Abstract: This work explains the need for plasma models, introduces arguments for choosing the type of model that better fits the purpose of each study, and presents the basics of the most common nonequilibrium low-temperature plasma models and the information available from each one, along with an extensive list of references for complementary in-depth reading. The paper presents the following models, organised according to the level of multi-dimensional description of the plasma: kinetic models, based on either a statistical particle-in-cell/Monte-Carlo approach or the solution to the Boltzmann equation (in the latter case, special focus is given to the description of the electron kinetics); multi-fluid models, based on the solution to the hydrodynamic equations; global (spatially-average) models, based on the solution to the particle and energy rate-balance equations for the main plasma species, usually including a very complete reaction chemistry; mesoscopic models for plasma–surface interaction, adopting either a deterministic approach or a stochastic dynamical Monte-Carlo approach. For each plasma model, the paper puts forward the physics context, introduces the fundamental equations, presents advantages and limitations, also from a numerical perspective, and illustrates its application with some examples. Whenever pertinent, the interconnection between models is also discussed, in view of multi-scale hybrid approaches.

Abstract: This work examines the properties of a dielectric barrier discharge (DBD) reactor, built for CO2 decomposition, by means of electrical characterization, optical emission spectroscopy and gas chromatography. The discharge, formed in an electronegative gas (such as CO2, but also O2), exhibits clearly different electrical characteristics, depending on the surface conductivity of the reactor walls. An asymmetric current waveform is observed in the metaldielectric (MD) configuration, with sparse high-current pulses in the positive half-cycle (HC) and a more uniform regime in the negative HC. This indicates that the discharge is operating in two alternating regimes with rather different properties. At high CO2 conversion regimes, a conductive coating is deposited on the dielectric. This so-called coated MD configuration yields a symmetric current waveform, with current peaks in both the positive and negative HCs. In a double-dielectric (DD) configuration, the current waveform is also symmetric, but without current peaks in both the positive and negative HC. Finally, the DD configuration with conductive coating on the inner surface of the outer dielectric, i.e. so-called coated DD, yields again an asymmetric current waveform, with current peaks in the negative HC. These different electrical characteristics are related to the presence of the conductive coating on the dielectric wall of the reactor and can be explained by an increase of the local barrier capacitance available for charge transfer. The different discharge regimes affect the CO2 conversion, more specifically, the CO2 conversion is lowest in the clean DD configuration. It is somewhat higher in the coated DD configuration, and still higher in the MD configuration. The clean and coated MD configuration, however, gave similar CO2 conversion. These results indicate that the conductivity of the dielectric reactor walls can highly promote the development of the high-amplitude discharge current pulses and subsequently the CO2 conversion.

Abstract: Low-temperature plasma chemical kinetic models are particularly important to the plasma community. These models typically require dozens of inputs, especially rate coefficients. The latter are not always precisely known and it is not surprising that the error on the rate coefficient data can propagate to the model output. In this paper, we present a model that uses N = 400 different combinations of rate coefficients based on the uncertainty attributed to each rate coefficient, giving a good estimation of the uncertainty on the model output due to the rate coefficients. We demonstrate that the uncertainty varies a lot with the conditions and the type of output. Relatively low uncertainties (about 15%) are found for electron density and temperature, while the uncertainty can reach more than an order of magnitude for the population of the vibrational levels in some cases and it can rise up to 100% for the CO2 conversion. The reactions that are mostly responsible for the largest uncertainties are identified. We show that the conditions of pressure, gas temperature and power density have a great effect on the uncertainty and on which reactions lead to this uncertainty. In all the cases tested here, while the absolute values may suffer from large uncertainties, the trends observed in previous modeling work are still valid. Finally, in accordance with the work of Turner, a number of ‘good practices’ is recommended.

Abstract: The use of microfluidic devices in the field of plasma-liquid interaction can unlock unique possibilities to investigate the effects of plasma-generated reactive species for environmental and biomedical applications. So far, very little simulation work has been performed on microfluidic devices in contact with a plasma source. We report on the modelling and computational simulation of physical and chemical processes taking place in a novel plasma-microfluidic platform. The main production and transport pathways of reactive species both in plasma and liquid are modelled by a novel modelling approach that combines 0D chemical kinetics and 2D transport mechanisms. This combined approach, applicable to systems where the transport of chemical species occurs in unidirectional flows at high Péclet numbers, decreases calculation times considerably compared to regular 2D simulations. It takes advantage of the low computational time of the 0D reaction models while providing spatial information through multiple plug-flow simulations to yield a quasi-2D model. The gas and liquid flow profiles are simulated entirely in 2D, together with the chemical reactions and transport of key chemical species. The model correctly predicts increased transport of hydrogen peroxide into the liquid when the microfluidic opening is placed inside the plasma effluent region, as opposed to inside the plasma region itself. Furthermore, the modelled hydrogen peroxide production and transport in the microfluidic liquid differs by less than 50% compared with experimental results. To explain this discrepancy, the limits of the 0D–2D combined approach are discussed.

