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At least 613 records · Page 34

Planar Strain-Rate-Free Diffusion Flames: Initiation, Properties, and Extinction

An effectively strain-rate-free diffusion flame constitutes the most vigorous laminar combustion of initially unmixed reactive gases. Such a diffusion flame is characterized by a relatively long residence time and by a relatively large characteristic length scale. If such a flame were also planar, providing high symmetry, it would be particularly suitable for experimental and theoretical investigations of key combustion phenomena, such as multicomponent diffusion, chemical kinetics, and soot inception, growth, and oxidation. Unfortunately, a planar strain-rate-free diffusion flame is highly disrupted in earth-gravity (e.g., in a counterflow-diffusion-flame apparatus) because of the very rapid onset (approx. 100 ms) of gravity-induced instability. Accordingly, a specially dedicated apparatus was designed, fabricated, and initially checked out for the examination of a planar strain-rate-free diffusion flame in microgravity. Such a diffusion flame may be formed within a hollowed-out squat container (initially configured as 25 cm x 25 cm x 9 cm), with isothermal, noncatalytic, impervious walls. At test initiation, a thin metallic sheet (approx. 1 mm in thickness) that separates the internal volume into two equal portions, each of dimensions 25 cm x 25 cm x 4.5 cm, is withdrawn, by uniform translation (approx. 50 cm/s) in its own plane, through a tightly fitting slit in one side wall. Thereupon, diluted fuel vapor (initially confined to one half-volume of the container) gains access to diluted oxygen (initially with the same pressure, density, and temperature as the fuel, but initially confined to the other half-volume). After a brief delay (approx. 10 ms), to permit limited but sufficient-for-flammability diffusional interpenetration of fuel vapor and oxidizer, burning is initiated by discharge of a line igniter, located along that side wall from which the trailing edge of the separator withdraws. The ignition spawns a triple-flame propagation across the 25 cm x 25 cm centerplane. When a diffusion flame is emplaced in the centerplane, any subsequent travel, and change in temperature, of that planar diffusion flame may be tracked, along with the effectively spatially uniform but temporally evolving pressure within the container. Eventually, nearly complete depletion of the stoichiometrically deficient reactant, along with heat loss to the container surfaces, effects extinction. These data afford an opportunity to check theoretical models of diffusion and chemical kinetics under conditions ranging from intense burning to flame out, or, alternatively, to evolve simple empirical representations of these phenomena. Thus, the project sought to utilize microgravity testing to elucidate commonly encountered phenomenology, arising in the commonly-encountered mode of combustion (whether related to heating, manufacturing, boiling, and propulsion, or to uncontrolled, free-burning fire in structures and wildland vegetation), of those commonly utilized fuels usually categorized as gaseous fuels (such as hydrogen, natural gas, and propane, which are gaseous under atmospheric conditions).

Fendell, Francis↗

Mapping the Temperature-dependent and network site-specific onset of spectral diffusion at the surface of a water cluster cage

We explore the kinetic processes that sustain equilibrium in a microscopic, finite system. This is accomplished by monitoring the spontaneous, time-dependent frequency evolution (the frequency autocorrelation) of a single OH oscillator, embedded in a water cluster held in a temperature-controlled ion trap. The measurements are carried out by applying two-color, IR-IR photodissociation mass spectrometry to the D3O+?(HDO)(D2O)19 isotopologue of the “magic number” protonated water cluster, H+?(H2O)21. The OH group can occupy any one of the five spectroscopically distinct sites in the distorted pentagonal dodecahedron cage structure. The OH frequency is observed to evolve over tens of milliseconds in the temperature range (90-120 K). Starting at 100 K, large “jumps” are observed between two OH frequencies separated by ~300 cm-1 indicating migration of the OH group from the bound OH site at 3350 cm-1 to the free position at 3686 cm-1. Increasing the temperature to 110 K leads to partial interconversion among many sites. All sites are observed to interconvert at 120 K such that the distribution of the unique OH group among them adopts the form one would expect for a canonical ensemble. The spectral dynamics displayed by the clusters thus offer an unprecedented view into the molecular-level processes that drive spectral diffusion in an extended network of water molecules.

