We study the dynamics of small droplets of polydimethylsiloxane (PDMS)
silicone oil on a vertical, perfectly-wetting, silicon wafer. Interference
videomicroscopy allows us to capture the dynamics of these droplets. We use
droplets with a volumes typically ranging from 100 to 500 nanolitres
(viscosities from 10 to 1000 centistokes) to understand long time derivations
from classical solutions. Past researchers used one dimensional theory to
understand the typical t1/3 scaling for the position of the tip of the
droplet in time t. We observe this regime in experiment for intermediate
times and discover a two-dimensional, similarity solution of the shape of the
droplet. However, at long times our droplets start to move more slowly down the
plane than the t1/3 scaling suggests and we observe deviations in droplet
shape from the similarity solution. We match experimental data with simulations
to show these deviations are consistent with retarded van der Waals forcing
which should become significant at the small heights observed