Strong Diffusion Limit Research Articles

Thermally regulated gating phenomenon in bio-derived ultra-narrow nanoporous carbon for enhancing hydrogen isotope separation

The temperature-triggered gating in flexible nanoporous frameworks exhibits dynamic nanopore regulation under external stimuli, leading to optimum pore sizes and enhanced selectivity for isotopologue separation. In this work, we report one of the very rare observations of temperature-responsive gating in efficient bio-derived ‘nanoporous carbon’ material. The distinctive characteristics of this material, such as its suitable pore sizes for Kinetic Quantum Sieving (KQS) that lead to strong diffusion limitation, as well as its capacity to operate at higher temperatures, overcome the limitations of existing crystalline porous materials. It is remarkable that this activated carbon derived from biological sources, even without any strong binding sites, can release hydrogen isotopologues at a higher temperature of 180 K in comparison to MOF-74(Ni), which possesses many open metal sites but releases mostly at 90–100 K. The separation performance is also demonstrated to reach up to 120 K, and only six separation cycles are needed to enrich from a low concentration of 4 % to –92 % D2 in a mixture of deuterium (D2/H2). This finding suggests that inexpensive porous carbon’s thermal pore size modulation can significantly increase the operating temperature for precise separation of hydrogen isotopologues.

Anthropogenic Extremely Low Volatility Organics (ELVOCs) Govern the Growth of Molecular Clusters Over the Southern Great Plains During the Springtime

AbstractNew particle formation (NPF) often drives cloud condensation nuclei concentrations and the processes governing nucleation of molecular clusters vary substantially in different regions. The growth of these clusters from ∼2 to >10 nm diameters is often driven by the availability of extremely low volatility organic vapors (ELVOCs). Although the pathways to ELVOC formation from the oxidation of biogenic terpenes are better understood, the mechanistic pathways for ELVOC formation from oxidation of anthropogenic organics are less well understood. We integrate measurements and detailed regional model simulations to understand the processes governing NPF and secondary organic aerosol formation at the Southern Great Plain (SGP) observatory in Oklahoma and compare these with a site within the Bankhead National Forest (BNF) in Alabama, southeast USA. During our two simulated NPF event days, nucleation rates are predicted to be at least an order of magnitude higher at SGP compared to BNF largely due to lower sulfuric acid (H2SO4) concentrations at BNF. Among the different nucleation mechanisms in WRF‐Chem, we find that the dimethylamine (DMA) + H2SO4 nucleation mechanism dominates at SGP. We find that anthropogenic ELVOCs are critical for explaining the growth of particles observed at SGP. Treating organic particles as semisolid, with strong diffusion limitations for organic vapor uptake in the particle phase, brings model predictions into closer agreement with observations. We also simulate two non‐NPF event days observed at the SGP site and show that low‐level clouds reduce photochemical activity with corresponding reductions in H2SO4 and anthropogenic ELVOC concentrations, thereby explaining the lack of NPF.

Chorus wave power at the strong diffusion limit overcomes electron losses due to strong diffusion

Earth’s radiation belts consist of high-energy charged particles trapped by Earth’s magnetic field. Strong pitch angle diffusion of electrons caused by wave-particle interaction in Earth’s radiation belts has primarily been considered as a loss process, as trapped electrons are rapidly diffused into the loss cone and lost to the atmosphere. However, the wave power necessary to produce strong diffusion should also produce rapid energy diffusion, and has not been considered in this context. Here we provide evidence of strong diffusion using satellite data. We use two-dimensional Fokker-Planck simulations of electron diffusion in pitch angle and energy to show that scaling up chorus wave power to the strong diffusion limit produces rapid acceleration of electrons, sufficient to outweigh the losses due to strong diffusion. The rate of losses saturates at the strong diffusion limit, whilst the rate of acceleration does not. This leads to the surprising result of an increase, not a decrease in the trapped electron population during strong diffusion due to chorus waves as expected when treating strong diffusion as a loss process. Our results suggest there is a tipping point in chorus wave power between net loss and net acceleration that global radiation belt models need to capture to better forecast hazardous radiation levels that damage satellites.

