2008 Annual Meeting
(186u) Dense Suspensions and Granular Media - from Stokesium to Mohr-Coulombium
Author
Goddard, J. D. - Presenter, University of California, San Diego
Fluid-particle
systems with internal forces arising only from viscosity or
intergranular friction represent an important special case of "purely
dissipative" materials described by a 4th-rank viscosity tensor η depending on deformation history. In a recently proposed simplification [1], η is given by a tensor polynomial in a symmetric 2nd-rank structure or "fabric" tensor A,
whose evolution is determined by the history of deformation. Expressing
the latter as a corotational integral, with memory function involving
two exponential relaxation modes, one obtains a good fit to existing
data on viscosity and normal stress in steady shear reversal
experiments on concentrated suspensions. A recent extension [2] gives
predictions for shear and normal stress in sinsuoidal simple shear.
In
contrast to existing phenomenological models, the present approach
provides a clear-cut distinction between instantaneous Stokesian
response and non-linear effects arising from Stokesian-dynamical
evolution of microstructure or from non-Stokesian friction at particle
contacts. The latter serves as an essential link between the viscosity
idealized suspensions ("Stokesium") and the plasticity of dry granular
media ("Mohr-Coulombium").
A discussion is given of a recent
extension [2] of the above model to non-homogeneous suspensions, with
particle flux induced by gradients in particle concentration,
deformation rate, and fabric. Also, some connections are made to
elastoplastic models with evolutionary microstructure.
[1] J. D. Goddard. J. Fluid Mech., 568,1–17, 2006.
[2] J. D. Goddard. Phys. Fluids, 20, 040601,1-15. 2008.
systems with internal forces arising only from viscosity or
intergranular friction represent an important special case of "purely
dissipative" materials described by a 4th-rank viscosity tensor η depending on deformation history. In a recently proposed simplification [1], η is given by a tensor polynomial in a symmetric 2nd-rank structure or "fabric" tensor A,
whose evolution is determined by the history of deformation. Expressing
the latter as a corotational integral, with memory function involving
two exponential relaxation modes, one obtains a good fit to existing
data on viscosity and normal stress in steady shear reversal
experiments on concentrated suspensions. A recent extension [2] gives
predictions for shear and normal stress in sinsuoidal simple shear.
In
contrast to existing phenomenological models, the present approach
provides a clear-cut distinction between instantaneous Stokesian
response and non-linear effects arising from Stokesian-dynamical
evolution of microstructure or from non-Stokesian friction at particle
contacts. The latter serves as an essential link between the viscosity
idealized suspensions ("Stokesium") and the plasticity of dry granular
media ("Mohr-Coulombium").
A discussion is given of a recent
extension [2] of the above model to non-homogeneous suspensions, with
particle flux induced by gradients in particle concentration,
deformation rate, and fabric. Also, some connections are made to
elastoplastic models with evolutionary microstructure.
[1] J. D. Goddard. J. Fluid Mech., 568,1–17, 2006.
[2] J. D. Goddard. Phys. Fluids, 20, 040601,1-15. 2008.