We address theoretically adiabatic regime of charge transport for a model of two tunnel-coupled quantum dots connected
in series. The energy levels of the two dots are harmonically modulated by an external potential with a constant phase shift
between the two. Motivated by recent experiments with surface-acoustic-wave excitation, we consider two situations: (a)
pure pumping in the absence of external voltage (also at finite temperature), and (b) adiabatic modulation of the current
driven by large external bias. In both cases we derive results consistent with published experimental data. For the case
(b) we explicitly derive the adiabatic limit of Tien-Gordon formula for photon-assisted tunneling and compare it to the
outcome of simple conductance modulation. A tutorial for adiabatic pumping current calculations with the Green function
formalism is included.