Kinetic Transport Model Research Articles

Fractional diffusion limit of a linear kinetic equation in a bounded domain

A version of fractional diffusion on bounded domains, subject to 'homogeneous Dirichlet boundary conditions' is derived from a kinetic transport model with homogeneous inflow boundary conditions. For nonconvex domains, the result differs from standard formulations. It can be interpreted as the forward Kolmogorow equation of a stochastic process with jumps along straight lines, remaining inside the domain.

Acid strength and metal-acid proximity effects on methylcyclohexane ring contraction turnover rates and selectivities

Methylcyclohexane ring contraction is used here to assess the effects of acid strength and metal-acid site proximity on turnover rates and selectivities for bifunctional catalysts consisting of Keggin type polyoxometalates (POM) with different central atoms that act as Brønsted acids. Bifunctional catalysts with metal sites that fully equilibrate cycloalkanes and cycloalkenes give methylcyclohexene conversion rate constants that decreased exponentially with increasing deprotonation energy, a rigorous descriptor of acid strength, consistent with the ion-pair character of transition states that mediate the kinetically-relevant ring contraction of bound methylcyclohexoxide intermediates. The measured rates of formation of each alkylcyclopentane isomer, however, do not reflect their intrinsic formation kinetics, because of fast diffusion-enhanced interconversions within acid domains; thus, isomer selectivities cannot be used to infer, even indirectly, the strength of acid sites, as often proposed in previous studies. Selectivities reflect instead diffusional effects that become more severe as the number and strength of acid sites and the size and diffusive resistances increase within these acid domains, which shift, in turn, the products formed from relative abundances dictated by kinetics to those prescribed by thermodynamics. A rigorous accounting of these diffusional effects using a kinetic-transport model leads to ratios of intrinsic rate constants for the formation of the different alkylcyclopentane isomers that do not depend on acid strength, because all isomerization routes are mediated by bicyclo[3.1.0]hexyl cation transition states similar in the amount and location of charge and that therefore benefit to the same extent from the more stable conjugate anions characteristic of stronger acids.

Second order kinetic theory of parallel momentum transport in collisionless drift wave turbulence

A second order kinetic model for turbulent ion parallel momentum transport is presented. A new nonresonant second order parallel momentum flux term is calculated. The resonant component of the ion parallel electrostatic force is the momentum source, while the nonresonant component of the ion parallel electrostatic force compensates for that of the nonresonant second order parallel momentum flux. The resonant component of the kinetic momentum flux can be divided into three parts, including the pinch term, the diffusive term, and the residual stress. By reassembling the pinch term and the residual stress, the residual stress can be considered as a pinch term of parallel wave-particle resonant velocity, and, therefore, may be called as “resonant velocity pinch” term. Considering the resonant component of the ion parallel electrostatic force is the transfer rate between resonant ions and waves (or, equivalently, nonresonant ions), a conservation equation of the parallel momentum of resonant ions and waves is obtained.

Three-dimensional scrape off layer transport in the helically symmetric experiment HSX

The edge topology of helically symmetric experiment (HSX) in the quasi-helically symmetric configuration is characterized by an 8/7 magnetic island remnant embedded in a short connection length scrape-off layer (SOL) domain. A 2D mapping of edge plasma profiles within this heterogeneous SOL has been constructed using a movable, multi-pin Langmuir probe. Comparisons of these measurements to edge simulations using the EMC3-EIRENE 3D plasma fluid and kinetic neutral gas transport model have been performed. The measurements provide strong evidence that particle transport is diffusive within the island region and dominantly convective in the SOL region. Measurements indicate that phenomenological cross-field diffusion coefficients are low in the SOL region between the last closed flux surface and edge island (i.e. m2 s−1). This level of transport was found to increase by a factor of two when a limiter is inserted almost completely into the magnetic island. A reduction in gradients of the edge electrostatic plasma potential was also measured in this configuration, suggesting that the reduced electric field may be linked to the increased cross-field transport observed.

The kinetic model for slow photoinduced electron transport in the reaction centers of purple bacteria.

