Basic Kinetic Equation Research Articles

Thermoporometry of mesoporous carbons: Application of octamethylcyclotetrasiloxane as probe liquid for small mesopores

The mesoporosity of carbons can be determined using traditional methods such as gas physisorption or mercury intrusion, as well as by an alternative technique, thermoporometry (TPM). TPM focuses on determining porosity in the wet state. If water is used as probe liquid, the mesopores larger than 10 nm are hard to evaluate due to the overlapping of pore and bulk melting peaks. To overcome this problem, octamethylcyclotetrasiloxane (OMCTS) is used. Due to the fact that OMCTS undergoes solid-solid phase change in the same temperature range as melting in small mesopores, its use for mesopores below 10 nm is problematic. Thus, the applicability of OMCTS as a probe liquid for TPM characterization of small mesopores was tested in this work. The separation of melting in small pores from solid-solid transition was elaborated by several approaches like changes of heating rate, implementation of prefreezing step, deconvolution of experimental DSC records with the use of basic kinetic equation as underlying functions). It was found that the prefreezing step and a measurement of pure OMCTS under the same conditions as expected for TPM measurement is useful since the solid-solid transition depends on the measurement conditions. The usefulness of the suggested measurement conditions and deconvolution method was successfully demonstrated on carbonaceous samples with exclusively small mesopores (5 nm), as well as carbons containing both small and large mesopores. The results indicate that this approach enables the investigation of the entire mesoporous range and makes OMCTS a more versatile probe liquid for TPM.

Thermogravimetric approach to efflorescence of sodium carbonate decahydrate

The efflorescence of sodium carbonate decahydrate (SC-DH), characterized by the solid-state thermal dehydration to form its monohydrate (SC-MH), occurs below its melting point positioned slightly above room temperature and at a lower atmospheric water vapor pressure (p(H2O)). Applying a thermogravimetry (TG) that covers temperatures lower than room temperature enabled us to systematically trace the efflorescence of SC-DH under various heating programs in a dry N2 stream, using which the kinetics of the efflorescence was formally described by the basic kinetic equation. Meanwhile, when the sample temperature reached the melting point of SC-DH midway through the efflorescence process, the thermal dehydration switched from solid-state mode to liquid-state one and exhibited a complex multistep mass loss behavior to form SC-MH. The multistep mass loss behavior and its changes with the reaction conditions were overviewed using a humidity-controlled TG at various atmospheric p(H2O).

Physics of turbulence spreading and explicit nonlocality

In this paper, we systematically derive a model for turbulence spreading from the basic kinetic equation. The model contains explicit nonlocal nonlinear diffusion and nonlocal growth. When the nonlocality scale parameter δ b (banana width) vanishes, this model reduces to the usual turbulence spreading model. We elucidate the mechanisms of nonlinear saturation and nonlocal growth. Results show that nonlocal effects, especially the nonlocal growth, thicken the turbulence spreading front and increase the speed of front propagation. More turbulence intensity penetrates the stable region when δ b increases. The penetration depth Δ p is proportional to , therefore the fraction of turbulence in the unstable region scales as 1 − δ b*. The transport scales the same way.

Распределение кислородных вакансий во внешнем электрическом поле и кислородная проводимость в акцепторно допированных ионных проводниках флюоритной структуры

The distribution of current carriers over the lattice sites in the fluorite structure of (AO₂)₁₋ₓ(BO₁.₅)ₓ oxides for the region of not too large values of the dopant concentration in an external electric field has been calculated by solving the basic kinetic equation under stationary conditions. The influence of carrier redistribution in the external field on the value of ionic conductivity and the position of the maximum of its dependence on the impurity content has been studied. The conductivity is considered in the framework of a model in which the impurity effect on transport is reduced to blocking jumps of current carriers along the edges of the oxygen lattice closest to the dopant ions. The analytical results are confirmed by numerical calculations using the Monte Carlo method and can be used to explain the position of experimentally observed maxima of the dependence of conductivity on the dopant concentration in such structures.

On the origin of alkali feldspar megacrysts in granitoids: the case against textural coarsening