Variation of Electron Lifetime Due To Scattering by Electrostatic Electron Cyclotron Harmonic Waves in the Inner Magnetosphere With Electron Distribution Parameters

AbstractThrough resonant wave‐particle interactions with electrostatic electron cyclotron harmonic (ECH) waves, low‐energy plasma sheet electrons can be scattered into the atmospheric loss cone and precipitate. This process can be investigated by calculating bounce‐averaged quasi‐linear diffusion coefficients. However, the numerical calculation of ECH wave‐induced scattering rates requires the specification of several parameters, including the properties of the hot plasma sheet electrons responsible for the wave excitation. The dependence of the diffusion coefficients on these parameters and the exact contribution of scattering by ECH waves to diffuse auroral precipitation is still poorly understood and has not been carefully quantified yet. In this study, we calculate bounce‐averaged quasi‐linear scattering rates and compare the resulting lifetimes to the strong diffusion limit. We vary the temperature, plasma density, and loss cone parameters of the hot component in the electron loss cone distribution over a large range based on previous studies and observations. By adopting a new model that derives the wave normal angle from the midpoint and the angular width of the growth rate profile, our findings suggest that the electron lifetime near the loss cone is not significantly affected by the hot electron temperature and loss cone parameters. However, there is an increase in electron lifetimes with increasing plasma density. For an electric field amplitude of 1 mV/m, the electron lifetime is below or equal to the lifetime calculated using the strong diffusion limit up to E = 0.25 keV when n = 1.5 cm−3, and up to E = 0.22 keV when n = 9 cm−3.

Energetic electron scattering by kinetic Alfvén waves at strong magnetic field gradients of dipolarization front

Energetic electron scattering and precipitation from the Earth's plasma sheet to the ionosphere is an important contributor to magnetosphere–ionosphere coupling. In this study, we investigate the role of one of the most intense wave emissions, kinetic Alfvén waves (KAWs), in energetic electron scattering. We have evaluated the effect of KAWs on energetic electrons within a curved magnetic field configuration exhibiting sharp cross field gradients. The magnetic field in Earth's magnetotail plasma sheet with an embedded dipolarization front is used as a working example. Taking into account electron bounce motion and perpendicular guiding-center drifts, we have shown that electrons with energies of tens to hundreds of keV can be scattered by KAWs in pitch angle and momentum through Doppler-shifted Landau resonance near the magnetic equator. The bounce-averaged pitch-angle diffusion coefficients for near-loss-cone (∼2°) electrons are on the order of 10–7–10–6 rad2/s for a characteristic KAW amplitude of 1 mV/m and approach the strong diffusion limit of ∼10–4 rad2/s for amplitudes of greater than 10 mV/m. These results suggest that under such ambient conditions, KAWs can pitch-angle scatter energetic electron population into the loss cone. In Earth's plasma sheet, this scattering is, thus, very likely to cause significant precipitation during active times. The diffusion coefficients of energetic electrons at large pitch angles (∼45°–∼80°) are more than two orders of magnitude larger than those of electrons near the loss cone, suggesting that KAWs contribute to isotropization of anisotropic electrons due to adiabatic heating should they drift into the vicinity of the magnetic field gradient.

Loss of Energetic Ions Comprising the Ring Current Populations of Jupiter's Middle and Inner Magnetosphere

AbstractThe low‐altitude, polar orbit of the Juno mission allows the Jupiter Energetic Particle Detector Instrument to view into, and resolve, the loss cone of energetic ions comprising the low‐altitude extension of Jupiter's ring current ions. For regions mapping from just inside Ganymede's orbit to well beyond Ganymede's orbit, energetic ions (>50 keV H+ and >130 keV Oxygen and Sulfur ions) are strongly scattered into the loss cone and lost to the magnetosphere at the “strong diffusion limit” at essentially all times. We conclude, by arguing against magnetic curvature scattering, that the cause is waves, perhaps associated with Alfvénic variations previously documented in this equatorial region. Scattering is generally weak or nonexistent near the orbits of the moons Europa and Io, except for the regions just downstream of the corotating plasmas. For Io, we sometimes observe moderate, but not saturated, scattering within roughly 60° downstream. Significantly, scattering is weak or nonexistent just upstream of Io's position, an asymmetry echoed in some previous wave observations. A preliminary accounting of the total (longitude‐averaged) scattering losses near Io's orbit yields loss rates of order 4%–5% of the strong diffusion limit for H+ and 5%–7% for heavy ions (O + S). We conclude that near Io's orbit, charge exchange losses likely dominate over scattering losses for heavy ions and for the lower energy H+ ions (roughly <200 keV).

