Effect of point viscosity variations in a fluid on the dynamics of a particle

We derive the flow field disturbance produced by point viscosity variations in a heterogeneous fluid when subject to a background flow while neglecting fluid inertia. The disturbance flow field is found to be identical to that generated by a force-dipole called stresslet. Using a combination of theory and numerical simulations based on boundary element method, we show how the hydrodynamics of an active rigid particle is altered due to the presence of point viscosity variations. In particular, we model areas of the fluid with viscosity lower than the mean viscosity as sinks and those higher as sources. Modelling a fluid with viscosity gradient in this manner, we reproduce the phenomena published by Oppenheimer et al. Phys. Rev. Fluids 1, 014001 (2016) where it was shown that the translation and rotation of a spherical particle can get coupled giving rise to non-trivial dynamics.