Effects Of Molecular Diffusion Research Articles

Gravity Wave Heating and Cooling in Jupiter's Thermosphere

A numerical model to explore the possibility that the dissipation of two upward propagating internal gravity waves, identified in the temperature measurements of the Galileo Probe, provide the energy to maintain Jupiter's high thermospheric temperatures ∼900 K is used. The propagation and dissipation of the gravity waves are simulated by a full-wave model that is used to calculate the thermal mean-state forcing. The observed temperature is the result of this forcing and other energy sources. The equation of heat transfer, including the effects of eddy and molecular thermal diffusion, is solved to provide the gravity wave contribution to the steady-state temperature distribution. For the smallest values of eddy diffusion considered, the waves can heat the entire thermosphere, while for the largest values of eddy diffusion, the waves can cool the entire thermosphere. However, in all cases considered the net heating and cooling effects are not large, being typically ∼15–20 K or less. To the extent that the Galileo data characterize gravity waves in Jupiter's atmosphere, gravity wave dissipation is unlikely to be the source of energy maintaining Jupiter's high thermospheric temperatures. Other waves not identified in the Galileo data or other energy sources must be responsible for heating the jovian thermosphere. We demonstrate that the viscous heating can only be calculated using the viscous stress tensor, and that the use of the wave mechanical energy flux divergence for this purpose in previous studies is invalid.

Simulation of electrophoretic separations: effect of numerical and molecular diffusion on pH calculations in poorly buffered systems.

A poorly buffered cationic isotachophoresis separation, first simulated by Reijenga and Kasica, has been revisited to demonstrate that an inconsistent description of solute and charge transport can lead to significant errors in the pH calculation. The separation is first simulated using a second-order finite difference scheme to show that omission of molecular diffusion from the charge balance results in a pH profile with spurious dips in the steady-state zone boundaries. The separation is also simulated using two first-order methods that employ numerical diffusion to stabilize solutions against spatiotemporal oscillations. Similar pH dips are generated by these first-order schemes, even when molecular diffusion is included in the charge balance, if numerical diffusion is not considered amongst the charge transport mechanisms. When numerical diffusion, inherent in the discretization of the component balances, is introduced to the charge balance, the spurious pH dips are eliminated. The results indicate that (i) pH dips originally reported by Reijenga and Kasicka are merely artifacts of their numerical model, and (ii) nonoscillatory numerical techniques, such as upwinding and flux limiters, should incorporate artificial transport mechanisms in the charge as well as the solute balances.

Characteristics of fluorescein dye and temperature fluctuations in a turbulent near-wake

The Laser Induced Fluorescence (LIF) technique was used to determine a few characteristics of a high Schmidt number (Sc) passive scalar (fluorescein) in the near-wake of a circular cylinder. The mean and rms concentration indicate that increasing the Reynolds number (Re) improves the large-scale mixing and accelerates the homogenisation of the scalar. As Re increases, the intensity of segregation decreases because of turbulent diffusion but the scale of segregation increases due to dispersion. Comparison between concentration and temperature rms profiles indicates that molecular diffusion has a much smaller effect on the decay of the scalar variance than the Reynolds number. The ratio of mean-squared values of lateral and streamwise spatial derivatives of the scalar fluctuation deviates from isotropy, the departure increasing with Re. This reflects more the effect of dispersion by the turbulent velocity field rather than any molecular diffusion effect. At a given Re, the ratio decreases as the distance from the cylinder increases. This trend is more accentuated near the edge of the wake than at the centreline.

Chaotic advection, diffusion, and reactions in open flows.

We review and generalize recent results on advection of particles in open time-periodic hydrodynamical flows. First, the problem of passive advection is considered, and its fractal and chaotic nature is pointed out. Next, we study the effect of weak molecular diffusion or randomness of the flow. Finally, we investigate the influence of passive advection on chemical or biological activity superimposed on open flows. The nondiffusive approach is shown to carry some features of a weak diffusion, due to the finiteness of the reaction range or reaction velocity. (c) 2000 American Institute of Physics.

