Particle Diffusion Coefficient Research Articles

Coal particle size-dependent gas diffusion coefficient

The tests on gas (CH4 or CO2) desorption-diffusion in coal particles, together with the analytical unipore or bidisperse diffusion model, are widely used to study the gas diffusion behavior, but the fitted diffusion coefficient always increases with particle size, which makes it difficult to determine an identical diffusion coefficient for coal particles. In this work, five sets of anthracite particles with different sizes are prepared, and tests on CO2 desorption-diffusion in different coal particles are carried out. Four continuum models (including an analytical unipore diffusion model, an analytical bidisperse diffusion model, a numerical unipore diffusion model, and a dual-porosity model) and a discrete fracture model are established. The continuum models can all fit the experimental results well, while the fitted diffusion coefficients always increase with particle size. Based on the identical matrix’s side length, matrix diffusion coefficient, and fracture diffusion coefficient, the discrete fracture model fits the experimental results of different coal particles successfully, and the size effect of diffusion coefficient is resolved. The diffusion coefficient fitted by the continuum models is the equivalent diffusion coefficient of matrix diffusion and fracture diffusion, so the equivalent diffusion coefficient increases with fracture path (i.e., particle size), and the size effect of diffusion coefficient occurs. The results provide an insight into the size effect of diffusion coefficient and make it possible to determine an identical diffusion coefficient for coal particles of different sizes.

Molecular dynamic modeling and analysis of the sintering behaviors of GDC modified BSCF nanorods for rSOC oxygen electrode

Degradation including segregation and high stress related issues are significant challenges for reversible solid oxide cells (rSOCs), particularly concerning the oxygen electrode. Understanding the sintering preparation is crucial for enhancing the performance and reliability of the oxygen electrode under long-term dual-mode operation. In this study, the sintering process of Ba0.5Sr0.5Co0.8Fe0.2O3-δ nanorods anchored with Gd-doped CeO2 nanoparticles (GDC-BSCF-NR) was predicted by using molecular dynamics method. To optimize the sintering process, the stress distribution, A-site ion migration behavior and thermal properties of the composite electrode materials were analyzed at different sintering temperature, the effects of nanoparticle size were also investigated. Both thermal conductivity and thermal expansion increase with sintering temperature. The particle stress of the composites correlates positively with the diffusion coefficient of ions. The diffusion coefficients of surface and internal Ba/Sr ions increase by 6%-9% from 973 K to 1373 K, while stress increases by 19%-33%. The diffusion coefficient of BSCF particles decrease by 15.1% with an increase in GDC nanoparticle size, which is beneficial for suppressing Ba/Sr segregation.

Effect of a high-gradient magnetic field on particle concentration distribution in a magnetic fluid seal: Rivalry of the diffusion and magnetophoresis

In this paper, the unsteady process of particle concentration distribution in a magnetic fluid is studied. Diffusion and the effect of a high-gradient magnetic field in a magnetic fluid seal (MFS) are taken into consideration. It is crucial to take into account how particle mobility and diffusion coefficient vary on particle concentration in order to determine the possibility and time of the formation of a close packing of particles. The Carnaghan-Starling approximation was employed. It is demonstrated numerically that the geometry of the MFS, namely its gap width and pole base width, as well as the magnitude of the magnetic field strength under the pole tooth of the MFS, both influence the time of the formation of a close packing of particles. This period can be regarded as the MFS's uptime. Depending on the design of the working gap, the uptime seal for magnetic fluid based on vacuum oil may require between two weeks and six months. The uptime seal also becomes shorter when the carrier fluid's viscosity decreases.

