Hydraulic droplet coarsening in open-channel capillaries.

Over a range of liquid-solid contact angles, an open-channel capillary with curved or angled sides can show a maximum in the Laplace pressure as a function of the filling state. Examples include double-angle wedges, grooves scored into flat surfaces, steps on surfaces, and the groove between touching parallel cylinders. The liquid in such a channel exhibits a beading instability if the channel is filled beyond the Laplace pressure maximum. The subsequent droplet coarsening takes place by hydraulic transport through the connecting liquid columns that remain in the groove. A mean-field scaling argument predicts the characteristic droplet radius R∼t^{1/7}, as a function of time t. This is confirmed by one-dimensional simulations of the coarsening kinetics. Some remarks are also made on the spreading kinetics of an isolated drop deposited in such a channel.