Yang, Nan↗

How Does Water Dissociation Work in Bipolar Membranes?

Bipolar membranes (BPMs) create counteracting spatial gradients of pH and electrostatic potential in electrochemical systems, enabling applications in pH regulation, electrocatalysis, and separations. At the polarized junction of a BPM the water dissociation (WD, 2H2O ⇌ H3O+ + OH-) reaction can be driven, but it remains poorly understood. In this Perspective, we integrate molecular insights from bulk-water autoionization and the associated field effects with continuum descriptions of BPM electrostatics and experimental WD kinetic analyses to describe possible mechanisms of voltage-driven WD. Pristine BPM junctions highlight both the limits of primarily electric-field-driven WD and the practical challenges of junction stability at extreme reverse bias. Introducing heterogeneous catalyst layers, commonly metal oxides and graphene oxides, accelerates WD by orders of magnitude through hypothesized coupled effects in which surface acid-base functionality and high-density hydroxyl sites mediate proton-transfer steps, and catalyst mobile electronic/ionic charges redistribute the junction electric potential drop to shape the local electric fields and reactive microenvironments. Kinetic analyses suggest two regimes of heterogeneous WD mechanism, including field-driven ordering of interfacial water and a Second-Wien-Effect dissociation-barrier lowering. We conclude by defining the key unknown variables (local pH, electrostatic potential, catalyst charge state and relationships among mechanisms) and outlining experimental and multiscale modeling strategies needed for predictive WD catalysis and for controlling related ion-transfer reactions.

Wu, Yifan↗

The Atacama Cosmology Telescope: The Polarization-Sensitive ACTPol Instrument

The Atacama Cosmology Telescope (ACT) makes high angular resolution measurements of anisotropies in the Cosmic Microwave Background (CMB) at millimeter wavelengths. We describe ACTPol, an upgraded receiver for ACT, which uses feedhorn-coupled, polarization-sensitive detector arrays, a 3deg field of view, 100 mK cryogenics with continuous cooling, and meta material antireflection coatings. ACTPol comprises three arrays with separate cryogenic optics: two arrays at a central frequency of 148 GHz and one array operating simultaneously at both 97 GHz and 148 GHz. The combined instrument sensitivity, angular resolution, and sky coverage are optimized for measuring angular power spectra, clusters via the thermal Sunyaev-Zel'dovich (SZ) and kinetic SZ signals, and CMB lensing due to large-scale structure. The receiver was commissioned with its first 148 GHz array in 2013, observed with both 148 GHz arrays in 2014, and has recently completed its first full season of operations with the full suite of three arrays. This paper provides an overview of the design and initial performance of the receiver and related systems.

Telescope↗

Reducing the Susceptibility of Lumped-Element KIDs to Two-Level System Effects

Arrays of lumped-element kinetic inductance detectors (LEKIDs) optically coupled through an antenna-coupled transmission line are a promising candidate for future cosmic microwave background experiments. However, the dielectric materials used for the microstrip architecture are known to degrade the performance of superconducting resonators. In this paper, we investigate the feasibility of microstrip coupling to a LEKID, focusing on a systematic study of the effect of depositing amorphous silicon nitride on a LEKID. The discrete and spatially separated inductive and capacitive regions of the LEKID allow us to vary the degree of dielectric coverage and determine the limitations of the microstrip coupling architecture. We show that by careful removal of dielectric from regions of high electric field in the capacitor, there is minimal degradation in dielectric loss tangent of a partially covered lumped-element resonator. We present the effects on the resonant frequency and noise power spectral density and, using the dark responsivity, provide an estimate for the resulting detector sensitivity.

