Mean Free Path In Air Research Articles

Gap in drop collision rate between diffusive and inertial regimes explains the stability of fogs and non-precipitating clouds

Rain drops form in clouds by collision of submillimetric droplets falling under gravity: larger drops fall faster than smaller ones and collect them on their path. The puzzling stability of fogs and non-precipitating warm clouds with respect to this avalanche mechanism has been a longstanding problem. How can droplets of diameter around 10 $\mathrm {\mu }$ m have a low collision probability, inhibiting the cascade towards larger and larger drops? Here we review the dynamical mechanisms that have been proposed in the literature and quantitatively investigate the frequency of drop collisions induced by Brownian diffusion, electrostatics and gravity, using an open-source Monte Carlo code taking all of them into account. Inertia dominates over aerodynamic forces for large drops, when the Stokes number is larger than $1$ . Thermal diffusion dominates over aerodynamic forces for small drops, when the Péclet number is smaller than $1$ . We show that there exists a range of size (typically 3–30 $\mathrm {\mu }$ m for water drops in air) where neither inertia nor Brownian diffusion are significant, leading to a gap in the collision rate. The effect is particularly important, due to the lubrication film forming between the drops immediately before collision, and secondarily to the long-range aerodynamic interaction. Two different mechanisms regularise the divergence of the lubrication force at vanishing separation: the transition to a non-continuum regime in the lubrication film, when the separation is comparable to the mean free path of air, and the induction of a flow inside the drops due to shear at their surfaces. In the gap between inertia-dominated and diffusion-dominated regimes, dipole–dipole electrostatic interactions becomes the major effect controlling the efficiency of drop collisions.

A new equation for the mean free path of air

A new equation for the mean free path of air

Dissipation-range fluid turbulence and thermal noise.

We revisit the issue of whether thermal fluctuations are relevant for incompressible fluid turbulence and estimate the scale at which they become important. As anticipated by Betchov in a prescient series of works more than six decades ago, this scale is about equal to the Kolmogorov length, even though that is several orders of magnitude above the mean free path. This result implies that the deterministic version of the incompressible Navier-Stokes equationis inadequate to describe the dissipation range of turbulence in molecular fluids. Within this range, the fluctuating hydrodynamics equationof Landau and Lifschitz is more appropriate. In particular, our analysis implies that both the exponentially decaying energy spectrum and the far-dissipation-range intermittency predicted by Kraichnan for deterministic Navier-Stokes will be generally replaced by Gaussian thermal equipartition at scales just below the Kolmogorov length. Stochastic shell model simulations at high Reynolds numbers verify our theoretical predictions and reveal furthermore that inertial-range intermittency can propagate deep into the dissipation range, leading to large fluctuations in the equipartition length scale. We explain the failure of previous scaling arguments for the validity of deterministic Navier-Stokes equationsat any Reynolds number and we provide a mathematical interpretation and physical justification of the fluctuating Navier-Stokes equation as an "effective field theory" valid below some high-wave-number cutoff Λ, rather than as a continuum stochastic partial differential equation. At Reynolds number around a million, comparable to that in Earth's atmospheric boundary layer, the strongest turbulent excitations observed in our simulation penetrate down to a length scale of about eight microns, still two orders of magnitude greater than the mean free path of air. However, for longer observation times or for higher Reynolds numbers, more extreme turbulent events could lead to a local breakdown of fluctuating hydrodynamics.

Humidity-Dependent Thermal Boundary Conductance Controls Heat Transport of Super-Insulating Nanofibrillar Foams

Summary Cellulose nanomaterial (CNM)-based foams and aerogels with thermal conductivities substantially below the value for air attract significant interest as super-insulating materials in energy-efficient green buildings. However, the moisture dependence of the thermal conductivity of hygroscopic CNM-based materials is poorly understood, and the importance of phonon scattering in nanofibrillar foams remains unexplored. Here, we show that the thermal conductivity perpendicular to the aligned nanofibrils in super-insulating ice-templated nanocellulose foams is lower for thinner fibrils and depends strongly on relative humidity (RH), with the lowest thermal conductivity (14 mW m−1 K−1) attained at 35% RH. Molecular simulations show that the thermal boundary conductance is reduced by the moisture-uptake-controlled increase of the fibril-fibril separation distance and increased by the replacement of air with water in the foam walls. Controlling the heat transport of hygroscopic super-insulating nanofibrillar foams by moisture uptake and release is of potential interest in packaging and building applications.