The motion of Brownian particles suspended in a non-uniform fluid flow

The effect of the type of fluid flow velocity profile on the motion of a Brownian particle in a circular tube has been studied using a Monte Carlo technique to simulate particle trajectories. Three types of fluid flow were studied: uniform (UF), parabolic (PF), and an initial uniform flow which evolves and may eventually attain the parabolic velocity profile, i.e. transient flow (TF). For UF and PF, radial and axial particle diffusion were simultaneously considered in some cases; for TF, where fluid dynamics equations had to be solved in addition to the Monte Carlo simulations, axial diffusion was neglected for fluid and particles, so that calculations had to be restricted to tube aspect ratios (radius/length) smaller than 0.1, a common scenario in most practical aerosol applications. A first series of simulations were performed to determine the overall particle penetration through the tube. For fixed tube geometry and particle diffusion coefficient, penetration in TF lied between those in PF (highest) and UF (lowest), in such a manner that, for a given value of the diffusion coefficient, the larger the degree of flow development (i.e., the smaller the values of the tube aspect ratio and the Reynolds number), the larger the penetration. These findings are coherent with those found in a former investigation dealing with the particle residence time in the tube. In a second series of simulation runs, calculations were done for selected initial locations of the particle within the tube entrance cross section, to examine the effect that the proximity of the particle starting position to the tube wall or to the tube axis has on variables such as penetration, mean first hitting time and length, mean first exit time, and mean axial velocity of lost and survived particles. When the fluid flow is not uniform but varies from place to place, the mean particle axial velocity is larger than that of the fluid. This counterintuitive fundamental result allows interpretation of the trends observed in penetration and residence time.

Validation of SOLPS-ITER simulations against the TCV-X21 reference case

This paper presents a quantitative validation of Scrape-Off Layer Plasma Simulation-ITER (SOLPS-ITER) simulations against the TCV-X21 reference case and provides insights into the neutral dynamics and ionization source distribution in this scenario. TCV-X21 is a well-diagnosed diverted L-mode sheath-limited plasma scenario in both toroidal field directions, designed specifically for the validation of turbulence codes (Oliveira, Body et al 2022 Nucl. Fusion 62 096001). Five new, neutrals-related observables are added here to the extensive, publicly available TCV-X21 dataset. These are three deuterium Balmer lines in the divertor and neutral pressure measurements in the common and private flux regions. The quantitative agreement metric used in the validation is combined with the conjugate gradient method to approach the SOLPS-ITER input parameters that return the best overall agreement with the experiment. A proof-of-principle test of this method results in a modest improvement in the level-of-agreement; the shortcomings impacting the result and how to improve the methodology are discussed. Alternatively, a scan of the particle and heat diffusion coefficients shows an improvement of 10.4% in the level-of-agreement, approximately twice as high as that achieved by the gradient method. This result is found for an increased transport coefficient compared to what is usually used for TCV L-mode plasmas. The simulations further indicate that ∼65% of the total ionization occurs in the SOL, from which ∼70% in the divertor regions, despite being a sheath-limited regime, motivating the inclusion of self-consistent neutral models in future turbulence simulations on the path towards improved agreement with the experiment.

Computational fluid dynamics method for determining the rotational diffusion coefficient of cells

This work presents a straightforward computational method to estimate the rotational diffusion coefficient (Dr) of cells and particles of various sizes using the continuum fluid mechanics theory. We calculate the torque (Γ) for cells and particles immersed in fluids to find the mobility coefficient μ and then obtain the Dr by substituting Γ in the Einstein relation. Geometries are constructed using triangular mesh, and the model is solved with computational fluid dynamics techniques. This method is less intensive and more efficient than the widely used models. We simulate eight different particle geometries and compare the results with previous literature.

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 1018 r 1.17±0.08 E 0.71±0.02 (cm2 s−1) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

Mechanism insight of sorption of Er(III) and Nd(III) ions onto Aluminium barium tungstate synthesized via streamlined sol–gel technique: Time-transient study

Aluminium barium tungstate powder (ABT) was chemically synthesized via streamlined sol–gel technique and exploited as a sorbent material for sorption of erbium and neodymium ions from aqueous solutions under simulated conditions using batch technique. The pH influence, time and temperature factors have been studied. The sorption of neodymium ions was found to be marginally higher than that of erbium ions and the apparent sorption capacity has a progressive influence with temperature. Thermodynamic parameters such as Gibbs free energy change (ΔG◦), enthalpy change (ΔH◦) and entropy change (ΔS◦) were calculated. The negative ΔG◦ values declines with an increase in temperature value, demonstrating that the sorption reaction for both studied ions was spontaneous and more promising at greater temperature. The positive ΔH◦ values affirm that the nature of the sorption processes is endothermic. The comparison of different time transient models applied to the sorption data was assessed for the pseudo first-order (PFO), the pseudo second-order, (PSO) and homogeneous particle diffusion (HPD) models. The results revealed that both PSO and HPD models were found to best correlate the experimental sorption rate data and a monolayer model was adopted as the best suitable model to explore the sorption mechanism for both studied ions. The attained particle diffusion coefficients and rate constant values were acquired from the graphical illustration of the anticipated models. Activation energy change (Ea) and activation entropy change (ΔS±) were also calculated from the linearized Arrhenius model and indicated that the binding process between the sorbent and the studied ions occurred through chemisorption and the sorption of both ions onto synthetic sorbent took place through associative mechanism.

