Flow classification Type A transition refers to multiple collisions, Type B transition refers to force chain formations, and Quasistatic state refers to persistent force chains. The vertical axis is the dimensionless shear rate and the horizontal axis is the solid concentration [schematic regime chart, reproduced from Fig. 13 of Babic et al. (1990)].
An example at solid concentration . (a) Particles packing where darker shading indicates smaller particles, and (b) shear velocity distribution where darker shading indicates slower particles.
Effective friction coefficient vs dimensionless shear rates and concentrations.
The relationship between dimensionless stress and shear rate with different concentrations. In (b) the analytic solution from kinetic theory is also included for comparison, in which parameter is a complex combination of , , and the ratio of tangent to normal velocity at each contact. An average value is used to derive the analytic solution [Lun (1991)]. The choice of corresponds to , and the velocity ratio is 1.
Contact time number vs (a) dimensionless stiffness and (b) concentration.
Intersections of different contact duration curves for (a) low dimensionless stiffness and (b) high dimensionless stiffness.
Intersections of different contact duration curves for different material properties: (a) low restitution and (b) high friction.
Particle group size vs shear rates and concentrations.
Coordination number versus (a) shear rates and (b) concentrations.
Details of the intersecting curves of the coordination number (a) low dimensionless stiffness and (b) high dimensionless stiffness.
Details of the intersecting curves of the coordination number (a) and (b) low restitution and (c) and (d) high friction.
Contours of coordination number. In all cases the contours begin with the value of 0.5 from the left at intervals of 0.5.
Contour of in the constitutive model. All contours begin with the value of 0.95 from the left with an interval of 0.1.
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