Capillary imbibition in a square tube

Abstract

When a square tube is brought in contact with bulk liquid, the liquid wets the corners of the tube, and creates finger-like wetted region. The wetting of the liquid then takes place with the growth of two parts, the bulk part where the cross section is entirely filled with the liquid and the finger part where the cross section of the tube is partially filled. In the previous works, the growth of these two parts has been discussed separately. Here we conduct the analysis by explicitly accounting for the coupling of the two parts. We propose coupled equations for the liquid imbibition in both parts and show that (a) the length of each part, $h_0$ and $h_1$, both increases in time $t$ following the Lucas-Washburn's law, $h_0\sim t^{1/2}$ and $h_1\sim t^{1/2}$, but that (b) the coefficients are different from those obtained in the previous analysis which ignored the coupling.

arXiv comment20 pages, 5 figures, submitted to Soft Matter

References in corpus (4)

• Capillary Rise in Nanopores: Molecular Dynamics Evidence for the Lucas-Washburn Equation
• Ring to Mountain Transition in Deposition Pattern of Drying
• Cross-interaction drives stratification in drying film of binary colloidal mixtures
• Vapor-Induced Motion of Liquid Droplets on an Inert Substrate

Cited by in corpus (10)

• Application of Onsager Machlup integral in solving dynamic equations in non-equilibrium systems
• Dynamics of Taylor Rising
• Theoretical analysis for dynamic contact angle hysteresis on chemically patterned surfaces
• Capillary rising in a tube with corners
• Edge Wetting: Steady State of Rivulets in Wedges
• Dynamics of a viscoelastic liquid filament connected to two mobile droplets
• Wetting dynamics in an angular channel
• Wetting equilibrium in a rectangular channel
• Capillary Filling Dynamics in Polygonal Tubes
• Existent condition of partially wet state in capillary tubes