Adsorption characteristics of S-Metolachlor onto the sawdust biochar derived from Acacia auriculiformis

The adsorption mechanism of S-Metolachlor in an aqueous solution by sawdust biochar derived from Acacia auriculiformis (SAB) was studied. SAB was manufactured at 500 °C for 4 h under oxygen-limited conditions and characterized for SEM, EDS, pHpzc, BET, and FTIR. The adsorption kinetics, isotherm, and diffusion studies of S-Metolachlor and SAB were further explored. Moreover, the effects of the solution pH were examined on the adsorption of S-Metolachlor by SAB. The BET analysis of SAB was achieved at 106.74 m2.g − 1 and the solution pH did not significantly influence the S-Metolachlor adsorption. The adsorption data were fitted into a Langmuir isotherm and the PSO model. The film diffusion coefficient Df (4.93 × 10 − 11 to 8.17 × 10 − 11 m2.s − 1) and the particle diffusion coefficient Dp (1.68 × 10 − 11 to 2.65 × 10 − 11 m2.s − 1) were determined and the rate-limiting step of S-Metolachlor adsorption and SAB was governed by liquid film diffusion. The S-Metolachlor adsorption process onto SAB was controlled by multiple mechanisms, including pore filling, H-bonding, hydrophobic interaction, and π-π EDA interactions. H-bonding is the main interaction for the adsorption of S-Metolachlor and SAB. Conclusively, the study illustrates that biochar produced from Acacia auriculiformis sawdust possessed effective adsorption properties for S-Metolachlor herbicide.

Time-dependent properties of run-and-tumble particles: Density relaxation.

We characterize collective diffusion of hardcore run-and-tumble particles (RTPs) by explicitly calculating the bulk-diffusion coefficient D(ρ,γ) for arbitrary density ρ and tumbling rate γ, in systems on a d-dimensional periodic lattice. We study two minimal models of RTPs: Model I is the standard version of hardcore RTPs introduced in [Phys. Rev. E 89, 012706 (2014)10.1103/PhysRevE.89.012706], whereas model II is a long-ranged lattice gas (LLG) with hardcore exclusion, an analytically tractable variant of model I. We calculate the bulk-diffusion coefficient analytically for model II and numerically for model I through an efficient Monte Carlo algorithm; notably, both models have qualitatively similar features. In the strong-persistence limit γ→0 (i.e., dimensionless ratio r_{0}γ/v→0), with v and r_{0} being the self-propulsion speed and particle diameter, respectively, the fascinating interplay between persistence and interaction is quantified in terms of two length scales: (i) persistence length l_{p}=v/γ and (ii) a "mean free path," being a measure of the average empty stretch or gap size in the hopping direction. We find that the bulk-diffusion coefficient varies as a power law in a wide range of density: D∝ρ^{-α}, with exponent α gradually crossing over from α=2 at high densities to α=0 at low densities. As a result, the density relaxation is governed by a nonlinear diffusion equationwith anomalous spatiotemporal scaling. In the thermodynamic limit, we show that the bulk-diffusion coefficient-for ρ,γ→0 with ρ/γ fixed-has a scaling form D(ρ,γ)=D^{(0)}F(ρav/γ), where a∼r_{0}^{d-1} is particle cross sectionand D^{(0)} is proportional to the diffusion coefficient of noninteracting particles; the scaling function F(ψ) is calculated analytically for model II (LLG) and numerically for model I. Our arguments are independent of dimensions and microscopic details.