Passive scalar transport in a random flow with a finite renewal time: Mean-field equations

A mean-field equation for a passive scalar (e.g., for a mean number density of particles) in a random velocity field (incompressible and compressible) with a finite constant renewal time is derived. The finite renewal time of a random velocity field results in the appearance of high-order spatial derivatives in the mean-field equation for a passive scalar. We considered three models of a random velocity field: (i) a velocity field with a small renewal time; (ii) the Gaussian approximation for Lagrangian trajectories; and (iii) a small inhomogeneity of the velocity and mean passive scalar fields. For a small renewal time we recovered results obtained using the $\ensuremath{\delta}$-function-correlated in time random velocity field. The finite renewal time and compressibility of the velocity field can cause a depletion of turbulent diffusion and a modification of an effective drift velocity. For a compressible velocity field the form of the mean-field equation for a passive scalar depends on the details of the velocity field, i.e., the universality is lost. For an incompressible velocity field the universality exists in spite of the finite renewal time. Results by Saffman [J. Fluid Mech. 8, 273 (1960)] for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of a compressible and anisotropic random velocity field. The obtained results may be of relevance in some atmospheric phenomena (e.g., atmospheric aerosols and smog formation).

Modeling the formation of flammable atmospheres within cylindrical containers containing some liquid fuel

A two-dimensional axisymmetric mathematical model has been developed to describe the transient formation of flammable atmospheres within the confines of a partially empty open-topped liquid fuel container. The model was numerically solved using a finite volume scheme. The formulation included consideration of local changes in density and thermophysical properties of the formed gaseous mixtures due to the concentration and temperature variations within the container. The flammable zone was assumed to be defined by all the spatial locations inside the container where the fuel vapor concentration is within the lean and the rich flammable concentrations range. It was found that the transient development of the flammable zone above the liquid-gas interface was controlled by the combined effects of molecular and convective diffusion of the fuel vapor from interface. The fuel vapor diffusion and mixing process was also enhanced by natural convection, which was induced by the presence of temperature and concentration gradients within the container. Different flammable zone development regimes evolve that depend on the fuel properties, the fuel flammable concentration range, and the surrounding ambient conditions. Two liquid fuels, namely n-pentane and methanol, are considered to address some of the effects related to fuel properties and the fuel flammable concentration range. The effect of the surrounding ambient temperature conditions on the development of the flammable zone is also considered.

Turbulent transport of atmospheric aerosols and formation of large-scale structures

Turbulent transport of aerosols and droplets in a random velocity field with a finite correlation time is studied. We derived a mean-field equation and an equation for the second moment for a number density of aerosols. The finite correlation time of random velocity field results in the appearance of the high-order spatial derivatives in these equations. The finite correlation time and compressibility of the velocity field can cause a depletion of turbulent diffusion and a modification of an effective mean drift velocity. The coefficient of turbulent diffusion in the vertical direction can be depleted by 25 % due to the finite correlation time of a turbulent velocity field. The latter result is in compliance with the known anisotropy of the coefficient of turbulent diffusion in the atmosphere. The effective mean drift velocity is caused by a compressibility of particles velocity field and results in formation of large-scale inhomogeneities in spatial distribution of aerosols in the vicinity of the atmospheric temperature inversion. Results obtained by Saffman (1960) for the effect of molecular diffusivity in turbulent diffusion are generalized for the case of compressible and anisotropic random velocity field. A mechanism of formation of small-scale inhomogeneities in particles spatial distribution is also discussed. This mechanism is associated with an excitation of a small-scale instability of the second moment of number density of particles. The obtained results are important in the analysis of various atmospheric phenomena, e.g., atmospheric aerosols, droplets and smog formation.

Simulated Ground Deposition Of Fine Airborne Particles In An Array Of Idealized Tree Crowns

Wind-tunnel experiments were used to investigate the ground deposition of fine airborne particles in an array of idealized tree crowns. The particle ground deposition was modelled with a gaseous tracer instead of solid particles, which is an approach for very fine particles. A chemical method based on the reaction of ammonia and manganese chloride was used to quantify the mass transfer from the simulated atmospheric boundary-layer flow to the surface. Using a tracer gas instead of solid particles can be considered only if turbulent diffusion is the decisive deposition mechanism and effects of sedimentation, impaction, interception or molecular diffusion can be approximately ignored. These constraints are necessary due to scaling problems concerning particle modelling in the small-scale experiment. The intention was to determine the obstacle arrangement density in which the mean ground deposition is maximized for a defined crown form. A deposition amplification factor α was defined as the quotient of deposition efficiencies for an area with tree crowns and an open ground with identical similarity parameters. Based on this calculation an increase of the ground deposition by up to 60% should be realistic through a favourable arrangement of tree crowns and tree number density. An increase in turbulence intensity in the flow leads to a significant amplification of the mean ground deposition.

