Session X24: Granular Flow II
8:00 AM–10:24 AM, Friday, March 25, 2005
LACC Room: 411
Sponsoring Units:
GSNP DCMP DFD
Chair: Jeremay Lechman, Sandia National Laboratory
Abstract ID: BAPS.2005.MAR.X24.12
Abstract: X24.00012 : Shear viscosity of suspensions and the glass: Turning power-law divergence into an essential singularity
10:12 AM–10:24 AM
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Abstract
Author:
Narendra Kumar
(Raman Research Institute, Bangalore 560080, India)
Extreme slow dynamics defines approach to the glassy state. At the macroscopic scale, it manifests as a rise of shear viscosity as that state is reached through supercooling. The Vogel-Fulcher (VF) law describes that growth of viscosity. This work derives the VF law. Starting with an expression, due originally to Einstein, for the shear viscosity $\eta(\delta\phi)$ of a liquid having a small fraction $\delta\phi$ by volume of solid particulate matter suspended in it at random, we derive an effective-medium viscosity $\eta(\phi)$ for arbitrary $\phi$ which is precisely of the Vogel-Fulcher form. An essential point of the derivation is the incorporation of the excluded-volume effect at each turn of the iteration $\phi_{n+1} = \phi_{n} +\delta\phi$. The model is frankly mechanical, but applicable directly to soft matter like a dense suspension of microspheres in a liquid as function of the number density. Extension to a glass forming supercooled liquid is plausible.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2005.MAR.X24.12