  We study the dynamics of simple reactions where the chemical species are
confined on a general, time-modulated surface, and subjected to
externally-imposed stirring. The study of these inhomogeneous effects requires
a model based on a reaction-advection-diffusion equation, which we derive. We
use homogenization methods to show that up to second order in a small scaling
parameter, the modulation effects on the concentration field are asymptotically
equivalent for systems with or without stirring. This justifies our
consideration of the simpler reaction-diffusion model, where we find that by
modulating the substrate, we can modify the reaction rate, the total yield from
the reaction, and the speed of front propagation. These observations are
confirmed in three numerical case studies involving the autocatalytic and
bistable reactions on the torus and a sinusoidally-modulated substrate