Numerical simulation of detonation initiation in a flame brush: the role of hot spots

This is the final paper in a series describing numerical simulations of deflagration-to-detonation transition (DDT) for conditions similar to reflected shock-tube experiments in an acetylene–air mixture (100 Torr, 298 K). In the experiments and calculations, the interaction of a shock wave and an expanding flame front leads to the rapid creation of a turbulent flame brush and, for sufficiently high Mach numbers of the incident shock, to the subsequent transition to a detonation. The two-dimensional reactive Navier-Stokes equations, including the effects of viscosity, thermal conduction, molecular diffusion, and chemical reaction, are solved on a high-resolution adapting mesh. Shock-flame interactions, through the Richtmyer-Meshkov instability, create and maintain a highly turbulent flame brush and are responsible for injecting unburned material into the region of burned material. Hot spots are created by pressure fluctuations and shocks generated in the flame brush. At relatively low Mach numbers, hot spots that transition to detonation are created outside of the flame brush. For higher Mach numbers, such hot spots are created in pockets of unreacted material inside the flame brush. In both cases, the hot spots give rise to detonations by the gradient mechanism, in which a gradient in induction time leads to a supersonic spontaneous wave that later becomes a detonation.

A model study of kBH−1 for vegetated surfaces using ‘localized near-field’ Lagrangian theory

Models of energy and mass exchange between vegetation canopies and the atmosphere usually include some formulation of the bulk boundary layer resistance ( R b or the related parameter kB −1) to describe the effects of molecular diffusion occurring near the leaf and soil surfaces. Present formulations of kB −1 are either empirical expressions or are physically based models derived from a K-theory approach. However, K-theory does not describe the observed counter gradient flow within canopies and the empirical expressions usually lump both canopy and soil effects into a single surface resistance (single source approach). For areas of partial canopy cover, single source formulations have been difficult to formulate with any certainty and often do not agree with observations. This study uses ‘localized near-field’ (LNF) Lagrangian theory to develop a model of kB −1 (for heat transfer) for the vegetation component of a dual source model and for the combined effects of canopy and soil in a single source approach. The present model also uses a physically based, one-dimensional, analytical model to describe the influence of canopy structure and density upon the within-canopy far field diffusivity and Lagrangian time scale which are central to the LNF Lagrangian theory. The canopy turbulence model is designed for arbitrary foliage structure and density and kB −1 is defined in terms of heat and momentum fluxes rather than the more conventional logarithm of the ratio of the momentum and thermal roughness lengths. The resulting kB −1 model is used for sensitivity studies of kB −1 for canopies only (i.e. no soil contribution) and for the coupled canopy–soil system (i.e. a single source model). Results indicate that foliage density (Drag Area Index or Leaf Area Index), wind speed, leaf size, possible sheltering effects, and, to a lesser extent, the vertical foliage distribution and the vertical variation of the temperature difference between the foliage and the near-leaf air space can influence kB −1. For the single source model the soil boundary layer resistance was found to be significant for areas of partial canopy cover. In spite of the relative complexity of the full LNF model of kB −1, a simple expression that varies smoothly between bare soil and full canopy cover is developed that captures much of the modeled and observed variation in kB −1 for the single source approach.

Monitoring Reaction Kinetics in Solution by Continuous-Flow Methods: The Effects of Convection and Molecular Diffusion under Laminar Flow Conditions

Continuous-flow methods are a simple and efficient tool for monitoring the kinetics of chemical reactions in solution. After a reaction has been initiated by a mixing step, liquid flows down an obs...