Abstract: In recent years there has been growing interest in the use of plasma technology for CO2 conversion. To improve this application, a good insight into the underlying mechanisms is of great importance. This can be obtained from modeling the detailed plasma chemistry in order to understand the chemical reaction pathways leading to CO2 conversion (either in pure form or mixed with another gas). Moreover, in practice, several plasma reactor types are being investigated for CO2 conversion, so in addition it is essential to be able to model these reactor geometries so that their design can be improved, and the most energy efficient CO2 conversion can be achieved. Modeling the detailed plasma chemistry of CO2 conversion in complex reactors is, however, very time-consuming. This problem can be overcome by using a combination of two different types of model: 0D chemical reaction kinetics models are very suitable for describing the detailed plasma chemistry, while the characteristic features of different reactor geometries can be studied by 2D or 3D fluid models. In the first instance the latter can be developed in argon or helium with a simple chemistry to limit the calculation time; however, the ultimate aim is to implement the more complex CO2 chemistry in these models. In the present paper, examples will be given of both the 0D plasma chemistry models and the 2D and 3D fluid models for the most common plasma reactors used for CO2 conversion in order to emphasize the complementarity of both approaches. Furthermore, based on the modeling insights, the paper discusses the possibilities and limitations of plasma-based CO2 conversion in different types of plasma reactors, as well as what is needed to make further progress in this field.

Abstract: Plasma–liquid interactions represent a growing interdisciplinary area of research involving plasma science, fluid dynamics, heat and mass transfer, photolysis, multiphase chemistry and aerosol science. This review provides an assessment of the state-of-the-art of this multidisciplinary area and identifies the key research challenges. The developments in diagnostics, modeling and further extensions of cross section and reaction rate databases that are necessary to address these challenges are discussed. The review focusses on nonequilibrium plasmas.

Abstract: The conversion of methane to value-added chemicals and fuels is considered to be one of the challenges of the 21st century. In this paper we study, by means of fluid modeling, the conversion of methane to higher hydrocarbons or oxygenates by partial oxidation with CO2 or O2 in a dielectric barrier discharge. Sixty-nine different plasma species (electrons, ions, molecules, radicals) are included in the model, as well as a comprehensive set of chemical reactions. The calculation results presented in this paper include the conversion of the reactants and the yields of the reaction products as a function of residence time in the reactor, for different gas mixing ratios. Syngas (i.e. H2 + CO) and higher hydrocarbons (C2Hx) are typically found to be important reaction products.

Abstract: In this study we report on a 2D fluid model of a gliding arc discharge in argon. Despite the 3D nature of the discharge, 2D models are found to be capable of providing very useful information about the operation of the discharge. We employ two modelsan axisymmetric and a Cartesian one. We show that for the considered experiment and the conditions of a low current arc (around 30 mA) in argon, there is no significant heating of the cathode surface and the discharge is sustained by field electron emission from the cathode accompanied by the formation of a cathode spot. The obtained discharge power and voltage are relatively sensitive to the surface properties and particularly to the surface roughness, causing effectively an amplification of the normal electric field. The arc body and anode region are not influenced by this and depend mainly on the current value. The gliding of the arc is modelled by means of a 2D Cartesian model. The arcelectrode contact points are analysed and the gliding mechanism along the electrode surface is discussed. Following experimental observations, the cathode spot is simulated as jumping from one point to another. A complete arc cycle is modelled from initial ignition to arc decay. The results show that there is no interaction between the successive gliding arcs.

Abstract: We use a zero-dimensional reaction kinetics model to simulate CO2 conversion in microwave discharges where the excitation of the vibrational levels plays a significant role in the dissociation kinetics. The model includes a description of the CO2 vibrational kinetics, taking into account state-specific VT and VV relaxation reactions and the effect of vibrational excitation on other chemical reactions. The model is used to simulate a general tubular microwave reactor, where a stream of CO2 flows through a plasma column generated by microwave radiation. We study the effects of the internal plasma parameters, namely the reduced electric field, electron density and the total specific energy input, on the CO2 conversion and its energy efficiency. We report the highest energy efficiency (up to 30%) for a specific energy input in the range 0.41.0 eV/molecule and a reduced electric field in the range 50100 Td and for high values of the electron density (an ionization degree greater than 10−5). The energy efficiency is mainly limited by the VT relaxation which contributes dominantly to the vibrational energy losses and also contributes significantly to the heating of the reacting gas. The model analysis provides useful insight into the potential and limitations of CO2 conversion in microwave discharges.

