Granular materials exhibit unique secondary flow behaviors upon
shearing. We demonstrate, using particle dynamics simulations, that the
secondary flow patterns are controlled by a pressure exerted on the
particle bed. The threshold pressure, at which vortex flow transitions
to disturbed or chaotic flow, depends on particle shape, that influences
interparticle contacts and rheological performance. Our results show
that the flow patterns are essentially determined by a dimensionless
term combining the pressure and granular temperature for all the
spherical and Platonic particles explored. Particle mixing is promoted
by the vortex flow or the disturbed flow with strong diffusion. The
highest mixing rate under a specified pressure is obtained for cubic
particles, due to the remarkable microstructural ordering near the
boundaries causing a high gradient of packing density. These findings
may shed light on optimal control of granular secondary flows and mixing
by tuning the applied pressure and particle shape.