Capillary rise in wedges

A wetting liquid put into contact with a thin vertical tube rises spontaneously in it, reaching a final height $z=h_{e}$ given by Jurin's law: $\frac{h_{e}}{r}=2\left(\frac{a}{r}\right)^2cos\theta_{c}$ where $r$ is the radius of the tube, $a=\sqrt{\frac{\gamma}{\rho g}}$ is the capillary length, based on the liquid surface tension $\gamma$, liquid density $\rho$ and gravity $g$, and $\theta_{c}$ is the contact angle characterizing the wetting of the liquid on the solid.--- Also, when $z\ll h_{e}$, where gravity can be neglected, the front of the liquid follows Washburn's law: $z=\sqrt{2\frac{\gamma r cos\theta_{c}}{\eta}t}$, where $\eta$ is the liquid viscosity.--- This works for all systems having a ``closed'' geometry, that is a scaling length, provided this scaling length is smaller than $a$.--- We use systems of ``open'' geometry, without scaling length, typically wedges with different geometries and show both experimentally and theoretically that the meniscus rises following the universal law : $\frac{h(t)}{a}\sim(\frac{\gamma}{\eta a}t)^{1/3}$. It differs from the case of ``closed'' geometry because it rises indefinitely and with a different dynamic. It is universal in the sense that it does not depend on the special geometry of the wedge.