Grain dynamics in zero gravity

The dynamics of granular materials has proved difficult to model, primarily because of the complications arising from inelastic losses, friction, packing, and the effect of many grains being in contact simultaneously. The kinetic model of granular systems is similar to the kinetic theory of gases, except that collisional energy losses are always present in the former and must be treated explicity. Few granular materials on Earth are describable by this limiting model, since gravity tends to collapse the grains into a high density state where Coulombic friction effects are dominant. The planned Space Station offers an unusual opportunity to test the kinetic grain model and to explore its predictions. Without gravity, the regime of low interparticle velocities (where an elastic description of the collision is still valid) can be investigated. This will allow for direct interpretation by dynamical computer simulations as well as by the kinetic theory. The dynamics of spherical grains inside a clear box would be examined. Results would be compared with the predictions of the kinetic theory and computer simulations

On the sputtering of binary compounds

A simple physical model is presented to describe some aspects of the sputtering of compound targets. In particular, expressions are developed for the partial sputtering yields for binary systems in terms of the elemental sputtering rates, the stoichiometric concentrations and surface binding energy. The partial yields depend non-linearly on the bulk target concentrations. Comparison of the theoretical predictions with the data on sputtering of PtSi, NiSi and Cu3Au indicates that the general features are well described

Grain dynamics in zero gravity

The dynamics of granular materials has proved difficult to model, primarily because of the complications arising from inelastic losses, friction, packing, and the effect of many grains being in contact simultaneously. One interesting limit for which it was recently possible to construct a theory is that where the grain-grain interactions are dominated by binary collisions. The kinetic model of granular systems if similar to the kinetic theory of gases, except that collisional energy losses are always present in the former and must be treated explicitly. Few granular materials on Earth are describable by this limiting model, since gravity tends to collapse the grains into a high-density state where Coulombic friction effects are dominant. The planned Space Station offers an unusual opportunity to test the kinetic grain model and to explore its predictions. Without gravity, the regime of low interparticle velocities, where an elastic description of the collision is still valid, is investigated. This will allow direct interpretation by dynamical computer simulations as well as by kinetic theory

Grain flow as a fluid-mechanical phenomenon

The behaviour of granular material in motion is studied from a continuum point of view. Insofar as possible, individual grains are treated as the ‘molecules’ of a granular ‘fluid’. Besides the obvious contrast in shape, size and mass, a key difference between true molecules and grains is that collisions of the latter are inevitably inelastic. This, together with the fact that the fluctuation velocity may be comparable to the flow velocity, necessitates explicit incorporation of the energy equation, in addition to the continuity and momentum equations, into the theoretical description. Simple ‘microscopic’ kinetic models are invoked for deriving expressions for the ‘coefficients’ of viscosity, thermal diffusivity and energy absorption due to collisions. The ‘coefficients’ are not constants, but are functions of the local state of the medium, and therefore depend on the local ‘temperature’ and density. In general the resulting equations are nonlinear and coupled. However, in the limit s « d, where s is the mean separation between neighbouring grain surfaces and d is a grain diameter, the above equations become linear and can be solved analytically. An important dependent variable, in this formulation, in addition to the flow velocity u, is the mean random fluctuation (‘thermal’) velocity v of an individual grain. With a sufficient flux of energy supplied to the system through the boundaries of the container, v can remain non-zero even in the absence of flow. The existence of a non-uniform v is the means by which energy can be ‘conducted’ from one part of the system to another. Because grain collisions are inelastic, there is a natural (damping) lengthscale, governed by the value of d, which strongly influences the functional dependence of v on position. Several illustrative examples of static (u = 0) systems are solved. As an example of grain flow, various Couette-type problems are solved analytically. The pressure, shear stress, and ‘thermal’ velocity function v are all determined by the relative plate velocity U (and the boundary conditions). If v is set equal to zero at both plates, the pressure and stress are both proportional to U^2, i.e. the fluid is non-Newtonian. However, if sufficient energy is supplied externally through the walls (v ≠ 0 there), then the forces become proportional to the first power of U. Some examples of Couette flow are given which emphasize the large effect on the grain system properties of even a tiny amount of inelasticity in grain–grain collisions. From these calculations it is suggested that, for the case of Couette flow, the flow of sand is supersonic over most of the region between the confining plates

Solar wind sputtering effects in the Martian atmosphere

A Monte Carlo simulation of the sputtering of the upper atmosphere of Mars by the solar wind was performed. The calculated sputtering yields imply loss rates (molecules/cm square - sec escaping the planet) for carbon dioxide, carbon, and oxygen of R(CO2) = 2.6 X 1000000/cm square - sec, R(C) = 6.6 X 1000000/cm square - sec, and R(O) = 7.7 X 1000000/cm - sec. The total mass loss by sputtering is only about 10% of that due to chemical and photo-chemical processes, but sputtering provides a major exospheric sink for carbon. The erosion process described here preferentially removes the lighter components of the atmosphere. Calculations based on a Monte Carlo simulation suggest that for a model atmosphere, 97% of the N2 and 33% of the CO2 originally present may have been sputtered away over 4.5 X 10 to the 9th power y. In the same length of time the (15)N/(14)N isotopic ratio for the bulk atmosphere would have increased by a factor 1.7

