  We consider the dynamics of thin two-dimensional viscous droplets on
chemically heterogeneous surfaces moving under the combined effects of slip,
mass transfer and capillarity. The resulting long-wave evolution equation for
the droplet thickness is treated analytically via the method of matched
asymptotic expansions in the limit of slow mass transfer rates, quasi-static
dynamics and vanishingly small slip lengths to deduce a lower-dimensional
system of integrodifferential equations for the two moving fronts. We
demonstrate that the predictions of the deduced system agree excellently with
simulations of the full model for a number of representative cases within the
domain of applicability of the analysis. Specifically, we focus on situations
where the mass of the drop changes periodically to highlight a number of
interesting features of the dynamics, which include stick-slip, hysteresis-like
effects, as well as the possibility for the droplet to alternate between the
constant-radius and constant-angle stages which have been previously reported
in related works. These features of the dynamics are further scrutinized by
investigating how the bifurcation structure of droplet equilibria evolves as
the mass of the droplet varies.