47 OTHER INSTRUMENTATION↗

Broadband Rotational Spectroscopy in Uniform Supersonic Flows: Chirped Pulse/Uniform Flow for Reaction Dynamics and Low Temperature Kinetics

ConspectusThe study of gas-phase chemical reactions at very low temperatures first became possible with the development and implementation of the CRESU (French acronym for Reaction Kinetics in Uniform Supersonic Flows) technique. CRESU relies on a uniform supersonic flow produced by expansion of a gas through a Laval (convergent-divergent) nozzle to produce a wall-less reactor at temperatures from 10 to 200 K and densities of 1016-1018 cm-3 for the study of low temperature kinetics, with particular application to astrochemistry. In recent years, we have combined uniform flows with revolutionary advances in broadband rotational spectroscopy to yield an instrument that affords near-universal detection for novel applications in photodissociation, reaction dynamics, and kinetics. This combination of uniform supersonic flows with chirped-pulse Fourier-transform microwave spectroscopy (Chirped-Pulse/Uniform Flow, CPUF) permits detection of any species with a modest dipole moment, thermalized to the uniform temperature of the gas flow, with isomer, conformer, and vibrational state specificity. In addition, the use of broadband, high-resolution, and time-dependent (microsecond time scale) micro- and mm-wave spectroscopy makes it an ideal tool for characterizing both transient and stable molecules, as well as studying their spectroscopy and dynamics.In this Account, we review recent advances made using the CPUF technique, including studies of photodissociation, radical-radical reaction dynamics, and low temperature kinetics. These studies highlight both the strength of universal and multiplexed detection and the challenges of coupling it to a high-density collisional environment. Product branching and product evolution as a function of time have been measured for astrochemically relevant systems, relying on the detailed characterization of these flow conditions via experiments and fluid dynamics simulations. In the photodissociation of isoxazole, an unusual heterocyclic molecule with a very low-energy conical intersection, we have identified 7 products in 5 reaction channels and determined the product branching, pointing to both direct and indirect pathways. We have also approached the same system from separated NO and C3H3 reactants to explore a broader range of the potential energy surface, demonstrating the power of multichannel branching measurements for complex radical-radical reactions. We determined the product branching in the C3H2 isomers in the photodissociation of the propargyl radical and identified the importance of a hydrogen atom catalyzed isomerization to the lowest energy cyclic form. This then motivated a study of direct D-H exchange reaction in radicals, in which we demonstrate that it is an important and overlooked pathway for deuterium fractionation in astrochemical environments. Recently, we have shown the measurement of low temperature kinetics inside an extended Laval nozzle, after which a shock-free secondary expansion to low temperature and density affords an ideal environment for detection by rotational spectroscopy. These results highlight the power and potential of the CPUF approach, and future prospects will also be discussed in light of these developments.

Dias, Nureshan↗

Static and Dynamic Gradient Based Directional Transportation of Neutral Molecules in Swollen Polymer Films

Abstract Materials which selectively transport molecules offer powerful opportunities for concentrating and separating chemical agents. Here, utilizing static and dynamic chemical gradients, transport of molecules within swollen crosslinked polymers is demonstrated. Using an ≈200 μm static hydroxyl to hexyl gradient, the neutral ambipolar nerve agent surrogate diethyl (cyanomethyl)phosphonate (DECP) is directionally transported and concentrated 60‐fold within 4 hours. To accelerate transport kinetics, a dynamic gradient (a “travelling wave”) is utilized. Here, the non‐polar dye pyrene was transported. The dynamic gradient is generated by an ion exchange process triggered by the localized introduction of an aqueous NaCl solution, which converts the gel from hydrophobic to hydrophilic. As the hydrophilic region expands, associated water enters the gel, and pyrene is pushed ahead of the expansion front. The dynamic gradient provides about 10‐fold faster transport kinetics than the static gradient.

