On models of polydisperse sedimentation with particle-size-specific hindered-settling factors

Polydisperse suspensions consist of particles differing in size or density that are dispersed in a viscous fluid. During sedimentation, the different particle species segregate and create areas of different composition. Spatially one-dimensional mathematical models of this process can be expressed as strongly coupled, nonlinear systems of first-order conservation laws. The solution of this system is the vector of volume fractions of each species as a function of depth and time, which will in general be discontinuous. It is well known that this system is strictly hyperbolic provided that the Masliyah–Lockett–Bassoon (MLB) flux vector is chosen, the particles have the same density, and the hindered-settling factor (a multiplicative algebraic expression appearing in the flux vector) does not depend on the particle size but is the same for all species. It is the purpose of this paper to prove that this hyperbolicity result remains valid in a fairly general class of cases where the hindered-settling factor does depend on particle size. This includes the common power-law type hindered-settling factor in which the exponent, sometimes called Richardson–Zaki exponent, is determined individually for each species, and is a decreasing function of particle size. The importance of this paper is two-fold: it proves stability for a class of polydisperse suspensions that was not covered in previous work, and it offers a new analysis of real data.     

Über die Transformation einer Reihe nachBesselschen Funktionen

Ohne ZusammenfassungHerrn Professor W.Süss zum 60. Geburtstag gewidmetThe preparation of this note was sponsored by the European Office Air Research and Development Command, U.S. Air Force, Project No. AF 61(514)-442.     

Photoemission studies of clean and oxygen-covered Pt 6(111) × (100)

Employing the enhanced sensitivity obtained by using synchrotron radiation near the Cooper minimum for the 5d valence electrons, we have located the oxygen 2p and 2s levels for oxygen chemisorbed on a Pt 6(111) × (100) crystal. We find the oxygen 2p level located ?6 eV with a FWHM of 3 eV and the 2s at ?21.6 eV. A factor of four difference in saturation coverage is measured between temperatures of 300 and 120 K, but the position and width of the 2p level is independent of temperature. We observe also the 1b₁ orbital of weakly adsorbed H₂O molecules, which has pure O 2p parentage; from the intensity of this orbital, we are able to suggest why it is difficult to observe the oxygen 2p signal at low photon energies. In addition, we note a strong preferential attenuation in the Pt states near E_f for the adsorbed H₂O in spite of the weak nature of the bond.