous seeds during the operation of cooking in excess of water by microwave treatment. Kinetics of texture modification and mass gain of the seeds were performed for three different levels of microwave power (between 400 and 1200 W) and compared to hot plate cooking. Empirical models by multi-parameter equations were proposed and validated by a 1000 W treatment. The results show that the evolution of hardness and mass gain is strongly related to the evolution of mass transfer coupled with volume heat transfer phenomena, specific to electromagnetic wave heating. Two different profiles of hardness and mass gain were observed depending on the type and intensity of the treatment. This work is a preliminary experimental study allowing to express hypotheses, which will be validated later by a more thorough study.

Oxidation Kinetics of some Lower Oxyacids of Phosphorus by Picolinium Chlorochromate: Determination of Reactive Reducing Species

Picolinium chlorochromate (PICC) in dimethylsuloxide (DMSO) oxidizes lower oxyacids of phosphorus, forming matching oxyacids with phosphorus in a higher oxidation state. The reaction shows a stoichiometry of 1:1. In relation to PICC, the response is first order. Regarding the reductants, a kinetics of the Michaelis-Menten type was noticed. Acrylonitrile does not undergo polymerization as a result of the reaction. Hydrogen ions function as catalysts for reactions. The form of the hydrogen-ion dependency is: kobs = a + b[H+]. Deuterated phosphinic and phenylphosphinic acids showed a significant primary kinetic isotope impact during oxidation. Nineteen different organic solvents were used to study the oxidation. The multiparametric equations of Taft and Swain were used to analyze the solvent effects. The influence of the solvent shows that the polarity of the solvent is crucial to the process. The penta-coordinated tautomer of the phosphorus oxyacid has been shown to be the reactive reductant, and it has been determined that the tricoordinated forms of phosphorus oxyacids do not take part in the oxidation process. It has been hypothesized that the rate-determining phase involves the transfer of a hydride ion.

Correlation analysis of reactivity in the oxidation of some vicinal and non-vicinal diols by Tributylammonium chlorochromate: A kinetic and mechanistic approach

The kinetics of oxidation of four vicinal, four non-vicinal diols by tributylammonium chlorochromate (TBACC) has been studied in dimethylsulphoxide (DMSO). The main product of oxidation is the corresponding hydroxycarbonyl compound. The reaction is first order each in TBACC. Michaelies-Menten type of kinetics is observed with respect to the diols. The reaction is catalysed by hydrogen ions. The hydrogen ion dependence is taking the form: kobs = a + b[H+]. The oxidation of [1,1,2,2-2H4] ethanediol exhibits a substantial primary kinetic isotope effect (kH/kD = 5.81 at 298 K). The reaction has been studied in nineteen different organic solvents and the solvent effect has been analysed using Taft's and Swain's multiparametric equations. The temperature dependence of the kinetic isotope effect indicates the presence of a symmetrical transition state in the rate-determining step. A suitable mechanism has been proposed.

Predicting the sound speed of seafloor sediments in the Middle area of the Southern Yellow Sea based on a BP neural network model

Based on the data of the sound speed and the physical–mechanical properties of 300 seafloor sediment samples collected in the middle area of the Southern Yellow Sea, a backpropagation (BP) neural network algorithm is used herein to study the neural network topology and the corresponding neuron characteristic factors. A neural network model for predicting the sound speed of the seafloor sediment based on density, water content, porosity, void ratio, liquid limit, plastic limit, and clay content in the middle area of the Southern Yellow Sea is established. The results show that the sound speed prediction accuracy is the highest when the network model contains seven input layer neurons, ten hidden layer neurons, and one output node. According to the prediction results, the MAE(Mean Absolute Error) and the MAPE(Mean Absolute Percentage Error) are 13.19 m s−1 and 0.85%, respectively. The prediction results illustrate that the established BP neural network prediction method for the seafloor sediment sound speed is better than the traditional single, two and multi-parameter prediction equations.