Hollow silica nanoparticles: A tiny pore with big dreams

Hollow nanoparticles exhibit unique functions such as thermal insulation, low dielectricity, and abnormal light scattering, especially when the inner size reaches less than twice the mean free path of air molecules (mean free path of air is 68 nm). It is easy to imagine that a nano-sized pore improves the thermal insulation performance due to less air convection flow inside. However, not only the hollow interior but also the shell microstructure (size, thickness, and density) strongly affect the functionalities. For example, a lower apparent shell density induces a higher thermal insulation probably due to phonon scattering on the siloxane bond cleavages. The best performance for the thermal conductivity of the hollow particle/polymer composite was 0.019 W/m·K, which is superior to air. The structure design of the hollow nanoparticle is quite important to produce this effect. In this review, based on important parameters, how to design the structure and wide applications of hollow nanoparticles are reviewed and a bright outlook for the future is expected.

Vertical Field Emission Air-Channel Diodes and Transistors.

Vacuum channel transistors are potential candidates for low-loss and high-speed electronic devices beyond complementary metal-oxide-semiconductors (CMOS). When the nanoscale transport distance is smaller than the mean free path (MFP) in atmospheric pressure, a transistor can work in air owing to the immunity of carrier collision. The nature of a vacuum channel allows devices to function in a high-temperature radiation environment. This research intended to investigate gate location in a vertical vacuum channel transistor. The influence of scattering under different ambient pressure levels was evaluated using a transport distance of about 60 nm, around the range of MFP in air. The finite element model suggests that gate electrodes should be near emitters in vertical vacuum channel transistors because the electrodes exhibit high-drive currents and low-subthreshold swings. The particle trajectory model indicates that collected electron flow (electric current) performs like a typical metal oxide semiconductor field effect-transistor (MOSFET), and that gate voltage plays a role in enhancing emission electrons. The results of the measurement on vertical diodes show that current and voltage under reduced pressure and filled with CO2 are different from those under atmospheric pressure. This result implies that this design can be used for gas and pressure sensing.

Influence of CaCO3 pore-forming agent on porosity and thermal conductivity of cellulose acetate materials prepared by non-solvent induced phase separation

Thermal insulation materials with a low thermal conductivity are indeed demanded because they play the main role in the enhancement of energy conservation in various industries, especially lightweight constructive materials. Therefore, tubular cellulose acetate (CA) materials were firstly prepared by non-solvent induced phase separation (NIPS). In the NIPS process, the concentration of CA was varied in a range of 20–40 wt%. Also, the temperature of water used as a non-solvent was studied from 5 °C up to 50 °C. According to the FE-SEM results, the 30 wt% CA solution at 20 °C provides tubular CA materials with a higher porous structure than an original CA material but the pore size is quite larger than the mean free path of air leading to achieve a material with high thermal conductivity. To overwhelmed such a problem, the calcium carbonate (CaCO3) was used to be pore forming agents in order to decrease pore size of prepared CA sheet materials. The amount of CaCO3 particles in the CA sheet materials was varied as 50 and 60 wt% to investigate its effect on porosity and thermal conductivity of the prepared materials. As the results, the CA sheet materials prepared using NIPS process and after removing 60 vol% CaCO3 have an enlargement of pores with a size lower than the mean free path of air. They exhibit high porous materials leading to the reduction of their thermal conductivity, which has the lowest value about 0.043 W/mK. Consequently, the CA materials are potentially applied for constructive materials in order to reduce energy consumption in buildings.

