  A three-dimensional mathematical model of a viscous incompressible fluid with
two stiff particles is investigated in the near-contact regime. When one of the
particles approaches the other motionless particle with prescribed
translational and angular velocities, there always appears blow-up of
hydrodynamic force exerted on the moving particle. In this paper, we construct
explicit singular functions corresponding to the fluid velocity and pressure to
establish precise asymptotic formulas for hydrodynamic force with respect to
small interparticle distance, which show that its largest singularity is
determined by squeeze motion between two particles. Finally, the primal-dual
variational principle is employed to give a complete justification for these
asymptotics.
