Capillary Rising in a Tube with Corners.

We studied the dynamics of a fluid rising in a capillary tube with corners. In the cornered tube, unlike the circular tube, fluid rises with two parts, the bulk part where the entire cross-section is occupied by the fluid and the finger part where the cross-section is only partially filled. Using the Onsager principle, we derive coupled time-evolution equations for the two parts. We show the following: (a) At the early stage of rising, the dynamics is dominated by the bulk part and the fluid height () shows the same behavior as that in the circular tube. (b) At the late stage, the bulk part stops rising but the finger part continues, following the scaling law () ∼ . We also show that, due to the coupling between the two parts, the equilibrium bulk height is smaller than the Jurin's height, which ignores the effect of the finger part.