1,582 research outputs found
Shear dispersion in dense granular flows
We formulate and solve a model problem of dispersion of dense granular
materials in rapid shear flow down an incline. The effective dispersivity of
the depth-averaged concentration of the dispersing powder is shown to vary as
the P\'eclet number squared, as in classical Taylor--Aris dispersion of
molecular solutes. An extensions to generic shear profiles is presented, and
possible applications to industrial and geological granular flows are noted.Comment: 6 pages, 2 figures, Springer svjour3 format; to appear in Granular
Matte
Flow rate--pressure drop relation for deformable shallow microfluidic channels
Laminar flow in devices fabricated from soft materials causes deformation of
the passage geometry, which affects the flow rate--pressure drop relation. For
a given pressure drop, in channels with narrow rectangular cross-section, the
flow rate varies as the cube of the channel height, so deformation can produce
significant quantitative effects, including nonlinear dependence on the
pressure drop [{Gervais, T., El-Ali, J., G\"unther, A. \& Jensen, K.\ F.}\ 2006
Flow-induced deformation of shallow microfluidic channels.\ \textit{Lab Chip}
\textbf{6}, 500--507]. Gervais et. al. proposed a successful model of the
deformation-induced change in the flow rate by heuristically coupling a Hookean
elastic response with the lubrication approximation for Stokes flow. However,
their model contains a fitting parameter that must be found for each channel
shape by performing an experiment. We present a perturbation approach for the
flow rate--pressure drop relation in a shallow deformable microchannel using
the theory of isotropic quasi-static plate bending and the Stokes equations
under a lubrication approximation (specifically, the ratio of the channel's
height to its width and of the channel's height to its length are both assumed
small). Our result contains no free parameters and confirms Gervais et. al.'s
observation that the flow rate is a quartic polynomial of the pressure drop.
The derived flow rate--pressure drop relation compares favorably with
experimental measurements.Comment: 20 pages, 6 figures; v2 minor revisions, accepted for publication in
the Journal of Fluid Mechanic
Non-Fickian macroscopic model of axial diffusion of granular materials in a long cylindrical tumbler
We formulate and solve a non-Fickian macroscopic model of axial diffusion of
a granular material in a finite cylindrical tumbler. The model accounts for
localization of shear and, thus, diffusion induced by particle collisions in a
thin surface flowing layer in the cross-section of the drum. All model
parameters are related to measurable quantities in a granular flow. The
proposed non-Fickian model could address certain ``anomalous'' features
previously identified in experiments on axial diffusion and segregation of
granular materials. It is shown that the proposed model is a member of the
general class of linear constitutive relations with memory. The theoretical
predictions suggest new ideas to interpret the results of experimental
measurements.Comment: 7 pages, 2 figures, Springer journal class; submitted to Granular
Matter: Special Issue In Memoriam of Robert P. Behringer; v2: minor revision
Tracing chemical evolution over the extent of the Milky Way's Disk with APOGEE Red Clump Stars
We employ the first two years of data from the near-infrared, high-resolution
SDSS-III/APOGEE spectroscopic survey to investigate the distribution of
metallicity and alpha-element abundances of stars over a large part of the
Milky Way disk. Using a sample of ~10,000 kinematically-unbiased red-clump
stars with ~5% distance accuracy as tracers, the [alpha/Fe] vs. [Fe/H]
distribution of this sample exhibits a bimodality in [alpha/Fe] at intermediate
metallicities, -0.9<[Fe/H]<-0.2, but at higher metallicities ([Fe/H]=+0.2) the
two sequences smoothly merge. We investigate the effects of the APOGEE
selection function and volume filling fraction and find that these have little
qualitative impact on the alpha-element abundance patterns. The described
abundance pattern is found throughout the range 5<R<11 kpc and 0<|Z|<2 kpc
across the Galaxy. The [alpha/Fe] trend of the high-alpha sequence is
surprisingly constant throughout the Galaxy, with little variation from region
to region (~10%). Using simple galactic chemical evolution models we derive an
average star formation efficiency (SFE) in the high-alpha sequence of ~4.5E-10
1/yr, which is quite close to the nearly-constant value found in
molecular-gas-dominated regions of nearby spirals. This result suggests that
the early evolution of the Milky Way disk was characterized by stars that
shared a similar star formation history and were formed in a well-mixed,
turbulent, and molecular-dominated ISM with a gas consumption timescale (1/SFE)
of ~2 Gyr. Finally, while the two alpha-element sequences in the inner Galaxy
can be explained by a single chemical evolutionary track this cannot hold in
the outer Galaxy, requiring instead a mix of two or more populations with
distinct enrichment histories.Comment: 18 pages, 17 figures. Accepted for publication in Ap
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