Fokker–Planck equation for chemical reactions in plasmas

Longo, S.; Sanden, M.C.M. van de; Diomede, P.

doi:10.1007/s12210-019-00784-x

Cited by 3 publications

(6 citation statements)

References 12 publications

(29 reference statements)

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“…The use of this model (and eventual future versions) in higher-order problems requires the use of a reduced-order model to decrease the complexity and computational overhead. Two approaches known to the authors are binning ,, and Fokker–Planck methods, − which have already been applied to CO 2 SSH models and proven to be more computationally efficient than their state-to-state counterparts. The application of one of these models is of paramount importance when dealing with 2D or 3D geometries.…”

Section: Discussionmentioning

confidence: 99%

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

2021

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A heavy particle impact vibrational excitation and dissociation model for CO2 is presented. This state-to-state model is based on the forced harmonic oscillator (FHO) theory, which is more accurate than current state-of-the-art kinetic models of CO2 based on first-order perturbation theory. The first excited triplet state 3B2 of CO2, including its vibrational structure, is considered in our model, and a more consistent approach to CO2 dissociation is also proposed. The model is benchmarked against a few academic zero-dimensional (0D) cases and compared to decomposition time measurements in a shock tube. Our model is shown to have reasonable predictive capabilities, and the CO2 + O ↔ CO + O2 reaction is found to have a key influence on the dissociation dynamics of CO2 shocked flows, warranting further theoretical studies. We conclude this study with a discussion on the theoretical improvements that are still required for a more consistent analysis of the vibrational/dissociation dynamics of CO2.

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Section: Discussionmentioning

confidence: 99%

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

2021

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“…In recent publications by some of the authors of the present paper, − the FP approach has been implemented through numerical methods that avoid the approximations required in analytical solutions. In particular, in the work of Diomede et al, the FP equation for the CO 2 asymmetric stretching vibrational mode has been solved numerically in time using a Monte Carlo technique based on the short-time Green function of the FP equation.…”

Section: Introductionmentioning

confidence: 99%

Validation of the Fokker–Planck Approach to Vibrational Kinetics in CO₂ Plasma

et al. 2019

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The Fokker–Planck (FP) approach to describe vibrational kinetics numerically is validated in this work. This approach is shown to be around 1000 times faster than the usual state-to-state (STS) method to calculate a vibrational distribution function (VDF) in stationary conditions. Weakly ionized, nonequilibrium CO2 plasma is the test case for this demonstration, in view of its importance for the production of carbon-neutral fuels. VDFs obtained through the resolution of an FP equation and through the usual STS approach are compared in the same conditions, considering the same kinetic data. The demonstration is shown for chemical networks of increasing generality in vibrational kinetics of polyatomic molecules, including V–V exchanges, V–T relaxation, intermode V–V′ reactions, and excitation through e–V collisions. The FP method is shown to be accurate to describe the vibrational kinetics of the CO2 asymmetric stretching mode, while being much faster than the STS approach. In this way, the quantitative validity of the FP approach in vibrational kinetics is assessed, making it a fully viable alternative to STS solvers, that can be used with other processes, molecules, and physical conditions.

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“…In the last few years, many researchers, including two authors of the present paper, aimed to achieve a better understanding of this mechanism using computer simulations. For example, a recent scheme is based on the characterization of the upwards flux in energy space, J [ 76 , 77 , 78 ]. J is a functional of the function

, which is the distribution of molecules according to their internal energy

.…”

Section: Kinetics Of Molecular Activation By Plasma Electronsmentioning

confidence: 99%

“…It has been shown [ 76 , 77 , 78 ] that the two transport coefficients in Equation ( 5 ), namely the two jump moments

and

, can be calculated starting from the rate coefficients of the chemical reactions involving the different vibrational states. The calculation is not simple and the use of formulas requires the evaluation of numerous data; nevertheless the calculation is possible and produces results that are reliable and comparable with those based on the explicit discretization of the internal energy.…”

Section: Kinetics Of Molecular Activation By Plasma Electronsmentioning

confidence: 99%

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Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives

et al. 2021

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We review the recent progress in the modeling of plasmas or ionized gases, with compositions compatible with that of primordial atmospheres. The plasma kinetics involves elementary processes by which free electrons ultimately activate weakly reactive molecules, such as carbon dioxide or methane, thereby potentially starting prebiotic reaction chains. These processes include electron–molecule reactions and energy exchanges between molecules. They are basic processes, for example, in the famous Miller-Urey experiment, and become relevant in any prebiotic scenario where the primordial atmosphere is significantly ionized by electrical activity, photoionization or meteor phenomena. The kinetics of plasma displays remarkable complexity due to the non-equilibrium features of the energy distributions involved. In particular, we argue that two concepts developed by the plasma modeling community, the electron velocity distribution function and the vibrational distribution function, may unlock much new information and provide insight into prebiotic processes initiated by electron–molecule collisions.

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Fokker–Planck equation for chemical reactions in plasmas

Cited by 3 publications

References 12 publications

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

Validation of the Fokker–Planck Approach to Vibrational Kinetics in CO₂ Plasma

Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives

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Fokker–Planck equation for chemical reactions in plasmas

Cited by 3 publications

References 12 publications

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO2

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO2

Validation of the Fokker–Planck Approach to Vibrational Kinetics in CO2 Plasma

Plasma Modeling and Prebiotic Chemistry: A Review of the State-of-the-Art and Perspectives

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Product

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Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

Heavy Particle Impact Vibrational Excitation and Dissociation Processes in CO₂

Validation of the Fokker–Planck Approach to Vibrational Kinetics in CO₂ Plasma