Simulation study of the influence of the cross‐field anomalous diffusion on the tungsten impurity transport in the scrape‐off layer with activated drifts

AbstractTungsten (W) impurity eroded from the divertor target can degrade the confinement performance of future fusion reactors. The mechanism of the effect of E × B drift on the W transport in the scrape‐off layer (SOL) was investigated with a fixed cross‐field anomalous particle diffusion coefficient for W ions (D⊥,W) of 1 m2s−1 in our previous simulation work, which indicates that the W flux entering the confined region (Γenter) and mean W concentration in the confined region () can be increased by more than one order of magnitude by drifts. In this work, the influence of the cross‐field anomalous diffusion on the W transport in the SOL is further investigated. The basic flow pattern of the W ion flux (ΓW) keeps when D⊥,W varying from 0.5 to 3 m2s−1, and Γenter mainly comes from the hotter divertor region. Results show that D⊥,W value affects the W leakage from divertor region and entry into confined region. Therefore, Γenter and both decrease with increasing D⊥,W. Mechanisms for cases w/wo drifts are compared.

A stochastic lipid structured model for macrophage dynamics in atherosclerotic plaques.

We propose to model certain aspects of the dynamics of a macrophage that moves randomly in a one dimensional space in arterial wall tissue and grows by accumulating localized lipid particles, thus reducing its motility. This phenomenon has been observed in the context of atherosclerotic plaque formation. For this purpose, we use a system of stochastic differential equations satisfied by the position and diffusion coefficient of a Brownian particle whose diffusion coefficient is modified at each visit to the origin and with a dumping coefficient. The novelty of the model, with respect to Bénichou et al. (Phys Rev E 85(2):021137, 2012), Meunier et al. (Acta Appl Math 161:107-126, 2019), is to include offloading of lipids through the dumping term. We find explicit necessary and sufficient conditions for macrophage trapping in the locally enriched region.

Effect of Coal Particle Breakage on Gas Desorption Rate during Coal and Gas Outburst

The gas contained in coal plays a crucial role in triggering coal and gas outbursts. During an outburst, a large quantity of gas originally absorbed by coal is released from pulverized coal. The role this part of the gas plays in the process of coal and gas outbursts has not been clearly elucidated yet. Therefore, investigating the changes in gas desorption rate from coal particles of different sizes could provide some meaningful insights into the outburst process and improve our understanding of the outburst mechanism. First, combining the diffusivity of coal of different particle sizes and the distribution function of broken coal, we present a gas desorption model for fragmented gas-bearing coal that can quantify gas desorption from coal particles within a certain range of size. Second, the gas desorption rate ratio is defined as the ratio of the gas desorption rate from coal being crushed to that from coal before breaking. The desorption rate ratio is mainly determined by the desorption index (γ) and the granularity distribution index (α). Within the limit range of coal particle sizes, the ratio of effective diffusion coefficient for coal particles with different sizes is directly proportional to the reciprocal of the ratio of particle sizes. Under uniform particle size conditions before and after fragmentation, the gas desorption rate ratio is the square root of the reciprocal of the effective diffusion coefficient. The gas desorption model quantitatively elucidates the accelerated desorption of adsorbed gas in coal during the continuous fragmentation process of coal during an outburst.

The Effect of Solar Wind on Charged Particles’ Diffusion Coefficients

The transport of energetic charged particles through magnetized plasmas is ubiquitous in interplanetary space and astrophysics, and the important physical quantities are the parallel and perpendicular diffusion coefficients of energetic charged particles. In this paper, the influence of solar wind on particle transport is investigated. Using the focusing equation, we obtain parallel and perpendicular diffusion coefficients, accounting for the solar wind effect. For different conditions, the relative importance of the solar wind effect to diffusion is investigated. It is shown that, when energetic charged particles are close to the Sun, for parallel diffusion, the solar wind effect needs to be taken into account. These results are important for studying energetic charged particle transport processes in the vicinity of the Sun.