Thermal conductivity and characterization of compacted, granular silica aerogel

Abstract Monolithic silica aerogels are well known for their low thermal conductivity (approximately 15 mW/(m K)) (Aegerter et al. (Eds.), 2011. Aerogels Handbook, first ed., Springer-Verlag New York, LLC, New York, NY). Their low relative density (typically less than 5%) reduces conduction through the solid and their small pore size, typically less than one hundred nanometers, on the order of the mean free path of air, reduces conduction through air, as well as convection and radiation. As they are fragile and brittle, they are often used in a granular form in thermal insulation, with some increase in their thermal conductivity from the air between the granules. Here, we describe a technique for compacting a bed of granular silica aerogel that reduces the thermal conductivity from 24 mW/(m K) (when uncompacted) to 13 mW/(m K) (after compaction). We find that there is an optimum level of compaction to minimize the thermal conductivity: at higher levels of compaction, the contact area between the granules increases and the granules densify, increasing conduction through the solid.

Isothermal absorption of soluble gases by atmospheric nanoaerosols

We investigate mass transfer during the isothermal absorption of atmospheric trace soluble gases by a single droplet whose size is comparable to the molecular mean free path in air at normal conditions. It is assumed that the trace reactant diffuses to the droplet surface and then reacts with the substances inside the droplet according to the first-order rate law. Our analysis applies a flux-matching theory of transport processes in gases and assumes constant thermophysical properties of the gases and liquids. We derive an integral equation of Volterra type for the transient molecular flux density to a liquid droplet and solve it numerically. Numerical calculations are performed for absorption of sulfur dioxide (SO(2)), dinitrogen trioxide (N(2)O(3)), and chlorine (Cl(2)) by liquid nanoaerosols accompanied by chemical dissociation reaction. It is shown that during gas absorption by nanoaerosols, the kinetic effects play a significant role, and neglecting kinetic effects leads to a significant overestimation of the soluble gas flux into a droplet during the entire period of gas absorption.

The direct writing and focusing of nanoparticles generated by an electrical discharge

Direct writing aims to deposit materials onto substrates in localised positions. In this paper, we demonstrate a new method for direct writing of nanoparticles at ambient-air-pressure. An electrical discharge is used to generate gold nanoparticles of the order of 10 nm diameter, which are then transported and 'focused' by an electric field in air, through the process of electric field-assisted diffusion, as opposed to normal ballistic focusing since the mean free path in air is very short. This process is novel and allows for practical normal atmospheric-pressure focused deposition of nanoparticles. The focusing mechanism is capable of producing patterned arrays of deposited nanoparticles with widths that are less than 10 % of the diameter of the focusing apparatus; in the present experimental configuration, gold spots with diameters of a few tens of micrometres were achieved, with ultimate size being limited by transverse diffusion and by charged particle mutual repulsion. In this study, the process of generating nanoparticles from bulk material, transporting and focusing these particles takes place in one operation, which is a key advantage in rapid prototyping and manufacturing techniques

Temperature Effect on a HDD Slider’s Flying Performance at Steady State

The temperature inside modern hard disk drives (HDDs) can become as high as 100°C during operation. The effects of such high temperatures on the slider’s flying attitude and the shear forces on the slider and the disk are investigated in this paper. General formulae for the shear forces are derived, and the generalized Reynolds equation is modified to take into account the temperature effect on the mean free path of air as well as the air viscosity. Numerical results are obtained for two different air bearing surface designs. It is shown that the temperature changes result in non-negligible changes in the slider’s flying height and the shear forces. These changes could further induce changes in the deformation and instability of the lubricant layer and thereby affect the reliability of the HDDs.

The Effect of Water Evaporation on Photoacoustic Signals in Transition and Molecular Flow

Evaporation of water changes the response of photoacoustic instruments to light-absorbing particles. Previous calculations of this effect are valid for particles much larger than the mean free path of air. These calculations are extended here to include transition and molecular flow as well as various mass accommodation coefficients for water. For commonly encountered conditions, evaporation can significantly reduce the photoacoustic signal if the mass accommodation coefficient of water on aerosol particles is larger than about 0.01. Unlike the growth of cloud droplets, the photoacoustic signal is very sensitive to changes in the accommodation coefficient between 0.1 and 1. This may provide a way to measure large accommodation coefficients. For a given accommodation coefficient, the change in the photoacoustic signal depends more on absolute than relative humidity. To minimize the effects of evaporation it is better to remove water from the air rather than reduce relative humidity with heating.

