The Couette flow of dense and fluid-saturated granular media

摘要

A continuum-mechanical description is proposed for dense granular media submitted to steady shears. By dense granular media we mean high solid fractions in the range between the random loose and the random close packings. The description is based on a modeling of the stresses resulting from free-volume entropic effects, contacts and impacts between particles, and viscosity of the interstitial fluid. The non-homogeneity of the material is taken into account via several transport coefficients depending on the solid fraction, When applied to the tangential annular flow in a Couette cell, the model predicts velocity and solid fraction profiles which agree qualitatively with those found experimentally but which also present some conflicting features, possibly due to the difficulties to achieve a true steady profile for the solid fraction. More precisely, we obtain the following predictions: (a) a minimum shear is required for motion, (b) above this minimum the motion is localized and the solid fraction decreases when approaching the inner moving cylinder, (c) the width of the shear band increases with the applied shear stress up to a maximum value above which our description fails because the solid fraction at the inner moving cylinder becomes smaller than the random loose packing, (d) the maximum width of the shear band is proportional to the radius of the inner cylinder, with a proportionality coefficient which increases with the fluid viscosity and decreases with the confining pressure and the grain size, (e) for dry granular media the maximum width of the shear band is approximately half the radius of the inner cylinder so that localization is observed in almost all Couette cells, (f) when a very viscous fluid surrounds the grains the width of the shear band often exceeds the gap of the Couette cell, giving the (wrong) impression that shear localization has disappeared.