Oseen tensor (${\mathsf{G}}_{ij}(\mathbf{r})=({\delta }_{ij}+r_i{r}_j/r^2)/(8\pi \eta r)$)

The Oseen tensor is the unbounded three-dimensional incompressible Stokes flow Green tensor relating a point force to the velocity it produces: $u_i={\mathsf{G}}_{ij}{F}_j$. At separation $r$, its longitudinal mobility is twice its transverse mobility. It generates the leading far-field hydrodynamic interaction between externally forced particles. The singular value at $r=0$ is not a particle's self mobility; a no-slip sphere instead has self mobility $1/(6\pi \eta a)$. Walls and near-contact lubrication require different or corrected tensors.