The present work is related to the investigation of slow kinetics of electron transport in the reaction centers (RCs) of Rhodobacter sphaeroides. Experimental data on the absorption kinetics of aqueous solutions of reaction centers at different modes of photoexcitation are given. It is shown that the kinetics of oxidation and reduction of RCs are well described by the sum of three exponential functions. This allows to suggest a two-level kinetic model for electron transport in the RC as a system of four electron-conformational states which correspond to three balance differential equations combined with state equation. The solution of inverse problem made it possible to obtain the rate constant values in kinetic equations for different times and intensities of exciting light. Analysis of rate constant values in different modes of RC excitation allowed to suggest that two mechanisms of structural changes are involved in RC photo-oxidation. One mechanism leads to the increment of the rate of electron return, another one—to its drop. Structural changes were found out to occur in the RCs under incident light. After light was turned off, the reduction of RCs was determined by the second mechanism.

Influence of mixing model constant on local extinction effects and temperature prediction in LES for non-premixed swirling diffusion flames

The behavior of different viscous models on the non-premixed swirling diffusion flame and local extinction effect is investigated in this paper. A three dimensional numerical simulation is conducted on Sydney SMH1 flames using Wall-Modeled LES (WMLES) model, Kinetic Energy Transport model and realizable k–ε model coupled with laminar flamelet model. The scatter plots of temperature are analyzed when different mixing model constants Cvar are applied. Scalar dissipation rate theory is introduced to explain the influence of the Cvar on the local extinction prediction. The results of the present paper show that model constant Cvar has a significant effect on accuracy of prediction of the turbulent model. Among the three viscous models, the Kinetic Energy Transport model gives the best prediction on local extinction effect at the main recirculation zone. The analytic procedure may serve as a reference for further study on non-premixed swirling diffusion flames.

Solution of a generalized Boltzmann's equation for nonequilibrium charged-particle transport via localized and delocalized states.

We present a general phase-space kinetic model for charged-particle transport through combined localized and delocalized states, capable of describing scattering collisions, trapping, detrapping, and losses. The model is described by a generalized Boltzmann equation, for which an analytical solution is found in Fourier-Laplace space. The velocity of the center of mass and the diffusivity about it are determined analytically, together with the flux transport coefficients. Transient negative values of the free particle center-of-mass transport coefficients can be observed due to the trapping to, and detrapping from, localized states. A Chapman-Enskog-type perturbative solution technique is applied, confirming the analytical results and highlighting the emergence of a density gradient representation in the weak-gradient hydrodynamic regime. A generalized diffusion equation with a unique global time operator is shown to arise, reducing to the standard diffusion equation and a Caputo fractional diffusion equation in the normal and dispersive limits. A subordination transformation is used to solve the generalized diffusion equation by mapping from the solution of a corresponding standard diffusion equation.

Membrane reactors for isoamyl acetate production

In our previous paper (Chem. Eng. Process., 76 (2014) 70), a comprehensive study of conventional and hybrid membrane processes for isoamyl acetate synthesis, using experimentally certified models, was presented. Here, as an extension of that previous work, the performance of membrane reactors was analyzed, using the same thermodynamic, kinetic, and membrane transport models. Two different configurations were investigated by simulation using ASPEN Plus® together with a homemade Excel®-MatLab® interface for membrane reactor modules simulation. The goal was to gain more insight into the isoamyl acetate synthesis using membrane reactors, as a prelude to a detailed experimental research. The analysis procedure includes both the optimization of membrane reactor performance and the minimization of process energy consumption, including the energetic integration using the pinch point methodology. Total annualized costs were estimated and compared with the conventional and hybrid membrane schemes.

Fractional-Diffusion--Advection Limit of a Kinetic Model

A fractional diffusion equation with advection term is rigorously derived from a kinetic transport model with a linear turning operator, featuring a fat-tailed equilibrium distribution and a small directional bias due to a given vector field. The analysis is based on bounds derived by relative entropy inequalities and on two recently developed approaches for the macroscopic limit: a Fourier--Laplace transform method for spatially homogeneous data and the so called moment method, based on a modified test function.

