Capillary Rise in the Interstices of Tubes

We present experimental measurements of transient capillary rise in the corners of an interstice formed between an array of tubes/rods. The capillary rise shows an initial regime where the height of the corner meniscus shows a steeper dependence of \({t}^{4/5}\) compared to the \({t}^{1/3}\) dependence in a later regime. We develop a scaling law for the later regime by minimization of the sum of the free energy and viscous dissipation, using Onsager's principle. The obtained scaling law for the capillary height in the corner \({Z}_{m} \propto {\left(\frac{t(\sigma \mathrm{cos}\theta {)}^{2}}{\rho \mu g}\right)}^{1/3}\) matches the measurements in the later regime.