  Particle segregation is common in natural and industrial processes involving
flowing granular materials. Complex, and seemingly contradictory, segregation
phenomena have been observed for different boundary conditions and forcing.
Using discrete element method simulations, we show that segregation of a single
particle intruder can be described in a unified manner across different flow
configurations. A scaling relation for the net segregation force is obtained by
measuring forces on an intruder particle in controlled-velocity flows where
gravity and flow kinematics are varied independently. The scaling law consists
of two additive terms: a buoyancy-like gravity-induced pressure gradient term
and a shear rate gradient term, both of which depend on the particle size
ratio. The shear rate gradient term reflects a kinematics-driven mechanism
whereby larger (smaller) intruders are pushed toward higher (lower) shear rate
regions. The scaling is validated, without refitting, in wall-driven flows,
inclined wall-driven flows, vertical silo flows, and free surface flows down
inclines. Comparing the segregation force to the intruder weight results in
predictions of the segregation direction that match experimental and
computational results for various flow configurations.

Soft Condensed Matter;Fluid Dynamics