Rapid bacteriophage MS2 transport in an oxic sandy aquifer in cold climate: Field experiments and modeling

AbstractVirus removal during rapid transport in an unconfined, low‐temperature (6°C) sand and gravel aquifer was investigated at a riverbank field site, 25 km south of Trondheim in central Norway. The data from bacteriophage MS2 inactivation and transport experiments were applied in a two‐site kinetic transport model using HYDRUS‐1D, to evaluate the mechanisms of virus removal and whether these mechanisms were sufficient to protect the groundwater supplies. The results demonstrated that inactivation was negligible to the overall removal and that irreversible MS2 attachment to aquifer grains, coated with iron precipitates, played a dominant role in the removal of MS2; 4.1 log units of MS2 were removed by attachment during 38 m travel distance and less than 2 days residence time. Although the total removal was high, pathways capable of allowing virus migration at rapid velocities were present in the aquifer. The risk of rapid transport of viable viruses should be recognized, particularly for water supplies without permanent disinfection.

Transition modelling implications in the CFD analysis of a turbine nozzle vane cascade tested over a range of Mach and Reynolds numbers

The aerodynamic performance of a gas turbine nozzle vane cascade was investigated over a range of Mach and Reynolds numbers. The work is part of a vast research project aimed at the analysis of fluid dynamics and heat transfer phenomena in cooled blades. In this paper computed results on the “solid vane” (without cooling devices) are presented and discussed in comparison with experimental data. Detailed measurements were provided by the University of Bergamo where the experimental campaign was carried out by means of a subsonic wind tunnel. The impact of boundary layer transition is investigated by using a novel laminar kinetic energy transport model and the widely used Langtry-Menter γ-Reθ,t model. The comparison between calculations and measurements is presented in terms of blade loading distributions, total pressure loss coefficient contours downstream of the cascade, and velocity/turbulence-intensity profiles within the boundary layer at selected blade surface locations at mid-span. It will be shown how transitional calculations compare favorably with experiments.

Potential of BODIPY-cholesterol for analysis of cholesterol transport and diffusion in living cells

Cholesterol is an abundant and important lipid component of cellular membranes. Analysis of cholesterol transport and diffusion in living cells is hampered by the technical challenge of designing suitable cholesterol probes which can be detected for example by optical microscopy. One strategy is to use intrinsically fluorescent sterols, as dehydroergosterol (DHE), having minimal chemical alteration compared to cholesterol but giving low fluorescence signals in the UV region of the spectrum. Alternatively, one can use dye-tagged cholesterol analogs and in particular BODIPY-cholesterol (BChol), whose synthesis and initial characterization was pioneered by Robert Bittman. Here, we give a general overview of the properties and applications but also limitations of BODIPY-tagged cholesterol probes for analyzing intracellular cholesterol trafficking. We describe our own experiences and collaborative efforts with Bob Bittman for studying diffusion in the plasma membrane (PM) and uptake of BChol in a quantitative manner. For that purpose, we used a variety of fluorescence approaches including fluorescence correlation spectroscopy and its imaging variants, fluorescence recovery after photobleaching (FRAP) and fluorescence loss in photobleaching (FLIP). We also describe pulse-chase studies from the PM using BChol in direct comparison to DHE. Based on the gathered imaging data, we present a two-step kinetic model for sterol transport between PM and recycling endosomes. In addition, we highlight the suitability of BChol for determining transport of lipoprotein-derived sterol using electron microscopy (EM) and show that this approach ideally complements fluorescence studies.