Ali, Mohammad A.↗

Observation of an Intermediate to H 2 Binding in a Metal–Organic Framework

Coordinatively unsaturated metal sites within certain zeolites and metal–organic frameworks can strongly adsorb a wide array of substrates. While many classical examples involve electron-poor metal cations that interact with adsorbates largely through physical interactions, unsaturated electron-rich metal centers housed within porous frameworks can often chemisorb guests amenable to redox activity or covalent bond formation. Despite the promise that materials bearing such sites hold in addressing myriad challenges in gas separations and storage, very few studies have directly interrogated mechanisms of chemisorption at open metal sites within porous frameworks. Here, we show that nondissociative chemisorption of H 2 at the trigonal pyramidal Cu + sites in the metal–organic framework Cu I -MFU- 4 l occurs via the intermediacy of a metastable physisorbed precursor species. In situ powder neutron diffraction experiments enable crystallographic characterization of this intermediate, the first time that this has been accomplished for any material. Evidence for a precursor intermediate is also afforded from temperature-programmed desorption and density functional theory calculations. Here, the activation barrier separating the precursor species from the chemisorbed state is shown to correlate with a change in the Cu + coordination environment that enhances p-backbonding with H 2 . Ultimately, these findings demonstrate that adsorption at framework metal sites does not always follow a concerted pathway and underscore the importance of probing kinetics in the design of next-generation adsorbents.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Amplification, attenuation, and dispersion of sound in inhomogeneous flows

First order effects of gradients in nonuniform potential flows of a compressible gas are included in a dispersion relation for sound waves. Three nondimensional numbers, the ratio of the change in the kinetic energy in one wavelength to the thermal energy of the gas, the ratio of the change in the total energy in one wavelength to the thermal energy, and the ratio of the dillatation frequency (the rate of expansion per unit volume) to the acoustic frequency, play a role in the separation of the effects of flow gradients into isotropic and anisotropic effects. Dispersion and attenuation (or amplification) of sound are found to be proportional to the wavelength for small wavelength, and depend on the direction of wave propagation relative to flow gradients. Modification of ray acoustics for the effects of flow gradients is suggested, and conditions for amplification and attenuation of sound are discussed.

Kentzer, C. P.↗

Thermal Characterization of Fe3O4 Nanoparticles Formed from Poorly Crystalline Siderite

Increasing interest in environmental geochemistry has led to the recognition that crystals with sizes in the nanometer range (e.g., colloids and nanoscale precipitates) and poorly crystalline compounds (e.g., ferrihydrites) may comprise the majority of reactive mineral surface area near the Earth s surface. When the diameters of individual particles are in the range of 100 nm or less, the surface energy contribution to the free energy modifies phase stability. This results in stabilization of polymorphs not normally encountered in the macrocrystal domain. These phases potentially have very different surface-site geometries, adsorptive properties, and growth mechanisms, and exhibit size-dependent kinetic behavior. Thus nanophases dramatically modify the physical and chemical properties of soils and sediments. In a more general sense, the characteristics of nanocrystals are of intense technological interest because small particle size confers novel chemical, optical, and electronic properties. Thus, nanocrystalline materials are finding applications as catalytic substrates, gas phase separation materials, and even more importantly in the field of medicine. This is an opportune time for mineral physicists working on nanocrystalline materials to develop collaborative efforts with materials scientists, chemists, and others working on nanophase materials of technological interest (e.g., for magnetic memories). Our objective in this study was to synthesize submicron (<200 nm) magnetite and to study their thermal and particle size properties.

Lauer, H. V., Jr.↗

Multiphysics Modeling of Electrode Dissolution under Hydrodynamic Conditions in Low Conductivity Water

Efficient plug-flow electrochemical reactors are characterized by their ability to effectively convert species with significant ionic strength and/or with the assistance of a well-behaved electrolyte. Because of the classic electroconductivity requirement, electrochemical reactors are not particularly attractive options for applications with low-conductivity conditions, especially for low-pressure feeds. However, these reactors can still find application in dedicated processes such as ultra-clean water conditioning and biological-coupled separation systems. Consequently, a multi-physics model was developed using COMSOL Multiphysics to characterize different reactor-design conditions based on the Tertiary Current Distribution which accounts for the effects of expected variations in electrolyte composition and ionic strength on the electrochemical process, as well as solution resistance and electrode kinetics. The modelling framework presented here employs single-phase laminar fluid flow, the Nernst-Planck equation, the water-based electroneutrality condition, and concentration-dependent overpotentials. This investigation particularly explores the electrolysis process of “anodic dissolution,” in which elemental species dissociate from the solid matrix of the electrode and enter the liquid phase of the electrolyte as soluble ions. The reactor configuration of interest has a rectangular parallel-electrode design and is operated galvanostatically. A series of parametric studies are carried out to inspect the response of the system when hydrodynamic, kinetic, and geometric conditions are changed. The parametric sweep resulted in variable effluent concentrations and system voltage, which reveal underlaying optimization patterns for electrode dissolution in low conductivity water.

