  We consider a thin droplet that spreads over a flat, horizontal and
chemically heterogeneous surface. The droplet is subjected to changes in its
volume though a prescribed, arbitrary spatiotemporal function, which varies
slowly and vanishes along the contact line. A matched asymptotics analysis is
undertaken to derive a set of evolution equations for the Fourier harmonics of
nearly circular contact lines, which is applicable in the long-wave limit of
the Stokes equations with slip. Numerical experiments highlight the generally
excellent agreement between the long-wave model and the derived equations,
demonstrating that these are able to capture many of the features which
characterize the intricate interplay between substrate heterogeneities and mass
transfer on droplet motion.