Optical Interactions and Photoluminescence Properties of Wide-Bandgap Nanocrystallites

ABSTRACTThe UV-photoluminescence (PL) properties of GaN and ZnO nanocrystallites and nanocrystallite ensembles were studied utilizing micro-photoluminescence. We address the origin of the light emissions of the nanocrystallite as to whether it is due a bandgap or excitonic recombination process. The other topic presented here focuses on the interaction of the laser with a collective of crystallites; we address the phenomena of intensity saturation at a high density of laser excitations as well as the impact of the vacuum state on the PL characteristics. Our analysis indicates that the PL of both GaN and ZnO nanocrysallites is excitonic-like and very similar to the behavior of the free exciton in bulk materials. Additionally, we attribute the intensity saturation of GaN and ZnO to the laser heating and heat trapping which takes place in the enclosure of the nanocrystallite ensemble. In vacuum the PL energy was found to exhibit a strong PL energy redshift relative to the PL in air. We attribute the observed shift to a thermal effect and analyze it in terms of the conditions enabling a convective cooling in the ensemble: the mean free path of air in atmospheric pressure and in vacuum relative to the interparticle separation inside the ensemble.

Chemical Engineering of Aerogel Morphology Formed under Nonsupercritical Conditions for Thermal Insulation

Aerogels are among the best thermal insulating materials known. This property arises from the fact that in these materials the gaseous phase, which may occupy over 90% of the volume, is compartmentalized to a size smaller than the mean free path of air, thus severely restricting its thermal conductivity. The solid framework, which compartmentalizes the gaseous space with a minimum amount of solid, is fragile and thus must be assembled in a liquid phase that is later extracted under supercritical conditions to create the porosity. This requirement for supercritical liquid extraction, to eliminate surface tension, makes the process costly and often unsuitable for large-scale commercial applications. By computer-designed experiments, an investigation was conducted in order to produce aerogels under non-supercritical conditions. Silica aerogels having approximately 80% porosity were produced under atmospheric conditions. Moreover, the resulting pore morphology is more restrictive to thermal conductivity than ...

Resistance Force of a Spherical Particle Moving Towards Another Particle in Reduced Pressure.

In a continuum, the resistance force of a spherical particle moving towards another particle increases with decreasing separation distance between particles and finally becomes infinite just before touching. However, there has been no investigation on the effect of discontinuity. The air in the minimum separation of two particles whose diameters are less than several tens of microns creates the discontinuum, and without it, a fine particle would collide with another particle more easily. In this study, we measured the resistance force of a 6.3 mm foam styrene ball under reduced pressure by using a high-speed camera. At 10 Pa, the mean free path of air is 670μm and the Knudsen number of a 6.3 mm foam styrene ball is equivalent to that of a 0.6μm particle in air. The experimental data show that the increment of the resistance force acting on a 6.3 mm foam styrene ball near the spherical particle under reduced pressure decreases with decreasing air pressure. Hence, it is concluded that the resistance force of a fine particle moving towards another particle in the air is much less than that acting in a continuum.

The mean free path in air

Values for the mean free path l in air are presented for temperatures 15, 20, 23 and 25°C for both dry air and moist air at relative humidities of 50 and 100%, at atmospheric pressure (1.01325 × 10 5 Pa) and at pressure 1 × 10 5 Pa. Use is made of an expression which minimizes the dependence on physical ‘constants’ for mean free path: ▪ where μ is the viscosity of air, p is the density of air, P is the pressure and μ is a numerical factor equal to 0.4987445. Differences of up to 1.6% were obtained between the values of mean free path at 23°C from this work and that of other workers. Comparison between the Cunningham slip correction factor from the present work and that from other work shows differences up to 1.8%.

Portable Calculator Operating System for Aerosol Science Use

By employing the capabilities of a programmable calculator, we have developed a system of programs that calculates quantities often used in aerosol science. This system is suitable for use in the laboratory or in locations remote from normal laboratory environments and has the capability for executing complex calculations for data analysis from the keyboard in a manner similar to the functions supplied by a calculator manufacturer. Quantities calculated are particle real and aerodynamic diameter; slip correction factor; density, viscosity and mean free path of air at specified temperature and pressure; Reynolds number; particle stopping distance and velocity; as well as cascade impactor jet area and jet velocity. To provide flexibility for diverse data reduction needs, provisions are made to allow the user to write control programs that use the system programs to calculate desired quantities.