Методический подход к исследованию магнитного взаимодействия тонкодисперсных частиц в водной суспензии методом компьютерного моделирования

The need to increase the efficiency of mining operations determines the relevance of studying the properties of fine mineral particles for their extraction and reduction of environmental pollution. The development of approaches to studying magnetic interaction of fine particles is of scientific and practical importance and is associated with the complexity of calculating the superposition of their fields when solving the problem of controlling the magnetic properties of a suspension. A computer model of the dynamics of magnetic particle interaction was developed with account for their aggregation under the impact of the magnetic dipole-dipole interaction and the destruction of aggregates during thermal (Brownian) motion in order to predict the magnetic properties of the suspension using the example of magnetite deposits of the Zaimandrovsky iron ore region. The calculation shows that the electrostatic and dispersion interactions do not have a significant effect on the interaction dynamics of micron and submicron particles of magnetite with account of the experimentally measured zeta potential and the Hamaker's constant. A procedure has been developed for calibrating a computer model of the interaction dynamics of magnetic particles using the temperature dependence of the coefficient of translational diffusion of magnetite particles and the concentration dependence of the magnetic susceptibility of a suspension. An array of calculated values of the diffusion coefficient of the model particles and the initial magnetic susceptibility of their system is formed in a wide range of computer model parameters. A procedure has been developed for linking the calculated and experimental data by varying the normalization parameters of the particle size, viscosity of the medium, and thermal energy in order to minimize the maximum discrepancy between the values. The necessity is established of taking into account the change in magnetic properties with a decrease in the size of magnetite particles during the calibration of the magnetic susceptibility of a model system. The developed methodological approach ensures good convergence of the calculated and experimental data and makes it possible to visualize the aggregation of the model particles as the result of dipole-dipole interactions. The developed computer model of the interaction dynamics of magnetic particles can be used to study the effect of an external magnetic field on the aggregation ability of fine magnetite particles in order to control their extraction in separation processes.

Development of 1-phenyl-3-(4-(pyridin-4-ylmethyl)phenyl)urea derivatives as robust corrosion inhibitors for mild steel in 1 M HCl environment: Insight from ,molecular, experimental, and microscopic-scale modelling approaches

Cost-effective, novel urea derivatives, 1-phenyl-3-(4-(pyridin-4-ylmethyl)phenyl)urea (U-1), 1‐(4‐fluorophenyl)‐3‐(4‐(pyridin‐4‐ylmethyl)phenyl)urea (U-2), and 1‐(4‐methylphenyl)‐3‐(4‐(pyridin‐4‐ylmethyl)phenyl)urea (U-3) were synthesized to investigate as the corrosion inhibitors for mild steel/1 M HCl interface. Inhibition efficiency increases with the increasing inhibitor’s concentration but decreases with increasing temperature. Thermodynamic adsorption and activation parameters demonstrate that the adsorption of inhibitors follows Langmuir isotherm via physicochemical interactions. Potentiodynamic polarization measurements reveal that the inhibitors are mixed-type, impeding the charge-transfer process. Surface analysis supports a thin inhibitor film formation on the mild steel. The maximum inhibition efficiency of U-1, U-2 and U-3 are 94.97 ± 0.38%, 93.60 ± 0.62% and 97.42 ± 0.48% respectively. The calculated electrochemical impedance spectra (EIS) parameters such as ohmic resistance, double layer capacitance, relaxation time, effective thickness, and conductivity of grain and grain boundary are in-line with the efficiencies of NHUs. The performance of corrosion inhibitors follows a sequence U-3 > U-1 > U-2, emphasizing the influence of the substituent’s inductive effect (-CH3 > -H > -F) in inhibitors. Density functional theory (DFT) was performed to understand the correlation between molecular structure and inhibition efficiency. The Fukui indices confirm the presence of local attacking sites on the metal surface where inhibitors attack. A molecular dynamic (MD) simulation is used to determine the interaction energies between the inhibitors and mild steel. Radial Distribution Function (RDF) measurements confirm the existence of the chemical nature of the interaction. Furthermore, the diffusion coefficient of corrosive particles, self-diffusion coefficient of inhibitors, fractional free volume (FFV), and interaction between inhibitor’s film and corrosive particles are examined. Theoretical studies support experimental results.

Enhanced diffusion of tracer particles in nonreciprocal mixtures.

We study the diffusivity of a tagged particle in a binary mixture of Brownian particles with nonreciprocal interactions. Numerical simulations reveal that, for a broad class of interaction potentials, nonreciprocity can significantly increase the long-time diffusion coefficient of tracer particles and that this diffusion enhancement is associated with a breakdown of the Einstein relation. These observations are quantified and confirmed via two different and complementary analytical approaches: (i) a linearized stochastic density field theory, which is particularly accurate in the limit of soft interactions, and (ii) a reduced two-body description, which is exact at leading order in the density of particles. The latter reveals that diffusion enhancement can be attributed to the formation of transiently propelled dimers of particles, whose cohesion and speed are controlled by the nonreciprocal interactions.

