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 h 0 ( t ) 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 h 1 ( t ) ∼ t 1/3 . 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.