Portable Calculator Operating System for Aerosol Science Use

By employing the capabilities of a programmable calculator, we have developed a system of programs that calculates quantities often used in aerosol science. This system is suitable for use in the laboratory or in locations remote from normal laboratory environments and has the capability for executing complex calculations for data analysis from the keyboard in a manner similar to the functions supplied by a calculator manufacturer. Quantities calculated are particle real and aerodynamic diameter; slip correction factor; density, viscosity and mean free path of air at specified temperature and pressure; Reynolds number; particle stopping distance and velocity; as well as cascade impactor jet area and jet velocity. To provide flexibility for diverse data reduction needs, provisions are made to allow the user to write control programs that use the system programs to calculate desired quantities.

Calculated Leading-Edge Bluntness Effect on Transonic Compressor Noise

Theme A METHOD was developed for calculating forwardradiated shock waves and expansion regions of cylindrically blunted straight-entrance transonic compressor blades within constant-annulus inlet ducts. Tone noise at blade passing frequency and its subharmonics, caused by shock waves produced by blade curvature and nonuniformity, could be avoided in concept if all blades were precisely sharp, precisely straight, and precisely positioned. However, leadingedge thickness would necessarily be many orders of magnitude larger than the mean free path in air. Each blade, therefore, must support a detached curved wave that decays from a normal shock towards a Mach wave. It was shown by Morfeyl that if a transonic compressor generated a periodic pressure system, the upstream asymptotic pressure field was a periodic sawtooth pattern whose strength was independent of blade shape and initial shock wave strength. This prediction has been validated analytically2 and by numerical experiments3 for sharp, curved blades. It was not obvious how, or if the pressure pattern generated by straight, parallel, very slightly blunted blades would approach the same amplitudes. Contents An earlier solution4 had assumed that each detached shock wave had the shape of a hyperbola asymptotic to a Mach wave. In this solution, the strong inner-portion of each shock wave is approximated by a hyperbola with steeper asymptote. The hyperbola is matched to an isolated-blade weak-shock outer solution obtained from sonic boom theory5 for blunt two-dimensional shapes. The expansion field produced by an isolated blade's leading edge is distorted by the entropy gradient downstream of the curved strong shock. Each blade's expansion field was calculated from the sonic boom solution and corrsponds to a centered expansion whose hypothetical origin is significantly downstream of the leading edge. These portions of the solution were validated by comparisons with wind-tunnel data for isolated blunt flat plates at low supersonic speeds. Compressor cascades were represented by starting with isolated-blade shock waves and expansion regions and then calculating the upstream propagation. At moderate distances ahead of the cascade leading edge plane, the variation of static pressure with distance is given by a shock-wave compression, a linear expansion to the pressure ahead of the shock, and a region of constant pressure. Eventually each blade's shock wave overtakes the aft end of the preceding blade's expansion and the pressure pattern becomes a sawtooth waveform. As upstream distance is increased, the flowfield occurring within the expansion region. That is, the

Relativistic heavy cosmic rays

During three balloon flights of a 1 sq m sr ionization chamber/Cerenkov counter detector system, measurements were made of the atmospheric attenuation, flux, and charge composition of cosmic ray nuclei with 16 is less than or = Z is less than or = 30 and rigidity greater than 4.5 GV. The attenuation mean free path in air of VH (20 less than or = Z less than or = 30) nuclei is found to be 19.7 + or - 1.6 g/sq cm, a value somewhat greater than the best previous measurement. The attenuation mean free path of iron is found to be 15.6 + or - 2.2 g/sq cm, consistent with predictions of geometric cross-section formulae. An absolute flux of VH nuclei 10 to 20% higher than earlier experiments at similar geomagnetic cutoff and level of solar activity was measured. The relative abundances of even-charged nuclei are found to be in good agreement with results of other recent high resolution counter experiments. The observed cosmic ray chemical composition implies relative abundances at the cosmic ray source of Ca/Fe = 0.12 + or - 0.04 and S/Fe = 0.14 + or - 0.05.