Wetting Dynamics in a Rectangular Channel

We analyze the dynamics of liquid filling in a thin, slightly inflated rectangular channel driven by capillary forces. We show that although the amount of liquid in the channel increases in time following the classical Lucas-Washburn law (t^1/2 scaling), the prefactor is very sensitive to the deformation of the channel because the filling takes place by the growth of two parts, the bulk part (where the cross section is completely filled by the liquid), and the finger part (where the cross section is partially filled). We calculate the time evolution of bulk and finger accounting for the coupling between the two parts and show that the prefactor for the filling can be reduced significantly by a slight deformation of the rectangular channel, e.g., the prefactor is reduced 50% for a strain of 0.1%. This offers an explanation for the large deviation on the value of the prefactor reported previously.