Tight Coupling of Surface and In-Plant Biochemistry and Convection Governs Key Fine Particulate Components over the Amazon Rainforest

Combining unique high-altitude aircraft measurements and detailed regional model simulations, we show that in-plant biochemistry plays a central but previously unidentified role in fine particulate-forming processes and atmosphere–biosphere–climate interactions over the Amazon rainforest. Isoprene epoxydiol secondary organic aerosols (IEPOX-SOA) are key components of sub-micrometer aerosol particle mass throughout the troposphere over the Amazon rainforest and are traditionally thought to form by multiphase chemical pathways. Here, we show that these pathways are strongly inhibited by the solid thermodynamic phase state of aerosol particles and lack of particle and cloud liquid water in the upper troposphere. Strong diffusion limitations within organic aerosol coatings prevailing at low temperatures and low relative humidity in the upper troposphere strongly inhibit the reactive uptake of IEPOX to inorganic aerosols. We find that direct emissions of 2-methyltetrol gases formed by in-plant biochemical oxidation and/or oxidation of deposited IEPOX gases on the surfaces of soils and leaves and their transport by cloud updrafts followed by their condensation at low temperatures could explain over 90% of the IEPOX-SOA mass concentrations in the upper troposphere. Our simulations indicate that even near the surface, direct emissions of 2-methyltetrol gases represent a ubiquitous, but previously unaccounted for, source of IEPOX-SOA. Our results provide compelling evidence for new pathways related to land surface–aerosol–cloud interactions that have not been considered previously.

Evolution of Thermal Electron Distributions in the Magnetotail: Convective Heating and Scattering‐Induced Losses

AbstractEarth's magnetotail is filled with solar wind and ionospheric electrons, whose initial energies are significantly lower than the typical energies (temperatures) of plasmasheet electrons. One of the most common mechanisms responsible for heating of solar wind and ionospheric electrons in Earth's magnetotail is adiabatic heating caused by earthward convection of these electrons from the deep tail (i.e., from the region of a weak magnetic field) toward the region of stronger magnetic fields closer to Earth. This heating is moderated by electron losses into the ionosphere due to local wave scattering. In this study, we compare electron spectra from simultaneous observations of The Time History of Events and Macroscale Interactions during Substorms (THEMIS) spacecraft at different radial distances with spectra obtained from a simple model that includes adiabatic heating and losses. Our comparison shows that the model heating significantly overestimates the increase in energetic ( keV) electron fluxes, indicating that losses are essential for accurate modeling of the observed spectra. The required electron losses are similar to or even greater than the losses in the strong diffusion limit (when the loss cone is full). The latter can be interpreted as loss cone widening by field‐aligned electron acceleration.

Resonant interaction of relativistic electrons with realistic electromagnetic ion\u2013cyclotron wave packets

We study the influence of real structure of electromagnetic ion-cyclotron wave packets in the Earth’s radiation belts on precipitation of relativistic electrons. Automatic algorithm is used to distinguish isolated elements (wave packets) and obtain their amplitude and frequency profiles from satellite observations by Van Allen Probe B. We focus on rising-tone EMIC wave packets in the proton band, with a maximum amplitude of 1.2–1.6 nT. The resonant interaction of the considered wave packets with relativistic electrons 1.5–9 MeV is studied by numerical simulations. The precipitating fluxes are formed as a result of both linear and nonlinear interaction; for energies 2–5 MeV precipitating fluxes are close to the strong diffusion limit. The evolution of precipitating fluxes is influenced by generation of higher-frequency waves at the packet trailing edge near the equator and dissipation of lower-frequency waves in the text {He}^+ cyclotron resonance region at the leading edge. The wave packet amplitude modulation leads to a significant change of precipitated particles energy spectrum during short intervals of less than 1 minute. For short time intervals about 10–15 s, the approximation of each local amplitude maximum of the wave packet by a Gaussian amplitude profile and a linear frequency drift gives a satisfactory description of the resonant interaction.

Diffuse Auroral Electron Scattering by Electrostatic Electron Cyclotron Harmonic Waves in the Dayside Magnetosphere

AbstractAlthough electrostatic electron cyclotron harmonic (ECH) waves are frequently observed in the dayside magnetosphere, their effects on the formation of dayside diffuse aurora remain poorly understood. In this study, we quantitatively evaluate the efficiency of dayside ECH wave scattering in producing the electron diffuse aurora precipitation during a typical ECH wave event by calculating the quasi‐linear bounce‐averaged scattering rates. We find that dayside ECH waves can efficiently pitch angle scatter diffuse auroral electrons on timescales of a few hours to ∼1 day over a broad range of electron energy and equatorial pitch angle α eq, that is, from ∼300 eV to 10 keV with α eq from the loss cone to 45°. Especially for ∼300 eV–2 keV electrons, the scattering rates can even approach the strong diffusion limit, resulting in an almost fully filled loss cone. Our results confirm the significant role of ECH waves in driving the dayside diffuse aurora.