Universal properties of chaotic transport in the presence of diffusion

The combined, finite time effects of molecular diffusion and chaotic advection on a finite distribution of scalar are studied in the context of time periodic, recirculating flows with variable stirring frequency. Comparison of two disparate frequencies with identical advective fluxes indicates that diffusive effects are enhanced for slower oscillations. By examining the geometry of the chaotic advection in both high and low frequency limits, the flux function and the width of the stochastic zone are found to have a universal frequency dependence for a broad class of flows. Furthermore, such systems possess an adiabatic transport mechanism which results in the establishment of a “Lagrangian steady state,” where only the asymptotically invariant core remains after a single advective cycle. At higher frequencies, transport due to chaotic advection is confined to exchange along the perimeter of the recirculating region. The effects of molecular diffusion on the total transport are different in these two cases and it is argued and demonstrated numerically that increasing the diffusion coefficient (in some prescribed range) leads to a dramatic increase in the transport only for low frequency stirring. The frequency dependence of the total, long time transport of a limited amount of scalar is more involved since faster stirring leads to smaller invariant core sizes.

High resolution off-magic-angle spinning NMR for cholesteric liquid crystals

High resolution NMR of cholesteric liquid crystals is realized by off-magic-angle spinning (OMAS). Using the average potential theory, it is shown that the pitch axes of a cholesteric liquid crystal with a positive (negative) magnetic susceptibility anisotropy are aligned along the spinning axis with an OMAS angle larger (smaller) than the magic angle without any distortion of the helical structure, which is untwisted or distorted by the static magnetic field in some static samples. Hence, the line broadening due to the anisotropies of chemical shifts and/or quadrupole couplings is removed, while information of the anisotropies in cholesteric alignments can be obtained from the line positions. A detailed theoretical analysis of effects of spinning frequency and molecular diffusion along the pitch axis on the linewidth is given, predicting that the resolution is improved greatly at a spinning frequency much higher than the rotational diffusion coefficient. These theoretical results are verified by 13C OMAS experiments on a cholesteric liquid crystal of p-ethoxybenzyl-p-[(S)-2- methylbutyl]aniline (EBMBA) and cholesteric mixtures of p-methoxybenzylidene-p-n-butylaniline (MBBA) and cholesteryl chloride (CC).

Numerical simulation of deflagration-to-detonation transition: the role of shock–flame interactions in turbulent flames

Two-dimensional reactive Navier-Stokes equations for an acetylene–air mixture are solved numerically to simulate the interaction of a shock wave and an expanding flame front, the formation of a flame brush, and deflagration-to-detonation transition (DDT). The effects of viscosity, thermal conduction, molecular diffusion, and chemical reactions are included. A new method for adaptive mesh refinement was used to ensure that the structure of the flame front was resolved. The shock–flame interactions, through the Richtmyer-Meshkov instability, create and maintain a highly turbulent flame brush. The turbulence is not Kolmogorov turbulence, but it is driven at all scales by repeated shock–flame interactions. Pressure fluctuations generated in the region of the turbulent flame brush create, in turn, hot spots in unreacted material. These hot spots may then transition to DDT through the gradient mechanism. Repeated shock–flame interactions and merging shocks in unreacted material lead to the development of a high-speed shock that moves out in front of the turbulent flame. The region between this shock and the flame is subject to intense fluctuations generated in the flame. The simulations show that the interactions of shocks and flames create the conditions under which deflagration-to-detonation transition may occur.

Direct Numerical Simulation of Difference in Turbulent Diffusion between Active and Passive Scalars in Stable Stratification.

The effects of molecular diffusivity on the difference in turbulent diffusion between active scalar (heat) and passive scalar (mass) in stable thermal-stratification are numerically investigated. A direct numerical simulation (DNS) based on a finite difference method is applied to unsheared thermally stratified water (Pr=5.0) and air (Pr=0.7) mixing layer flows downstream of turbulence-generating grid. Passive mass having the same Schmidt number as the Prandtl number of active heat is released from a point source located at 60 mm downstream from the grid. The results are compared with previous laboratory measurements for different Schmidt and Prandtl numbers of Sc=600 and Pr=5.0. The comparison shows that the numerical predictions are in good agreement with the measurements despite the assumption of the same molecular diffusivities in the DNS between active heat and passive mass. This means that the large difference in the eddy diffusivities between active heat and passive mass is not caused by the effects of molecular diffusion but by the stable stratification. The results also suggest that an assumption of identical eddy diffusivity for active heat and passive mass, used in conventional turbulence models, gives significant errors in estimating heat and mass transfer in a plume under stably stratified conditions.

