  We present a molecular dynamics study of the motion of cylindrical polymer
droplets on striped surfaces. We first consider the equilibrium properties of
droplets on different surfaces, we show that for small stripes the
Cassie-Baxter equation gives a good approximation of the equilibrium contact
angle. As the stripe width becomes non-negligible compared to the dimension of
the droplets, the droplet has to deform significantly to minimize its free
energy, this results in a smaller value of the contact angle than the continuum
model predicts. We then evaluate the slip length, and thus the damping
coefficient as a function of the stripe width. For very small stripes, the
heterogeneous surface behaves as an effective surface, with the same damping as
an homogeneous surface with the same contact angle. However, as the stripe
width increases, damping at the surface increases until reaching a plateau.
Afterwards, we study the dynamics of droplets under a bulk force. We show that
if the stripes are large enough the droplets are pinned until a critical
acceleration. The critical acceleration increases linearly with stripe width.
For large enough accelerations, the average velocity increases linearly with
the acceleration, we show that it can then be predicted by a model depending
only the size of droplet, viscosity and slip length. We show that the velocity
of the droplet varies sinusoidally as a function of its position on the
substrate. On the other hand, for accelerations just above the depinning
acceleration we observe a characteristic stick-slip motion, with successive
pinnings and depinnings.