Electron impact ionization in the Martian atmosphere: Interplay between scattering and crustal magnetic field effects

Precipitating electrons are typically the dominant source of energy input into Mars' nighttime upper atmosphere, with consequences for atmospheric and ionospheric structure, composition, chemistry, and electrodynamics. Mars' spatially heterogeneous crustal magnetic fields affect the fluxes of precipitating electrons, via both the magnetic mirror force and Gauss' law of conservation of magnetic flux. We use a kinetic electron transport model to examine ionization rate profiles that result from the combination of these magnetic effects and elastic and inelastic scattering by atmospheric neutrals. Specifically, we calculate ionization rates as a function of altitude, crustal magnetic field strength, and the initial energy and pitch angle of the precipitating electrons, covering the relevant ranges of these parameters. Several complex behaviors are exhibited, including bifurcating ionization peaks with distinct characteristics and energy-dependent and crustal field strength-dependent increases in ionization with decreasing pitch angle. Elucidating such behavior is important for understanding the effect of Mars' unique crustal fields on the Mars upper atmosphere and ionosphere, both to predict the consequences of measured electron precipitation and to enable, for the first time, downward coupling of global plasma models with thermosphere-ionosphere models.

Large-eddy simulation of turbulent flow in stirred tank with a curved blade impeller

The turbulent flow field generated in a baffled stirred tank by a curved blade impeller has been investigated by employing large-eddy simulation (LES). The Smagorinsky-Lilly and kinetic energy transport model was used to model the unresolved, or subgrid, scales. The simulation has been validated by using available experimental observations on Rushton turbine and found reasonable agreement justifying the capability of the LES model in accurate prediction of turbulent characteristics in a stirred tank. Detailed analysis has been done for a stirred tank with a curved blade (CD-6) impeller to ascertain the flow characteristics of the curved blade impeller, which is generally considered to be the highly efficient impeller.

Kinetic model for transport of liquid molecules in the solid-liquid interface region: a molecular dynamics view

Kinetic model for transport of liquid molecules in the solid-liquid interface region: a molecular dynamics view

Fluctuations in a kinetic transport model for quantum friction

We study a linear Boltzmann equation describing the effective dynamics of a quantum particle moving through an ideal Bose gas at zero temperature. The particle emits sound waves into the Bose gas, a process causing it to slow down. This mechanism for friction is akin to one exhibited by a charged particle travelling through an optically dense medium at a speed larger than the speed of light and hence emitting Čerenkov radiation. We study the spatial trajectory of the Markov process corresponding to the Boltzmann equation and prove that this process converges to a multiple of Brownian motion after an exponential rescaling of time. We also show that the asymptotic position of the particle remains finite on average, but that its absolute value diverges logarithmically. Our unusual exponential rescaling of time is appropriate for a description of friction at zero temperature and is distinct from diffusive scaling appropriate at positive temperature. It is also shown that if random fluctuations of the particle position were neglected the latter would turn out to diverge.

PHOTOCHEMISTRY IN TERRESTRIAL EXOPLANET ATMOSPHERES. III. PHOTOCHEMISTRY AND THERMOCHEMISTRY IN THICK ATMOSPHERES ON SUPER EARTHS AND MINI NEPTUNES

Some super Earths and mini Neptunes will likely have thick atmospheres that are not H2-dominated. We have developed a photochemistry-thermochemistry kinetic-transport model for exploring the compositions of thick atmospheres on super Earths and mini Neptunes, applicable for both H2-dominated atmospheres and non-H2-dominated atmospheres. Using this model to study thick atmospheres for wide ranges of temperatures and elemental abundances, we classify them into hydrogen-rich atmospheres, water-rich atmospheres, oxygen-rich atmospheres, and hydrocarbon-rich atmospheres. We find that carbon has to be in the form of CO2 rather than CH4 or CO in a H2-depleted water-dominated thick atmosphere, and that the preferred loss of light elements from an oxygen-poor carbon-rich atmosphere leads to formation of unsaturated hydrocarbons (C2H2 and C2H4). We apply our self-consistent atmosphere models to compute spectra and diagnostic features for known transiting low-mass exoplanets GJ 1214 b, HD 97658 b, and 55 Cnc e. For GJ 1214 b like planets we find that (1) C2H2 features at 1.0 and 1.5 micron in transmission and C2H2 and C2H4 features at 9-14 micron in thermal emission are diagnostic for hydrocarbon-rich atmospheres; (2) a detection of water-vapor features and a confirmation of nonexistence of methane features would provide sufficient evidence for a water-dominated atmosphere. In general, our simulations show that chemical stability has to be taken into account when interpreting the spectrum of a super Earth/mini Neptune. Water-dominated atmospheres only exist for carbon to oxygen ratios much lower than the solar ratio, suggesting that this kind of atmospheres could be rare.

