  This work is focused on the development of a dynamic criterion for the
arching and bridging of spherical particles in a 3D suspension flow through a
channel with plane walls. Elasticity of the particles and the channel walls are
taken into account. The carrier fluid is viscous and incompressible. Bridging
occurs under the balance of the hydrodynamic force exerted from the fluid on
the particles and the friction force exerted from the walls on the particles.
The 3D motion of particles in fluid is analyzed by means of direct numerical
simulation. The bridging criterion is formulated as a domain on the plane in
terms of the two nondimensional parameters: the particle size to channel width
ratio and the flow velocity. For each scaled particle diameter there is a range
of critical velocities, in which bridging occurs. Various geometrical
configurations are considered: three and four particles across the slot.
Stability of the bridge is studied. The dynamic bridging criterion is different
from the earlier purely kinematic criteria, which were formulated in terms of
the particle-to-channel width ratio only. The bridging criterion is implemented
into the 2D width-averaged lubrication model of suspension flow through a plane
channel, and illustrative simulations are conducted. Application is for
proppant transport in hydraulic fractures.