Comparative study on the catalytic behaviors of zeolites with different diffusion limitation in ethane aromatization

The design of zeolite-based catalysts with reduced diffusion limitation has attracted much attention for the enhanced activity and stability in light alkane aromatization. Here we employed three types of zeolite-based catalysts including micron zeolite, solid nano zeolite, and hollow zeolite with nano size to investigate the effects of diffusion length and pore structure of zeolites on their mass transport efficiency and catalytic performance during ethane aromatization. It was indicated that the shortened diffusion length and increased mesoporosity of Zn/hollow-HZSM-5 endow it with substantial improvement in mass transport, leading to enhanced accessibility to active acid sites and rapid escape of formed lighter aromatics rather than further polymerization to form coke. Contrarily, the solid micron zeolites with long diffusion path experience strong diffusion limitation, which extends the contact time of reactants and products with the active acid sites within zeolites thus resulting in severe coke deactivation. After being subjected to ethane aromatization for 400 min, the aromatics selectivity toward Zn/hollow-HZSM-5 catalyst retained 50%, which is almost threefold with respect to that of the solid Zn/micro-HZSM-5 and Zn/nano-HZSM-5. Based on the Thiele modulus, it can be suggested that shortening diffusion length and introducing mesopores into zeolites can effectively alleviate diffusion resistance, then enhance their catalytic activity and stability toward ethane aromatization.

Potential Evidence of Low‐Energy Electron Scattering and Ionospheric Precipitation by Time Domain Structures

AbstractPlasma sheet electron precipitation is critical in magnetosphere‐ionosphere coupling and has long been attributed to electron scattering by whistler‐mode and electron cyclotron harmonic waves. Recent observations have revealed that time domain structures (TDSs) that appear as broadband electrostatic fluctuations may also scatter plasma sheet electrons. However, there has been no observational evidence of TDS scattering electrons into the ionosphere. This study presents potential evidence from conjugate observations between the Time History of Events and Macroscale Interactions during Substorms (THEMIS) mission and the low‐altitude Enhanced Polar Outflow Probe (e‐POP) spacecraft. During the five events presented, THEMIS observed intense electron injections accompanied by TDSs, while e‐POP captured precipitation of plasma sheet electrons with energies ∼100–325 eV over a broad pitch angle range. The observed TDSs can efficiently scatter these electrons exceeding the strong diffusion limit. Our results suggest that TDSs may contribute to plasma sheet electron scattering around times of injections.

Precipitation of Relativistic Electrons Under Resonant Interaction With Electromagnetic Ion Cyclotron Wave Packets

AbstractWe use numerical simulations to study the resonant interaction of relativistic electrons with rising‐frequency electromagnetic ion cyclotron (EMIC) wave packets in the band. We find that precipitating fluxes are formed by quasi‐linear interaction and several nonlinear interaction regimes having opposite effects. In particular, the direct influence of Lorentz force on the particle phase (force bunching) decreases precipitation for particles with low equatorial pitch angles (up to 15–25°) and can even block it completely. Four other nonlinear regimes are possible: nonlinear shift of the resonance point, which can cause pitch angle drift in both directions; phase bunching that slightly increases pitch angle for untrapped particles; directed scattering that strongly decreases pitch angle for untrapped particles; and particle trapping by the wave field that decreases pitch angle. The evolution of the equatorial pitch angle distribution during several passes of particles through the wave packet is studied. The precipitating fluxes are evaluated and compared with theoretical estimates. We show that strong diffusion limit is maintained for a certain range of energies by a wave packet with realistic amplitude and frequency drift. In this case, the quasi‐linear theory strongly underestimates the precipitating flux. With increasing energy, the precipitating fluxes decrease and become close to the quasi‐linear estimates.