Alkali feldspar megacrysts (up to 20 cm in length) are common in granitoids, but their origin has been a matter of continued debate. In particular, the relative role of various magmatic and subsolidus processes has proven difficult to assess given the protracted crystallization history of these megacrysts. Textural coarsening (also known as Ostwald ripening) has been invoked to explain the extraordinarily large sizes of these feldspar megacrysts. While coarsening is a thermodynamically spontaneous process, it is important to evaluate the timescales in which it operates during magmatic evolution. In this work, we consider theories of coarsening of a second phase in the melt in binary systems to evaluate if coarsening can explain the origin of alkali feldspar megacrysts in granitoids. The theories explored are all approximate and somewhat incomplete; however, all of them predict the same basic kinetic equation for the coarsening process. Calculation of the fundamental rate constant controlling the coarsening processes requires determination of parameters that are not particularly well constrained for minerals in silicate melts. Nonetheless, we demonstrate that diffusion rates are the main control on the rate constant for coarsening. Using a range of rate constants calculated using suitable parameters for silicate magmatic systems, we show that coarsening in silicate magmas cannot lead to crystals larger than tens of µm on timescales relevant for igneous processes. The timescales required to generate millimeter to centimeter crystals by coarsening are so prohibitively large that the weaknesses of the existing kinetic theories becomes unimportant, and the idea of generating megacrysts via textural coarsening can be conclusively abandoned. The origin of feldspar megacrysts probably results from the interplay between nucleation and growth rates in magmas, a problem that has not been dealt in detail in the literature.

Estimation of the kinetic triplet for in-situ combustion of crude oil in the presence of limestone matrix

Efficient design of in-situ combustion depends on accurate kinetic modeling of the crude oil oxidation. Kinetic triplet of the crude oil combustion was obtained and effect of the limestone matrix on kinetic triplet was investigated. Once the kinetic triplet is known, the basic kinetic equation would be deconvolved. Crude oil Samples (both pure and mixed with limestone) were analyzed using Differential Scanning Calorimetry (DSC) under atmospheric pressure at 297K–973K in four different heating rates. Three isoconversional kinetic models were used to obtain a variation of Arrhenius parameters during the course of the reaction. The presence of the limestone decreased activation energy (Eα) probably due to increased surface area. Moreover, both values and standard deviation of the preexponential factor (A) would be decreased due to the presence of limestone. Having Arrhenius parameters, the conversion function, f(α), was estimated using an advanced master plot method. It was observed that f(α) follows the Avrami–Erofeev (An) model with n=3. Furthermore, parameters of truncated Sestak–Berggren (SB) reaction model were obtained. It was shown that the SB was slightly better than A3 in fitting the experimental data. According to the results, neither change of heating rates nor addition of limestone caused a considerable change of the reaction model; HTO region in each case follows A3 model.

Research on ricochet and its regularity of projectiles obliquely penetrating into concrete target

To address the ricochet problem in penetration process, the mathematical model of projectile penetrating into concrete target is established according to the basic kinetic equation and surface layer mechanism. The motion trajectory of projectile nose is obtained. Experimental studies on projectiles with different nose penetrating into concrete targets are conducted to explain the ricochet problem. These studies analyze fifty-four penetration conditions under different initial velocities and oblique angles when the projectiles have flat, hemispherical, ogive noses and conical noses. The regularity and critical angles of ricochet are analyzed with different nose shapes at different velocities. Results show that the ricochet angle increases depending on nose sharp and penetration velocity. The factors affecting the ricochet from big to small were analyzed via orthogonal test. The results show that with increasing the velocity from 652 m/s to 1022 m/s, the critical angle increases from 44° to 66°. The order of factors affecting the ricochet from big to small is the shape of the nose, the material of the projectiles and the penetrating velocity respectively.

Brownian system in energy space

The main goal of this article is to present a simple way to describe non-equilibrium systems in energy space and to obtain new spacial solution that complements recent results of B.I. Lev and A.D. Kiselev, Phys. Rev. E82, (2010) 031101. The novelty of this presentation is based on the kinetic equation which may be further used to describe the non-equilibrium systems, as Brownian system in the energy space. Starting with the basic kinetic equation and the Fokker-Plank equation for the distribution function of the macroscopic system in the energy space, we obtain steady states and fluctuation relations for the non-equilibrium systems. We further analyze properties of the stationary steady states and describe several nonlinear models of such systems.

Vacuum particle creation under action of a strong external field: an example of irreversible behavior of a system with time reversal symmetry

On the basis of a kinetic equation (KE) of the Vlasov type, which is a strong non-perturbative consequence of the QED equations of motion in the quasiparticle representation, we investigate the irreversible behavior of the electron-positron plasma (EPP) created from vacuum under action of a pulsed external quasiclassical field. The basic KE is upon time reversal. Nevertheless the EPP reveals some features characteristic for irreversible processes. The nondecreasing entropy principle is introduced for the asymptotic in- and out-states: S out ≥ S in . Some features of the entropy evolution are investigated for different excitation levels of the EPP.

