Validation of a model for impact breakage incorporating particle size effect

Investigation of a breakage probability model published by Vogel and Peukert [Vogel, L. and Peukert, W., 2004. Determination of material properties relevant to grinding by practicable labscale milling tests. Int. J. Miner. Process., 74S, 329–338.] has led to a modification of their model to describe the degree of impact breakage, t₁₀. The modified model takes a form similar to the JKMRC prior art breakage model, but with particle size and breakage properties incorporated explicitly in the model.     

The strength and fractal dimension characteristics of alum–kaolin flocs

Flocs generated by various shear forces exhibit different characteristics of size, strength and structure. These properties were investigated by employing a continuous optical monitoring and a microscope with CCD camera to directly monitor aggregation under six different shear intensities. The floc structure was characterized by the fractal dimension. The results showed that the flocculation index (FI) decreased from 1.16 at 20 rpm to 0.25 at 250 rpm and the floc size decreased from 550 μm to 150 μm, meantime, the FI value showed a good correlation with floc size. In order to determine the floc strength, two methods were used. One was the strength factor, ranging from 18.3% to 62.5%, calculated from FI curve, and the other was a theoretical value between 0.005 N/m² and 0.240 N/m², estimated by calculation. The floc strength increased with the G value in both cases. Furthermore, the fractal dimension increased with G and its value was between 1.30 and 1.63. The relation between fractal dimension and strength was also obtained.     

On the flow structure and turbulence during sweep and ejection events in a wind-tunnel model canopy

Particle image velocimetry (PIV) data obtained in a wind-tunnel model of a canopy boundary layer is used to examine the characteristics of mean flow and turbulence. The vector spacing varies between 1.7 and 2.5 times the Kolmogorov scales. Conditional sampling based on quadrants, i.e. based on the signs of velocity fluctuations, reveals fundamental differences in flow structure, especially between sweep and ejection events, which dominate the flow. During sweeps, the downward flow generates a narrow, highly turbulent, shear layer containing multiple small-scale vortices just below canopy height. During ejections, the upward flow expands this shear layer and the associated small-scale flow structures to a broad region located above the canopy. Consequently, during sweeps the turbulent kinetic energy (TKE), Reynolds stresses, as well as production and dissipation rates, have distinct narrow peaks just below canopy height, whereas during ejections these variables have broad maxima well above the canopy. Three methods to estimate the dissipation rate are compared, including spectral fits, measured subgrid-scale (SGS) energy fluxes at different scales, and direct measurements of slightly underresolved instantaneous velocity gradients. The SGS energy flux is 40–60% of the gradient-based (direct) estimates for filter sizes inside the inertial range, while decreasing with scale, as expected, within the dissipation range. The spectral fits are within 5–30% of the direct estimates. The spectral fits exceed the direct estimates near canopy height, but are lower well above and below canopy height. The dissipation rate below canopy height increases with velocity magnitude, i.e. it has the highest values during sweep and quadrant 1 events, and is significantly lower during ejection and quadrant 3 events. Well above the canopy, ejections are the most dissipative. Turbulent transport during sweep events acts as a source below the narrow shear layer within the canopy and as a sink above it. Transport during ejection events is a source only well above the canopy. The residual term in the TKE transport equation, representing mostly the effect of pressure–velocity correlations, is substantial only within the canopy, and is dominated by sweeps.     

Changes of the cosmic-ray mass composition in the 10–10 eV energy range

Data taken with ten Cosmic Ray Tracking (CRT) detectors and the HEGRA air-shower array on La Palma, Canary Islands, have been analysed to investigate changes of the cosmic ay mass composition at the ‘knee’ of the cosmic-ray flux spectrum near 10¹⁵ eV energy. The analysis is based on the angular distributions of particles in air showers. HEGRA data provided the shower size, direction, and core position and CRT data the particle track information. It is shown that the angular distribution of muons in air showers is sensitive to the composition over a wide range of shower sizes and, thus, primary cosmic-ray energies with little systematic uncertainties. Results can be easily expressed in terms of ln A of primary cosmic rays. In the lower part of the energy range covered, we have considerable overlap with direct composition measurements by the JACEE collaboration and find compatible results in the observed rise of ln A. Above about 10¹⁵ eV energy we find no or at most a slow further rise of ln A. Simple cosmic-ray composition models are presented which are fully consistent with our results as well as the JACEE flux and composition measurements and the flux measurements of the Tibet ASγ collaboration. Minimal three-parameter composition models defined by the same power-law slope of all elements below the knee and a common change in slope at a fixed rigidity are inconsistent with these data.     