Comparison of light-off performance of Pt-Pd/γ-Al2O3 dual layer and dual brick diesel oxidation catalysts

A global kinetic model is used to study the light-off behavior of a mixture of CO and HCs (C2H4,C7H8,C6H14 &C2H6) on Pt, Pd and combined catalysts. The light-off curves are clustered around 550 K on Pt whereas species light-off temperatures range from 400–600 K on Pd. The self poisoning of CO is more pronounced on Pt than on Pd. As long chain HCs such as hexane have a better light-off performance on Pt than on Pd, it is beneficial to use dual layer or dual brick catalysts for optimising HC conversion on a C1 basis. Dual brick catalyst with Pd upstream showed superior performance compared to the configuration with Pd downstream. Pt in 50% of washcoat and Pd in the remaining 50% of washcoat has a better overall light-off performance than other fractions of Pt, Pd. It is found that the light-off behavior of all the species is nearly same for both dual layer and dual brick configurations at low space velocities. However, the strong diffusional limitations in the washcoat at high space velocities result in improved light-off performance of dual layer configuration. The more practical C1 basis conversion, which is the weighted average conversion of HCs, is investigated for different configurations. It is also shown that the exotherm generated by the oxidation of CO can be used to improve the C1 basis conversion of HCs.

Modelling and experimental validation of a CO2 methanation annular cooled fixed‐bed reactor exchanger

AbstractA simulation model of a fixed‐bed reactor‐exchanger dedicated to CO2 methanation on an industrial Ni/γ‐Al2O3 catalyst has been built on the basis of experimental characterization of heat transfer and kinetic parameters. An effective thermal conductivity of the bed and a wall heat transfer coefficient are determined from cooling experiments of different Ar‐H2 mixtures (thermal conductivity 0.02–0.25 W · m−1 · K−1) at different Reynolds numbers (particle Reynolds number 1–50). The flow dependent component of the Nusselt number correlates to the gas Prandtl number as Pr0.72. These heat transfer parameters and a kinetic model adapted to the Ni/γ‐Al2O3 catalyst are integrated in mass, heat, and momentum balance equations in the bed and at the particle scale to build a 2D heterogeneous model of the fixed‐bed reactor. CO2 methanation experiments in an annular fixed‐bed reactor‐exchanger filled with 400 g of Ni/γ‐Al2O3 catalyst at pressures from 0.4 to 0.8 MPa and coolant temperatures from 473 to 548 K (200 to 275 °C) are described in this paper and simulated by the model.CO2 conversion rate and CH4 selectivity at the reactor outlet and temperature elevations in the reactor are simulated by the model with a discrepancy lower than 10 %. For pressures above 0.4 MPa, a strong mass diffusion limitation inside the catalyst particles is shown and the efficiency decrease of the three reactions is explained.

Effect of particle shape on fluid flow and heat transfer for methane steam reforming reactions in a packed bed

Numerical simulations of a cylindrical packed bed with tube to particle diameter ratio of 1.4, containing 10 particles, were performed to understand the effect of particle shape on pressure drop, heat transfer and reaction performance. Six particle shapes namely, cylinder as the reference, trilobe and daisy having external shaping, hollow cylinder, cylcut, and 7‐hole cylinder including internal voids were chosen. Methane steam reforming reactions were considered for the heat transfer and reaction performance evaluation. The present study showed that the external shaping of particles offered lower pressure drop, but lower values of effectiveness factor indicating strong diffusion limitations. The internally shaped particles offered increased surface area, led to higher effectiveness factor and allowed to overcome the diffusion limitations. The effective heat transfer and effectiveness factor of the trilobe‐shaped particle per unit pressure drop was found to be the best among the particle shapes considered in the present work. © 2016 American Institute of Chemical Engineers AIChE J, 63: 366–377, 2017

CO2 gasification of woody biomass chars: The influence of K and Si on char reactivity

Abstract Although the influence of metallic and alkaline elements on biomass char reactivity is well known, a quantitative assessment of this catalytic effect is hard to obtain because of the chemical and textural complexity of biomass. The effect of K and Si on the CO2 gasification reactivity of a biomass char was studied using thermogravimetric analysis. A beech sample was pyrolyzed at 800 °C and then impregnated with known amounts of silicon or potassium allowing to obtain a wide range of K/Si ratios. The reactivity of the impregnated samples was studied under a CO2 (20% vol.) atmosphere. The results show that at low conversion ratios, the char reactivity depends on its textural properties, with strong diffusional limitations. When conversion reaches 60%, the presence of a catalyst (K) and an inhibitor (Si) becomes the major parameter influencing reactivity. From these experiments, a general trend was obtained between K/Si ratio and reactivity as a function of conversion.

