Abstract
We outline the development of theory to describe, dense, collisional shearing flows of identical compliant spheres. We begin with two simple theories: one for rigid, nearly elastic spheres that interact through instantaneous, binary collisions; the other for compliant spheres that interact through multiple, enduring contacts. We then join the two extremes by adding compliance to the collisions and collisions to the spheres in enduring contact. Finally, we compare the predictions of the resulting theory with the results of discrete numerical simulations of steady, homogeneous shearing of compliant frictional spheres.
Highlights
In steady, homogeneous shearing flows of identical spheres at volume fractions less than about 0.49, spheres interact through collisions that can be regarded as instantaneous, binary, and uncorrelated
The introduction of an additional length scale in the relation for the rate of collisional dissipation of fluctuation energy associated with the size of clusters of interacting spheres modifies the stress relations in an appropriate way [12,13,14,15]
The stresses at volume fractions beyond the hard-sphere singularity have parts that depend on the shear rate and parts that depend on the deformation of the contact
Summary
Homogeneous shearing flows of identical spheres at volume fractions less than about 0.49, spheres interact through collisions that can be regarded as instantaneous, binary, and uncorrelated. The length scale is determined by the competition between the orienting influence of the flow and the randomizing influence of the collisions, using a local balance between the rates of production and dissipation of fluctuation energy This approach has been tested against discrete element simulations of steady flows in a variety of flow configurations [16,17,18,19].
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
