  In this paper, a mathematical model of two adjacent rigid particles immersed
into a viscous incompressible fluid is considered. The main feature of the flow
is that the Cauchy stress tensor consisting of the strain tensor and the
pressure will appear blow-up as the distance between these two particles tends
to zero. For the purpose of making clear this high concentration, a family of
unified stress concentration factors are precisely captured in all dimensions,
which determine whether the Cauchy stress tensor will blow up or not. As a
direct application, we establish optimal gradient estimates and asymptotics of
the Cauchy stress tensor for Stokes flow, which indicate that its maximal
singularity comes from the pressure.
