  Active particles (living or synthetic) often move through inhomogeneous
environments, such as gradients in light, heat or nutrient concentration, that
can lead to directed motion (or taxis). Recent research has explored
inhomogeneity in the rheological properties of a suspending fluid, in
particular viscosity, as a mechanical (rather than biological) mechanism for
taxis. Theoretical and experimental studies have shown that gradients in
viscosity can lead to reorientation due to asymmetric viscous forces. In
particular, recent experiments with Chlamydomonas reinhardtii algae swimming
across sharp viscosity gradients have observed that the microorganisms are
redirected and scattered due to the viscosity change. Here we develop a simple
theoretical model to explain these experiments. We model the swimmers as
spherical squirmers and focus on small, but sharp, viscosity changes. We derive
a law, analogous to Snell's law of refraction, that governs the orientation of
active particles in the presence of a viscosity interface. Theoretical
predictions show good agreement with experiments and provide a mechanistic
understanding of the observed reorientation process.