Abstract: The electron bounce resonance heating (BRH) in dual-frequency capacitively coupled plasmas operated in oxygen is studied by different experimental methods and a particle-in-cell/Monte Carlo collision (PIC/MCC) simulation, and compared with the electropositive argon discharge. In comparison with argon, the experimental results show that in an oxygen discharge the resonance peaks in positive-ion density and light intensity tend to occur at larger electrode gaps. Moreover, at electrode gaps L > 2.5 cm, the positive-ion (and electron) density and the light emission drop monotonically in the oxygen discharge upon increasing L, whereas they rise (after an initial drop) in the argon case. At resonance gap the electronegativity reaches its maximum due to the BRH. All these experimental observations are explained by PIC/MCC simulations, which show that in the oxygen discharge the bulk electric field becomes quite strong and is out of phase with the sheath field. Therefore, it retards the resonance electrons when traversing the bulk, resulting in a suppressed BRH. Both experiment and simulation results show that this effect becomes more pronounced at lower high-frequency power, when the discharge mode changes from electropositive to electronegative. In a pure oxygen discharge, the BRH is suppressed with increasing pressure and almost diminishes at 12 Pa. Finally, the driving frequency significantly affects the BRH, because it determines the phase relation between bulk electric field and sheath electric field.

Abstract: In this experimental study, a flowing dielectric barrier discharge operating at atmospheric pressure is used for the splitting of CO2 into O2 and CO. The influence of the applied frequency and plasma power on the microdischarge properties is investigated to understand their role on the CO2 conversion. Electrical measurements are carried out to explain the conversion trends and to characterize the microdischarges through their number, their lifetime,
their intensity and the induced electrical charge. Their influence on the gas and electrode temperatures is also evidenced through optical emission spectroscopy and infrared imaging. It is shown that, in our configuration, the conversion depends mostly on the charge delivered in the plasma and not on the effective plasma voltage when the applied power is modified. Similarly, at constant total current, a better conversion is observed at low frequencies, where a less filamentary discharge regime with a higher effective plasma voltage than that at a higher
frequency is obtained.

Abstract: The aim of this work consists of the evaluation of atmospheric pressure dielectric barrier discharges for the conversion of greenhouse gases into useful compounds. Therefore, pure CO2 feed flows are administered to the discharge zone at varying discharge frequency, power input, gas temperature and feed flow rates, aiming at the formation of CO and O2. The discharge obtained in CO2 is characterized as a filamentary mode with a microdischarge zone in each half cycle of the applied voltage. It is shown that the most important parameter affecting the CO2-conversion levels is the gas flow rate. At low flow rates, both the conversion and the CO-yield are significantly higher. In addition, also an increase in the gas temperature and the power input give rise to higher conversion levels, although the effect on the CO-yield is limited. The optimum discharge frequency depends on the power input level and it cannot be unambiguously stated that higher frequencies give rise to increased conversion levels. A maximum CO2 conversion of 30% is achieved at a flow rate of 0.05 L min−1, a power density of 14.75 W cm−3 and a frequency of 60 kHz. The most energy efficient conversions are achieved at a flow rate of 0.2 L min−1, a power density of 11 W cm−3 and a discharge frequency of 30 kHz.

Abstract: A gliding arc plasmatron (GAP) is very promising for CO2 conversion into value-added chemicals, but to further improve this important application, a better understanding of the arc behavior is indispensable. Therefore, we study here for the first time the dynamic arc behavior of the GAP by means of a high-speed camera, for different reactor configurations and in a wide range of operating conditions. This allows us to provide a complete image of the behavior of the gliding arc. More specifically, the arc body shape, diameter, movement and rotation speed are analyzed and discussed. Clearly, the arc movement and shape relies on a number of factors, such as gas turbulence, outlet diameter, electrode surface, gas contraction and buoyance force. Furthermore, we also compare the experimentally measured arc movement to a state-of-the-art 3D-plasma model, which predicts the plasma movement and rotation speed with very good accuracy, to gain further insight in the underlying mechanisms. Finally, we correlate the arc dynamics with the CO2 conversion and energy efficiency, at exactly the same conditions, to explain the effect of these parameters on the CO2 conversion process. This work is important for understanding and optimizing the GAP for CO2 conversion.

Abstract: We present a 3D and 2D Cartesian quasi-neutral plasma model for a low current argon gliding arc discharge, including strong interactions between the gas flow and arc plasma column.
The 3D model is applied only for a short time of 0.2 ms due to its huge computational cost. It mainly serves to verify the reliability of the 2D model. As the results in 2D compare well with those in 3D, they can be used for a better understanding of the gliding arc basic characteristics. More specifically, we investigate the back-breakdown phenomenon induced by an artificially controlled plasma channel, and we discuss its effect on the gliding arc characteristics. The
back-breakdown phenomenon, or backward-jump motion of the arc, as observed in the experiments, results in a drop of the gas temperature, as well as in a delay of the arc velocity with respect to the gas flow velocity, allowing more gas to pass through the arc, and thus increasing the efficiency of the gliding arc for gas treatment applications.