  Within the framework of a semi-microscopic interface displacement model we
analyze the linear stability of sessile ridges and drops of a non-volatile
liquid on a homogeneous, partially wet substrate, for both signs and arbitrary
amplitudes of the three-phase contact line tension. Focusing on perturbations
which correspond to deformations of the three-phase contact line, we find that
drops are generally stable while ridges are subject only to the long-wavelength
Rayleigh-Plateau instability leading to a breakup into droplets, in contrast to
the predictions of capillary models which take line tension into account. We
argue that the short-wavelength instabilities predicted within the framework of
the latter macroscopic capillary theory occur outside its range of validity and
thus are spurious.
