Hydrodynamic particle interactions in linear and radial viscosity gradients

We present a versatile perturbative calculation scheme to determine the leading-order correction mobility matrix for particles in low-Reynolds-number fluid with spatially variant viscosity. To this end, we exploit Lorentz reciprocal theorem and reflection method far field approximation. demonstrate how apply framework particular choice of viscosity field, first study finite-size, interface-like, linear gradient. The extent latter should be significantly larger than particle separation. Both situations symmetrically asymmetrically placed within such an odd symmetric gradient are considered. As result, long-range flow fields identified that decay by one order slower their constant-viscosity counterparts. Self-mobilities rotations translations affected, while asymmetric placement, additional appears latter. terms associated hydrodynamic interactions between also need corrected, placement-specific manner. While results derived system two particles, they many-particle systems. Furthermore, treat gradients induced temperatures different from surrounding fluid. Assuming relation temperature viscosity, find both self-mobilities as well increase hot decrease cold particles.