The Stokes-Einstein-Sutherland Equationat the Nanoscale Revisited.

The Stokes-Einstein-Sutherland (SES) equationis at the foundation of statistical physics, relating a particle's diffusion coefficient and size with the fluid viscosity, temperature, and the boundary condition for the particle-solvent interface. It is assumed that it relies on the separation of scales between the particle and the solvent, hence it is expected to break down for diffusive transport on the molecular scale. This assumption is however challenged by a number of experimental studies showing a remarkably small, if any, violation, while simulations systematically report the opposite. To understand these discrepancies, analytical ultracentrifugation experiments are combined with molecular simulations, both performed at unprecedented accuracies, to study the transport of buckminsterfullerene C60 in toluene at infinite dilution. This system is demonstrated to clearly violate the conditions of slow momentum relaxation. Yet, through a linear response to a constant force, the SES equationcan be recovered in the long time limit with no more than 4% uncertainty both in experiments and in simulations. This nonetheless requires partial slip on the particle interface, extracted consistently from all the data. These results, thus, resolve a long-standing discussion on the validity and limits of the SES equationat the molecularscale.

Experimental study of turbulent thermal diffusion of particles in an inhomogeneous forced convective turbulence

We investigate experimentally the phenomenon of turbulent thermal diffusion of micrometer-size solid particles in an inhomogeneous convective turbulence forced by one vertically oriented oscillating grid in an air flow. This effect causes the formation of large-scale inhomogeneities in particle spatial distributions in a temperature-stratified turbulence. We perform detailed comparisons of the experimental results with those obtained in our previous experiments with an inhomogeneous and anisotropic stably stratified turbulence produced by a one oscillating grid in the air flow. Since the buoyancy increases the turbulent kinetic energy for convective turbulence and decreases it for stably stratified turbulence, the measured turbulent velocities for convective turbulence are larger than those for stably stratified turbulence. This tendency is also seen in the measured vertical integral turbulent length scales. Measurements of temperature and particle number density spatial distributions show that particles are accumulated in the vicinity of the minimum of the mean temperature due to the phenomenon of turbulent thermal diffusion. This effect is observed in both convective and stably stratified turbulence, where we find the effective turbulent thermal diffusion coefficient for micrometer-size particles. The obtained experimental results are in agreement with theoretical predictions.

Residence time distribution of ultrafine aerosol particles in a tube with transient and parabolic laminar flow

This paper presents a theoretical investigation concerning the residence time distribution (RTD) of ultrafine monodisperse aerosol particles flowing in a circular tube in laminar flow regime. If a fully developed, parabolic flow (PF) velocity profile is assumed for the whole tube length, the convection-diffusion process undergone by the aerosol particles can be described by means of two parameters, the dimensionless particle diffusion coefficient D and the tube aspect ratio a (radius/length). An additional parameter, the Reynolds number Re, must be taken into consideration when the flow develops starting from a given velocity profile at the tube entrance, which we have assumed to be a uniform (plug) flow. The latter situation is referred to as transient flow (TF). The RTD has been determined using two different variations of a Monte Carlo (MC) technique to simulate the particle trajectory within the tube. The difference between the two MC methods is the assumed distribution of Brownian random displacements of the particles; in both cases the distribution had zero mean and variance 2DΔt, but the distribution was uniform in one method and normal in the other. The simulation results obtained with the two methods were almost coincident. In either PF or TF, even for relatively small values of D the aerosol RTD is quite different from that of the fluid where the particles are suspended. In particular, the dimensionless mean particle residence time, which initially decreases with D, soon attains an asymptotic value of 0.65 for D ≥ 0.3 (the mean residence time of the fluid is 1) in PF; a similar asymptotic value is attained for TF but in this case it depends on the particular combination of a and Re considered. The relative influence of axial diffusion on the RTD is insignificant unless the tube ratio a is of the order of 0.5 (tube with a length equal to its diameter).