Dynamics of a droplet imbibing on a rough surface

We consider the imbibition of a liquid droplet of finite size on a rough surface and theoretically show that the imbibition dynamics is significantly slower than the familiar Washburn diffusive dynamics, ～t(0.5). The imbibition does not follow a simple power law. The droplet starts to imbibe with ～t(0.5) dynamics but progressively becomes slower with time. The slower imbibition is mainly attributed to the finite size of the droplet, resulting in a limited capillary driving force as compared to a steady capillary driving force in the case of imbibition from a steady source.