Singularities of hydrodynamic forces acting on particles in the near-contact regime

We consider a three-dimensional mathematical model of a viscous incompressible fluid in a bounded domain with two rigid particles modeled by spheres. One of the particles moves with prescribed translational and angular velocities, while the second one stays still. The near-contact regime of particles is considered. The hydrodynamic forces exerted on the moving particle exhibit singularity in terms of the small distance dd between the particles, and this asymptotic behavior is accurately captured and rigorously justified. It is shown that this singularity is of two dominant orders: O(d−1)O(d−1) and O(|logd|)O(|logd|). Previous investigations on the subject, being mostly formal, demonstrated disparities in the second dominant term of asymptotics of the forces. In contrast, this study presents rigorously justified, clear and concise procedure for the derivation of all asymptotic terms of the hydrodynamic forces.