Proton transport model in the ionosphere. 2. Influence of magnetic mirroring and collisions on the angular redistribution in a proton beam

We investigate the influence of magnetic mirroring and elastic and inelastic scattering on the angular redistribution in a proton/hydrogen beam by using a transport code in comparison with observations. H-emission Doppler profiles viewed in the magnetic zenith exhibit a red-shifted component which is indicative of upward fluxes. In order to determine the origin of this red shift, we evaluate the influence of two angular redistribution sources which are included in our proton/hydrogen transport model. Even though it generates an upward flux, the redistribution due to magnetic mirroring effect is not sufficient to explain the red shift. On the other hand, the collisional angular scattering induces a much more significant red shift in the lower atmosphere. The red shift due to collisions is produced by < 1 -keV protons and is so small as to require an instrumental bandwidth <0.2nm. This explains the absence of measured upward proton/hydrogen fluxes in the Proton I rocket data because no useable data concerning protons < 1 keV are available. At the same time, our model agrees with measured ground-based H-emission Doppler profiles and suggests that previously reported red shift observations were due mostly to instrumental bandwidth broadening of the profile. Our results suggest that Doppler profile measurements with higher spectral resolution may enable us to quantify better the angular scattering in proton aurora.     

Particle fabric in a small, type-2 ignimbrite flow unit (Laacher See, Germany) and implications for emplacement dynamics

 Ignimbrites of the 13-ka Upper Laacher See Tephra were deposited from small, highly concentrated, moderately fluidized pyroclastic flows. Their unconsolidated nature, and the prominence of accidental Devonian slate fragments, make these ignimbrites ideal for clast fabric studies. The upper flow unit of ignimbrite M14 has characteristics typical of a type-2 ignimbrite. Layer 2a and the lower part of layer 2b of the flow unit have strong, upstream-inclined a[p] fabrics (a[p] means long particle axes parallel to flow direction). Only clasts with a/b axial ratios of 2.5 or greater preserve good a[p] fabrics, whereas the a–b planes of flat fragments dip upstream irrespective of axial ratio. The a-axis fabric becomes weaker, flatter, and more girdle-like in the upper half of layer 2b. At one locality the a-axis fabric appears to rotate 40° up through the flow unit, suggesting either shear decoupling of different levels in the moving flow or unsteadiness effects in a flow depositing progressively at its base. The existence of similarly strong a[p] fabrics in layer 2a and the lower half of layer 2b appears inconsistent with the common interpretation that ignimbrite flow units are emplaced as a plug of essentially non-shearing material (layer 2b) on a thin shear layer (layer 2a), and that the entire flow freezes en masse to form the deposit. The data suggest that, if the flow froze en masse, it was shearing pervasively through at least half its thickness. Another possibility is that the flow unit aggraded progressively from the base up, and that the fabrics record the integrated history of shear directions and intensities immediately above the bed throughout the duration of deposition. Received: 13 February 1997 / Accepted: 4 April 1998     

A statistical study of field-aligned electron beams associated with ion conies events

A statistical study of field-aligned electron beams associated with upflowing ion conics is presented from Exos-D (Akebono) observations below 10 000 km. The electron beams are narrowly collimated along the field line and generally have energies of several tens of eV. They are divided in the analysis into three types: upflowing, downflowing, and counterstreaming. All the types of electron beams are almost equivalent in their energy and pitch angle characteristics and their association rate with upflowing ion events. About 50% of ion conies are found to be coincident with field-aligned electron beams. There is also a correlation in energy between the field-aligned electrons and ion conics. These show that the association is not a mere coincidence but rather that the field-aligned acceleration of electrons is related to the perpendicular energization of ions. The association rate of upflowing electrons is high on the nightside, while that of downflowing electrons is high on the dayside. The association rate of downflowing electrons is high at low altitudes, and the rates of the three types of electron beams become equivalent at high altitudes. Data indicate that the height of the electron acceleration region is lower on the nightside. It is suggested that the average height of the electron acceleration region is around the satellite apogee (–10000 km), and the average thickness of the region is about thousands km.     

