Dynamic osmocapillary phase separation at contact lines

When a drop of liquid is placed on top of a swollen solid, if the liquid is immiscible with the solvent of the swollen solid, the surface tension near the contact line can pull the solvent out from the solid, leading to a phase separation that converts the classical three-phase contact line into a four-phase contact zone. This phase separation can significantly affect the wetting properties of the swollen solid and the effect is known to be time dependent. This paper develops a dynamic osmocapillary model which predicts that the size of the phase separation increases with time, following the scaling relation of t^0.32. The prediction agrees well with existing experiments.