Multiphysics↗

Fabrication of OMT-Coupled Kinetic Inductance Detector for CMB Detection

Future cosmic microwave background (CMB) experiments, including the large scale ground-based Stage Four CMB Experiment (CMB-S4), satellites, and balloons, aim to map the CMB to an unprecedented precision in order to answer several key questions in cosmology. However, to reach the target noise sensitivity, more than 100,000 detectors will be needed. Arrays of kinetic inductance detectors (KIDs) are a promising alternative for experiments that require large number of detectors due to the intrinsic multiplexing capabilities. We present the fabrication procedure for a prototype planar orthomode transducer (OMT)-coupled multi-color KID array optimized for 220/270 GHz frequency bands. These devices are made from silicon-on-insulator wafers to provide a low-loss substrate for the KIDs. The OMT couples the two polarizations of light from a wide-band feedhorn to separate Nb/SiN/Nb microstrip lines, which are then coupled to Al/Nb lumped-element KIDs (LEKIDs). The silicon on the backside of the OMT is etched away using deep reactive ion etch to release the OMT membrane to enable operation over a wide bandwidth. Finally, the buried oxide is removed underneath the KID capacitors in order to minimize two-level system noise and loss mitigation. We achieved a good yield (> 80%) on our prototype devices.

47 OTHER INSTRUMENTATION↗

Cooperative Effects Drive Water Oxidation Catalysis in Cobalt Electrocatalysts through the Destabilization of Intermediates

A barrier to understanding the factors driving catalysis in the oxygen evolution reaction (OER) is understanding multiple over- lapping redox transitions in the OER catalysts. The complexity of these transitions obscure the relationship between the coverage of adsorbates and OER kinetics, leading to an experimental challenge in measuring activity descriptors, such as binding energies, as well as adsorbate interactions, which may destabilize intermediates and modulate their binding energies. Herein, we utilize a newly designed optical spectroelectrochemistry system to measure these phenomena in order to contrast the behavior of two electrocatalysts, cobalt oxyhydroxide (CoOOH) and cobalt-iron hexacyanoferrate (cobalt-iron Prussian blue, CoFe-PB). Three distinct optical spectra are observed in each catalyst, corresponding to three separate redox transitions, the last of which we show to be active for the OER using time-resolved spectroscopy and electrochemical mass spectroscopy. By combining predictions from density functional theory with parameters obtained from electroadsorption isotherms, we demonstrate that a destabilization of catalytic intermediates occurs with increasing coverage. In CoOOH, a strong (~0.34 eV/ monolayer) destabilization of a strongly bound catalytic intermediate is observed, leading to a potential offset between the accumulation of the intermediate and measurable O 2 evolution. We contrast these data to CoFe-PB, where catalytic intermediate generation and O 2 evolution onset coincide due to weaker binding and destabilization (~0.19 eV/monolayer). By considering a correlation between activation energy and binding strength, we suggest that such adsorbate driven destabilization may account for a significant fraction of the observed OER catalytic activity in both materials. Finally, we disentangle the effects of adsorbate interactions on state coverages and kinetics to show how adsorbate interactions determine the observed Tafel slopes. Crucially, the case of CoFe-PB shows that, even where interactions are weaker, adsorption remains non-Nernstian, which strongly influences the observed Tafel slope.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Towards the first plasma-electron screening experiment