The importance of energetic particle precipitation on the chemical composition of the middle atmosphere

An assessment is made of the relative contribution of certain classes of energetic particle precipitation to the chemical composition of the middle atmosphere with emphasis placed on the production of odd nitrogen and odd hydrogen species and their subsequent role in the catalytic removal of ozone. Galactic cosmic radiation is an important source of odd nitrogen in the lower stratosphere but since the peak energy deposition occurs below the region where catalytic removal of O₃ is most effective, it is questionable whether this mechanism is important in the overall terrestrial ozone budget. The precipitation of energetic solar protons can periodically produce dramatic enhancement in upper stratospheric NO. The long residence time of NO in this region of the atmosphere, where catalytic interaction with O₃ is also most effective, mandates that this mechanism be included in future modelling of the global distribution of O₃. Throughout the mesosphere the precipitation of energetic electrons from the outer radiation belt (60°70°) can sporadically act as a major local source of odd hydrogen and odd nitrogen leading to observable O₃ depletion. Future satellite studies should be directed at simultaneously measuring the precipitation flux and the concomitant atmosphere modification, and these results should be employed to develop more sophisticated models of this important coupling.     

A Lagrangian stochastic model for the trajectories of particle pairs and its application to the prediction of concentration variance within plant canopies

A simple Lagrangian stochastic model for the trajectories of particle pairs in high Reynolds-number turbulent flows is presented. In this model, the velocities of particle pairs are initially correlated but subsequently each particle moves independently. The independent single-particle trajectories are simulated using Thomson's model [J. Fluid Mech. 180, 529–556, 1987]. This two-particle model exactly satisfies the well-mixed condition for Gaussian turbulence when length scales, characterizing the two-point Eulerian velocity correlation function, vanish. Temperature variances, due to heat released as a passive scalar from an elevated plane source, within a model plant canopy (Coppin et al. Boundary Layer Meteorol. 35, 167–191, 1986) are shown to be well predicted by the model. It is suggested that for strongly inhomogeneous flows, the two-point Eulerian velocity function is of secondary importance in determining the simulated trajectories of particle pairs compared to the importance of ensuring satisfaction of the two-to-one constraint (Borgas and Sawford. J. Fluid Mech. 279, 69–99, 1994); i.e ensuring that one-particle statistics obtained from the two-particle model are the same as those obtained from the corresponding one-particle model. Limitations of this modelling approach are discussed.     

Further discussion on the intercomparison of the trace metal concentrations and particle size of fluvial sediment recovered from two centrifuge systems

A single large volume water sample taken at the mouth of the Upper Rhone River on Lake Geneva was processed directly in parallel through two continuous flow centrifuges, a Westphalia and an Alfa-Laval. Sediment was recovered from the Westphalia, and separately from the bowl and brass core of the Alfa-Laval. The three sediment samples were analyzed for particle size and the following elements: Zn, Cu, Mn, Cr, P, Co, B, V, Be, Sr, Na, Pb, Ni, Ba, Fe, Ca, and Mg. Results indicate that the particle size recovery of both machines is similar when sediment from the brass core and bowl of the Alfa-Laval are combined, and that the recovery for all elements other than Cu, V, B, and Pb are the same when the particle size differences are taken into account. Sediment from the Alfa-Laval brass core is clearly contaminated by Cu, B and is also elevated in V and Pb but not to a significant extent. The sediment recovered from the bowl of the Alfa-Laval is contaminated only with Cu, with a 10 ppm increase over the 52 ppm recovered in the Westphalia sediment. Operating procedures involve the discarding of the brass core sediment and the mixing of the Alfa-Laval bowl sediment with that from the Westphalia. The consequent increase in Cu is estimated at less than 5 ppm or within the confidence level of the analysis. These procedures are recommended to all operators of non modified Alfa-Laval units.