Resonant scattering of central plasma sheet protons by multiband EMIC waves and resultant proton loss timescales

AbstractThis is a companion study to Liang et al. (2014) which reported a “reversed” energy‐latitude dispersion pattern of ion precipitation in that the lower energy ion precipitation extends to lower latitudes than the higher‐energy ion precipitation. Electromagnetic ion cyclotron (EMIC) waves in the central plasma sheet (CPS) have been suggested to account for this reversed‐type ion precipitation. To further investigate the association, we perform a comprehensive study of pitch angle diffusion rates induced by EMIC wave and the resultant proton loss timescales at L = 8–12 around the midnight. Comparing the proton scattering rates in the Earth's dipole field and a more realistic quiet time geomagnetic field constructed from the Tsyganenko 2001 (T01) model, we find that use of a realistic, nondipolar magnetic field model not only decreases the minimum resonant energies of CPS protons but also considerably decreases the limit of strong diffusion and changes the proton pitch angle diffusion rates. Adoption of the T01 model increases EMIC wave diffusion rates at > ~ 60° equatorial pitch angles but decreases them at small equatorial pitch angles. Pitch angle scattering coefficients of 1–10 keV protons due to H+ band EMIC waves can exceed the strong diffusion rate for both geomagnetic field models. While He+ and O+ band EMIC waves can only scatter tens of keV protons efficiently to cause a fully filled loss cone at L > 10, in the T01 magnetic field they can also cause efficient scattering of ~ keV protons in the strong diffusion limit at L > 10. The resultant proton loss timescales by EMIC waves with a nominal amplitude of 0.2 nT vary from a few hours to several days, depending on the wave band and L shell. Overall, the results demonstrate that H+ band EMIC waves, once present, can act as a major contributor to the scattering loss of a few keV protons at lower L shells in the CPS, accounting for the reversed energy‐latitude dispersion pattern of proton precipitation at low energies (~ keV) on the nightside. The pitch angle coverage for H+ band EMIC wave resonant scattering strongly depends on proton energy, L shell, and field model. He+ and O+ band EMIC waves tend to cause efficient scattering loss of protons at higher energies, thereby importantly contributing to the isotropic distribution of higher energy (> ~ 10 keV) protons at higher L shells on the nightside where the geomagnetic field line is highly stretched. Our results also suggest that scattering by H+ band EMIC waves may significantly contribute to the formation of the reversed‐type CPS proton precipitation on the dawnside where both the wave activity and occurrence probability is statistically high.

Interplay of reaction and pore diffusion during cobalt-catalyzed Fischer–Tropsch synthesis with CO2-rich syngas

For cobalt-catalyzed Fischer–Tropsch synthesis (FTS), a model was developed to analyze numerically the reaction–diffusion performance in catalyst particles. The model is based on a mesoporous particle and is valid for CO2-free and -rich syngas. The kinetic parameters of all three relevant reactions, CO hydrogenation to C2+ hydrocarbons as well as CH4 and CO2 hydrogenation (mainly) to CH4, were derived at intrinsic conditions (dp=150μm). Thereafter, the effective kinetics considering pore diffusion limitations were derived by using a homemade catalyst in 5mm diameter. From the data measured, a kinetic approach for conversion of CO2 inside the catalyst particle was developed. The experimentally derived Langmuir–Hinshelwood type rate expressions and a variable chain growth parameter α, dependent on temperature and syngas ratio, were implemented into the model. Furthermore, the change of the local reaction rates and selectivities, as a consequence of changing syngas ratio due to diffusion limitation is taken into account. The simulated data of effective kinetics and selectivities are in agreement with the measured data. The simulation predicts that CO2 is only converted in the CO-free core region of large catalyst particles at high temperatures and strong pore diffusion limitations. For CO2 converts mainly to CH4 (selectivity 95%C), a slightly increased overall methane selectivity is expected indicating consumption of CO2. However, this effect was not measurable even with 5mm particles at high temperatures as methanation of CO2 occurs only to a minor extent even at pronounced diffusion limited conditions and is negligible at industrial conditions.

Finite gyroradius corrections in the theory of perpendicular diffusion 2. Strong velocity diffusion

The current paper is a sequel to an article where we have started to incorporate finite gyroradius effects in the theory of perpendicular diffusion of energetic particles interacting with turbulent magnetic fields. In the previous paper we have focused on the case that velocity diffusion is suppressed and we derived corrections to the perpendicular diffusion coefficient. In the current article we focus on the limit of strong non-linear velocity diffusion. If finite gyroradius effects are not present, we derive the well-known limit where the perpendicular diffusion coefficient is directly proportional to the parallel diffusion coefficient. As in the previous paper, we employ different turbulence models as examples, namely the slab model, noisy slab turbulence, and the two-dimensional model. We show that finite gyroradius effects reduce the perpendicular mean free path in all considered cases except for the slab model where such effects do not occur.