Understanding the Effect of Kinetic and Mass Transport Processes in Cathode Agglomerates

A 2D(1D) multi-scale membrane electrode assembly mathematical model is proposed to study the effect of micro-scale transport losses due to catalyst aggregation in the cathode catalyst layer of a fuel cell. In order to develop an analytical expression for micro-scale transport losses, previous agglomerate models assumed an oxygen reduction reaction order of one and neglected any proton transport effects. In this article, a numerical micro-scale spherical ionomer-filled agglomerate model is integrated with a two-dimensional membrane electrode assembly model in order to develop a flexible framework to study different charge, mass, and kinetic transport models that cannot generally be analyzed with an analytical formulation. Results show that there is a significant interplay between scales and that changes in micro-scale agglomerate properties can significantly affect agglomerate effectiveness and current density distributions in the catalyst layer while not significantly affecting overall cell performance. Using the proposed framework, the effects of: a) proton conductivity inside agglomerates, b) a non-equilibrium oxygen dissolution boundary condition, and c) electrochemical models with different oxygen reaction orders, are studied.

Transport of stabilized engineered silver (Ag) nanoparticles through porous sandstones

Engineered nanoparticles are increasingly applied in consumer products and concerns are rising regarding their risk as potential contaminants or carriers for colloid-facilitated contaminant transport. Engineered silver nanoparticles (AgNP) are among the most widely used nanomaterials in consumer products. However, their mobility in groundwater has been scarcely investigated. In this study, transport of stabilized AgNP through porous sandstones with variations in mineralogy, pore size distribution and permeability is investigated in laboratory experiments with well-defined boundary conditions. The AgNP samples were mainly characterized by asymmetric flow field-flow fractionation coupled to a multi-angle static laser light detector and ultraviolet-visible spectroscopy for determination of particle size and concentration. The rock samples are characterized by mercury porosimetry, flow experiments and solute tracer tests. Solute and AgNP breakthrough was quantified by applying numerical models considering one kinetic site model for particle transport. The transport of AgNP strongly depends on pore size distribution, mineralogy and the solution ionic strength. Blocking of attachment sites results in less reactive transport with increasing application of AgNP mass. AgNPs were retained due to physicochemical filtration and probably due to straining. The results demonstrate the restricted applicability of AgNP transport parameters determined from simplified experimental model systems to realistic environmental matrices.

Numerical simulations of ion and electron temperatures in the ionosphere of Mars: Multiple ions and diurnal variations

This study shows how ion and electron temperatures in the ionosphere of Mars, which affect plasma densities, vary with altitude and time of day. These new results can be used to support the interpretation of existing and anticipated measurements of ionospheric conditions. Here, a one-dimensional fluid model of the martian ionosphere has been coupled to a kinetic supra-thermal electron transport model in order to self-consistently calculate ion and electron densities and temperatures. The models include diurnal variations, revealing hundreds of degrees Kelvin changes in dayside electron and ion temperatures at fixed altitude. The models treat each ion species separately, revealing hundreds of degrees Kelvin differences between H+ and O2+ temperatures. The coupled models also include an adiabatic expansion term into the heating equation, which contribute significantly to temperatures of lighter ions. Consistent with previous studies using single-ion plasma, solar EUV heating alone is insufficient to heat the thermal electrons and ion species to observed temperatures, indicating the presence of additional heating sources. Best agreement with measurements is found when additional topside heating fluxes of 15×109 and 2×107eVcm−2s−1 produce topside heating rates that are 35 and 100 times higher than the nominal solar heating rate for electrons and ions, respectively.