The enhancement of fusion reaction rates in a thermonuclear plasma by electron screening of the Coulomb barrier is an important plasma-nuclear effect that is present in stellar models but has not been experimentally observed. Experiments using inertial confinement fusion (ICF) implosions may provide a unique opportunity to observe this important plasma-nuclear effect. Herein, we show that experiments at the National Ignition Facility (NIF) have reached the relevant physical regime, with respect to the density and temperature conditions, but the estimated impacts of plasma screening on nuclear reaction rates are currently too small and need to be increased to lower the expected measurement uncertainty. Detailed radiation hydrodynamics simulations show that practical target changes, like adding readily available high-Z gases, and significantly slowing the inflight implosion velocity, while maintaining inflight kinetic energy, might be able to push these conditions to those where plasma screening effects may be measurable. We also perform synthetic data exercises to help understand where the anticipated experimental uncertainties will become important. But challenges remain, such as the detectability of the reaction products, non-thermal plasma effects, species separation, and impacts of spatial and temporal gradients. This work lays the foundation for future efforts to develop an important platform capable of the first plasma electron screening observation.

inertial confinement fusion↗

Amplification, attenuation, and dispersion of sound in inhomogeneous flows

First order effects of gradients in nonuniform potential flows of a compressible gas are included in a dispersion relation for sound waves. Three nondimensional numbers, the ratio of the change in the kinetic energy in one wavelength to the thermal energy of the gas, the ratio of the change in the total energy in one wavelength to the thermal energy, and the ratio of the dilatation frequency (the rate of expansion per unit volume) to the acoustic frequency, play the dominant role permitting the separation of the effects of flow gradients into isotropic and anisotropic effects. Dispersion and attenuation (or amplification) of sound are proportional to the wavelength for small wavelength and depend on the direction of wave propagation relative to flow gradients. Modification of ray acoustics for the effects of flow gradients is suggested and conditions for amplification and attenuation of sound are discussed.

Kentzer, C. P.↗

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

Ram vehicle glow spectrum - Implication of NO2 recombination continuum

An experiment was operated on several Space Shuttle missions to provide spatial and spectral distributions of a ram glow associated with the Orbiter. The most recent data featured resolved spectrum and imagery of the glow with spectroscopic resolution of 34 A FWHM between 4000 and 8000 A. The spectrum of the glow on the Shuttle tail pod could be clearly separated from spectrum of the reflected light from the Orbiter. Analysis and comparison have been performed which strongly suggest the emission originates from recombination continuum of NO2. Both fast recombination (high temperature) and the spectral dependence in lifetime can describe the spectral difference. If the recombined NO2 retains 25 percent of the kinetic energy of the ram OI, the thickness of the glow layer can be explained by the lifetime of NO2 (2B1) recombination emission.

Swenson, G. R.↗

Grain formation around carbon stars. 1: Stationary outflow models

Asymptotic giant branch (AGB) stars are known to be sites of dust formation and undergo significant mass loss. The outflow is believed to be driven by radiation pressure on grains and momentum coupling between the grains and gas. While the physics of shell dynamics and grain formation are closely coupled, most previous models of circumstellar shells have treated the problem separately. Studies of shell dynamics typically assume the existence of grains needed to drive the outflow, while most grain formation models assume a constant veolcity wind in which grains form. Furthermore, models of grain formation have relied primarily on classical nucleation theory instead of using a more realistic approach based on chemical kinetics. To model grain formation in carbon-rich AGB stars, we have coupled the kinetic equations governing small cluster growth to moment equations which determine the growth of large particles. Phenomenological models assuming stationary outflow are presented to demonstrate the differences between the classical nucleation approach and the kinetic equation method. It is found that classical nucleation theory predicts nucleation at a lower supersaturation ratio than is predicted by the kinetic equations, resulting in significant differences in grain properties. Coagulation of clusters larger than monomers is unimportant for grain formation in high mass-loss models but becomes more important to grain growth in low mass-loss situations. The properties of the dust grains are altered considerably if differential drift velocities are ignored in modeling grain formation. The effect of stellar temperature, stellar luminosity, and different outflow velocities are investigated. The models indicate that changing the stellar temperature while keeping the stellar luminosity constant has little effect on the physical parameters of the dust shell formed. Increasing the stellar luminosity while keeping the stellar temperature constant results in large differences in grain properties. For small outflow velocities, grains form at lower supersaturation ratios and close to the stellar photosphere, resulting in larger but fewer grains. The reverse is true when grains form under high outflow velocities, i.e., they form at higher supersaturation ratios, farther from the star, and are much smaller but at larger quantities.

Egan, Michael P.↗