Theoretical investigation of pulsed microwave discharge innitrogen

A pulsed microwave discharge burning close to the centre of a cylindrical chamber (/2 = 2.45 GHz) in pure nitrogen at low pressure (5 mbar) has been investigated theoretically. Boltzmann equation analysis is applied for the description of the breakdown and the consecutive maintenance phase of the discharge. The breakdown electric field is estimated using the calculated ionization frequency and the losses by the free electron diffusion. A self-consistent model for electron and heavy-particle kinetics coupling the rate master equations for the vibrational levels N2(X,v) of the electronic ground state of the nitrogen molecule to the Boltzmann equation of electrons has been developed. Besides the momentum transfer, inelastic as well as superelastic e-V collisions, ionization and free diffusion of electrons have been taken into account in the Boltzmann equation. The balance of the populations of the vibrational levels includes e-V, V-V and V-T exchanges, dissociation, atom re-association, vibrational deactivation on the walls and the effect of molecular diffusion. A further relation used is the global energy balance of electrons. The calculated breakdown electric field strength and the temporal course of the population of vibrational levels have been compared with experimental breakdown data and CARS measurements. Calculations and measurements are found to agree well.

CENTRIFUGE MODELING OF ONE‐DIMENSIONAL SUBSURFACE CONTAMINATION1

ABSTRACT: One‐dimensional contaminant transport through a saturated soil is modeled using a 1.2‐m radius geotechnical centrifuge. Small‐scale physical modeling in the centrifuge is achieved in relatively short time, at stress distributions that are similar to those experienced in the prototype (actual site). A 0.05 mol/l of sodium chloride solution is used as a contaminant and conductivity cells measure the concentration of the contaminant throughout the porous medium. Scaling analysis for centrifuge modeling and 1‐g modeling are briefly discussed and it is concluded that centrifuge modeling simulates the effect of molecular diffusion; however, scaling of the effect of mechanical dispersion may be violated in the centrifuge if the interstitial fluid velocity is high. Centrifuge test results show good agreement with the predicted relationship between the coefficient of hydrodynamic dispersion and the Peclet number using column tests. Centrifuge modeling can be used as a complement of numerical modeling although the effect of mechanical dispersion may be overestimated in the former.

Simulation of Single-Molecule Photocount Statistics in Microdroplets

We present results of detailed calculations of photocount statistics for single molecules in microdroplets. A Monte Carlo approach is used to simulate effects of molecular occupancy, photobleaching, and fluorophor spatial diffusion within the droplet. The excitation rate and fraction of fluorescence collected are both position-dependent, and are computed using classical and semiclassical formalisms. Differences in the single-molecule photocount distributions (and consequently molecular detection efficiencies) are predicted for cases where the RMS diffusion length is either small or large compared to the droplet diameter on the measurement time scale. These calculations provide semiquantitative estimates of molecular detection efficiencies and illustrate some of the unique optical features of a microdroplet approach to single molecule detection.

Effects of Micro- and Macroscale Turbulent Mixing on the Chemical Processes in Engine Exhaust Plumes

Abstract Turbulent mixing and chemical reactions in the near field of an engine exhaust jet plume have been investigated using a mixing model that explicitly incorporates both large- and small-scale turbulent mixing and the molecular diffusion effects. A reduced reaction mechanism that accurately reproduces results of a detailed mechanism for the lower stratosphere was used to simulate the exhaust plume dynamics of a typical high-speed civil transport aircraft. This study shows that, compared to predictions based on models that do not include small-scale mixing and/or molecular diffusion effects, 30% less O3 and 15% less NOx are depleted in the near field of the plume. This suggests that the lack of local mixing can have an inhibiting effect on ozone depletion in the near-field plume. Inclusion of heterogeneous kinetics involving the formation of nitric and sulfuric acid due to water condensation on soot particles showed that 15% of the available NOx is converted into its inactive form but has a negligibl...

Theoretical estimate of NOx production in lightning corona

A theoretical estimate of the quantity of nitrogen oxides NO and NO2 produced by the corona phase of a lightning flash has been carried out. The procedure makes use of physical simulations of positive leader and streamer propagation, coupled to a chemical kinetics model including 35 species such as ions, radicals, and neutral molecules. The effects of molecular and turbulent diffusion in thunderstorms are also modeled. A parametric study with various values of pressure and temperature leads to the conclusion that the effect of the corona phase on NOx production is negligible compared to that of the return stroke of the flash.