Proton-driven spin diffusion in rotating solids via reversible and irreversible quantum dynamics

Proton-driven spin diffusion (PDSD) experiments in rotating solids have received a great deal of attention as a potential source of distance constraints in large biomolecules. However, the quantitative relationship between the molecular structure and observed spin diffusion has remained obscure due to the lack of an accurate theoretical description of the spin dynamics in these experiments. We start with presenting a detailed relaxation theory of PDSD in rotating solids that provides such a description. The theory applies to both conventional and radio-frequency-assisted PDSD experiments and extends to the non-Markovian regime to include such phenomena as rotational resonance (R(2)). The basic kinetic equation of the theory in the non-Markovian regime has the form of a memory function equation, with the role of the memory function played by the correlation function. The key assumption used in the derivation of this equation expresses the intuitive notion of the irreversible dissipation of coherences in macroscopic systems. Accurate expressions for the correlation functions and for the spin diffusion constants are given. The theory predicts that the spin diffusion constants governing the multi-site PDSD can be approximated by the constants observed in the two-site diffusion. Direct numerical simulations of PDSD dynamics via reversible Liouville-von Neumann equation are presented to support and compliment the theory. Remarkably, an exponential decay of the difference magnetization can be observed in such simulations in systems consisting of only 12 spins. This is a unique example of a real physical system whose typically macroscopic and apparently irreversible behavior can be traced via reversible microscopic dynamics. An accurate value for the spin diffusion constant can be usually obtained through direct simulations of PDSD in systems consisting of two (13)C nuclei and about ten (1)H nuclei from their nearest environment. Spin diffusion constants computed by this method are in excellent agreement with the spin diffusion constants obtained through equations given by the relaxation theory of PDSD. The constants resulting from these two approaches were also in excellent agreement with the results of 2D rotary resonance recoupling proton-driven spin diffusion (R(3)-PDSD) experiments performed in three model compounds, where magnetization exchange occurred over distances up to 4.9 Å. With the methodology presented, highly accurate internuclear distances can be extracted from such data. Relayed transfer of magnetization between distant nuclei appears to be the main (and apparently resolvable) source of uncertainty in such measurements. The non-Markovian kinetic equation was applied to the analysis of the R(2) spin dynamics. The conventional semi-phenomenological treatment of relxation in R(2) has been shown to be equivalent to the assumption of the Lorentzian spectral density function in the relaxatoin theory of PDSD. As this assumption is a poor approximation in real physical systems, the conventional R(2) treatment is likely to carry a significant model error that has not been recognized previously. The relaxation theory of PDSD appears to provide an accurate, parameter-free alternative. Predictions of this theory agreed well with the full quantum mechanical simulations of the R(2) dynamics in the few simple model systems we considered.

Modeling of the coalescence of gas pores during annealing

The kinetics of the coalescence of gas bubbles under the conditions of high-temperature annealing is modeled. The case where the growth of gas pores is controlled by thermal dissolution of gas atoms from bubbles is examined. The modeling is performed by solving the basic kinetic equation numerically. The numerical calculations are compared with the results of an analytical model which describes the asymptotic behavior of the gas pores. The time characteristics of the process which are obtained in this work are at variance with the results of the analytical model. The discrepancies found are discussed.

Study of the volume condensation process in supersaturated vapor by the direct numerical solution of the kinetic equation for the droplet size distribution function

The volume condensation of supersaturated vapor is investigated by the direct numerical solution of the basic kinetic equation for the droplet size distribution function by analogy with the corresponding solution of the Boltzmann kinetic equation. The proposed consideration of the condensation growth of droplets is applicable at any Knudsen number. The method is tested by the example of vapor condensation under the conditions of the rapid development of supersaturation in a vapor-gas mixture as a result of its adiabatic expansion. In a wide range of Knudsen numbers, the results of the modeling are compared with those obtained by the moment method.

On the possibility of modeling the bulk condensation of supersaturated vapor by the method of direct numerical solution of the basic kinetic equation

On the possibility of modeling the bulk condensation of supersaturated vapor by the method of direct numerical solution of the basic kinetic equation

Comparing macroscopic continuum models for rarefied gas dynamics: A new test method

We propose a new test method for investigating which macroscopic continuum models, among the many existing models, give the best description of rarefied gas flows over a range of Knudsen numbers. The merits of our method are: no boundary conditions for the continuum models are needed, no coupled governing equations are solved, while the Knudsen layer is still considered. This distinguishes our proposed test method from other existing techniques (such as stability analysis in time and space, computations of sound speed and dispersion, and the shock wave structure problem). Our method relies on accurate, essentially noise-free, solutions of the basic microscopic kinetic equation, e.g. the Boltzmann equation or a kinetic model equation; in this paper, the BGK model and the ES-BGK model equations are considered. Our method is applied to test whether one-dimensional stationary Couette flow is accurately described by the following macroscopic transport models: the Navier–Stokes–Fourier equations, Burnett equations, Grad’s 13 moment equations, and the regularized 13 moment equations (two types: the original, and that based on an order of magnitude approach). The gas molecular model is Maxwellian. For Knudsen numbers in the transition-continuum regime ( Kn ⩽ 0.1), we find that the two types of regularized 13 moment equations give similar results to each other, which are better than Grad’s original 13 moment equations, which, in turn, give better results than the Burnett equations. The Navier–Stokes–Fourier equations give the worst results. This is as expected, considering the presumed accuracy of these models. For cases of higher Knudsen numbers, i.e. Kn > 0.1, all macroscopic continuum equations tested fail to describe the flows accurately. We also show that the above conclusions from our tests are general, and independent of the kinetic model used.