Possible isotopic fractionation effects in sputtered minerals

A model which makes definite predictions for the fractionation of isotopes in sputtered material is discussed. The fractionation patterns are nonlinear, and the pattern for a particular set of isotopes depends on the chemical matrix within which those isotopes are contained. Calculations are presented for all nonmonoisotopic elements contained in the minerals perovskite, anorthite, ackermanite, enstatite, and troilite. All isotopes are fractionated at the level of approximately 4-6 deg/o per atomic mass unit. Oxygen is always positively fractionated (heavier isotopes sputtered preferentially), and heavier elements are generally negatively fractioned (light isotopes sputtered preferentially). The value of Delta (O-18:O-16) is always less by about 1.8 deg/o than a linear extrapolation based upon the calculated delta (O-17:O-16) value would suggest. The phenomenon of both negative and positive fractionation patterns from a single target mineral are used to make an experimental test of the proposed model

Mass fractionation of the lunar surface by solar wind sputtering

The sputtering of the lunar surface by the solar wind is examined as a possible mechanism of mass fractionation. Simple arguments based on current theories of sputtering and the ballistics of the sputtered atoms suggest that most ejected atoms will have sufficiently high energy to escape lunar gravity. However, the fraction of atoms which falls back to the surface is enriched in the heavier atomic components relative to the lighter ones. This material is incorporated into the heavily radiation-damaged outer surfaces of grains where it is subject to resputtering. Over the course of several hundred years an equilibrium surface layer, enriched in heavier atoms, is found to form. The dependence of the calculated results upon the sputtering rate and on the details of the energy spectrum of sputtered particles is investigated. It is concluded that mass fractionation by solar wind sputtering is likely to be an important phenomenon on the lunar surface

Booming sands of the Mojave Desert and the Basin and Range Province, California

The phenomenon of acoustically active desert sand dunes has been recorded since ancient times (1). These dunes are usually known in the present day as booming, barking, roaring, or singing sands. The most striking example of the phenomenon is associated with the displacement, on steep slopes exceeding the angle of shear of a large area of unstable sand. As the sand moves downhill a strong and persistent vibration is set up generating a readily noticeable shaking of the surrounding (undisplaced) sand, as well as a loud and pure audible tone similar to that made by a low-flying propellor aircraft. The sand displacement may occur naturally, or be induced by the observer. A list of references to old observations together with a recent study of the phenomenon at Sand Mountain, Nevada, may be found in ref. (2, 3). The present paper deals with the acoustic properties of sand from several sites in the Mojave Desert of California and from the Basin and Range Province of California and (in one case) western Nevada, See Fig. 1

Sputter ejection of matter from Io

The direct collisional interaction of magnetospheric particles with Io will lead to sputtering of atoms and molecules from the satellite into circum-Jovian space. The ∼520-eV S (and ∼260-eV O) ions composing the Io torus are the most effective agents for net sputter removal of matter from the satellite. An incident flux of ∼10^(10) cm^(−2) s^(−1) is estimated to provide ∼5 × 10^(10) S atoms cm^(−2) s^(−1) from sputtering of a (dayside) atmosphere with an exobase at a few hundred kilometers and up to ∼10^(12) S atoms cm^(−2) s^(−1) from an atmosphere at 1500°K with an exobase at ∼2.2 R_(Io). The supply of S (and O) required to stabilize the torus has been estimated by others to be from 10^(10) to 10^(12) cm^(−2) s^(−1). If Na and K are present in the atmosphere at a concentration level of 1%, the corresponding sputtering rates are calculated to be a few times 10^8 cm^(−2) s^(−1) for an exobase at several hundred kilometers. These numbers are large enough to supply the 10^7 cm^(−2) s^(−1) fluxes required to maintain the Na and K clouds. Sputtering can also remove heavy molecules, like Sn, from the atmosphere. At night, direct S sputtering of the unprotected surface is calculated to eject S and Na (1% concentration) at rates given approximately by ∼10^(10) and ∼10^8 cm^(−2) s^(−1), respectively. All atomic species residing on the surface must be ejected into circum-Jovian space at a rate approximately proportional to their (surface) abundances, if direct surface sputtering occurs, so that the particle content of the inner Jovian magnetosphere should map rather faithfully all species present on Io's surface. The processes of plume sputtering, avalanche cascading, and ionic saltation may lead to spatial and temporal variations in the number of ejected particles

Transport properties of negative muons in matter

In deriving a formula for atomic capture ratios involving negative muons, Daniel postulates a model leading to a muon energy spectrum of a different character from that indicated by a more complete analysis. In this Comment we emphasize the dependence of the energy spectrum on both inelastic and capture processes, and suggest several experiments which may distinguish between different theoretical models