The influence of memory effects on dispersions of kinetic energy at nuclear fission

Within the nuclear Fermi-liquid approach, the memory effect on the Landau–Vlasov–Langevin dynamics is considered. The basic collisional kinetic equation for the Wigner distribution function is reduced to a macroscopic equation of motion for the shape variables of the nucleus. Parametrizing the potential energy of the nucleus at descent from the fission barrier by the inverted oscillator potential, we derive analytical expressions for the mean value, ⟨Ekin, ps⟩, and the variance, σ(Ekin, ps), of the pre-scission kinetic energy. We show that the memory effect hinders the values of ⟨Ekin, ps⟩ and σ(Ekin, ps) due to an additional elastic force originating from the memory integral. The hindrance effect increases with the increase of the relaxation time.

Application of direct nonlinear regression from single TG curve to compounds undergoing simple and complex thermal decompositions

Nonlinear regression of the basic kinetic equation was used to determine kinetic parameters of simple and complex decomposition processes related to some pesticides and pharmaceutical substances. The method for this calculation was carried out using a single TG curve. These values were compared with those obtained with model-fitting and model-free methods. Nonlinear regression method is able to define a single mechanism for compounds undergoing one or few steps of decomposition processes. For compounds that undergo many steps of decomposition processes, only the mechanisms of some of them can be hypothesized. © 2003 Wiley Periodicals, Inc. Int J Chem Kinet 35: 611–622, 2003

Kinetic simulation of a quasisteady state in collisionless ion temperature gradient driven turbulence

Existence of a quasisteady state with a mean transport flux in the collisionless ion temperature gradient driven turbulence has been confirmed by means of a direct numerical simulation of a basic kinetic equation for the perturbed ion velocity distribution function δf. The phase mixing generates fine-scale fluctuations of δf and leads to continuous growth of high-order moments which balances the transport flux. The phase relation between the temperature and the parallel heat flux is also examined and compared with a fluid closure model.

Recombination population of highly excited CO2 states in a shock-heated jet

The spectral distribution of nonequilibrium emission from electron bands of partially dissociated CO2 in a supersonic jet was studied. A detailed model of kinetic and energy-exchange processes in a vibrationally nonequilibrium recombining CO2 flow is elaborated. Within this model, the basic kinetic equation for the distribution of CO2 excited state populations was solved in a ladder approximation. It is shown that inverse population for the 3B2 → X1Σ transition (λ=400 nm) is a possibility. The effect of mixture and flow parameters on the population inversion for electron vibrational transitions in CO2 was analyzed.

A thermodynamic approach to the systematic elucidation of unique reaction routes in catalytic reactions

The directness (uniqueness) of both reaction routes (mechanisms) and overall reactions is deduced from chemical thermodynamics. Namely, starting from general thermodynamic relations, the basic kinetic equation is shown to be identically transformed so as to be decomposable into a sum of contributions originating from a finite and unique set of reactions called response reactions (RERs). For a general chemical reaction system involving terminal species (reactants and products) and intermediates, the basic kinetic equation may be further partitioned into contributions coming from RERs involving only terminal species and those RERs involving at least one intermediate. When the intermediate are assumed to obey the quasi-steady state approximation, the contributions coming from the RERs involving at least one intermediate vanish. As a result, the basic kinetic equation may be presented as a sum of contributions coming from RERs involving only terminal species, i.e., overall RERs. This approach is shown to provide an adequate physicochemical basis of mechanisms and overall reactions as well as an effective algorithm of their enumeration.

Kinetic model of a collisional admixture in dusty gas and its application to calculating flow past bodies

Using the methods of statistical physics, the basic kinetic equation describing the dynamics of a polydisperse admixture of solid particles in a dilute dusty-gas flow is derived. Particle rotation, inelastic collisions, and interaction with the carrier gas are taken into account. The basic kinetic equation is used to obtain a Boltzmann-type equation for the one-particle distribution function, for which the boundary conditions for the problem of dusty-gas flow past a body are formulated. On the basis of the kinetic model developed, using direct statistical modeling, the flow patterns and the fields of the dispersed-phase macroparameters in a uniform crosswise dusty-gas flow past a cylinder are obtained for various free-stream particle sizes and concentrations.