Spontaneous capillary imbibition is a classical problem in interfacial fluid dynamics with a broad range of applications, from microfluidics to agriculture. Here we study the duration of the cross-over between an initial linear growth of the imbibition front to the diffusive-like growth limit of Washburn's law. We show that local-resistance sources, such as the inertial resistance and the friction caused by the advancing meniscus, always limit the motion of an imbibing front. Both effects give rise to a cross-over of the growth exponent between the linear and the diffusive-like regimes. We show how this cross-over is much longer than previously thought – even longer than the time it takes the liquid to fill the porous medium. Such slowly slowing-down dynamics is likely to cause similar long cross-over phenomena in processes governed by wetting.

We present a theoretical study of the statics and dynamics of a partially wetting liquid droplet, of equilibrium contact angle $\unicode[STIX]{x1D703}_{e}$ , confined in a solid wedge geometry of opening angle $\unicode[STIX]{x1D6FD}$ . We focus on a mostly non-wetting regime, given by the condition $\unicode[STIX]{x1D703}_{e}-\unicode[STIX]{x1D6FD}>90^{\circ }$ , where the droplet forms a liquid barrel – a closed shape of positive mean curvature. Using a quasi-equilibrium assumption for the shape of the liquid–gas interface, we compute the changes to the surface energy and pressure distribution of the liquid upon a translation along the symmetry plane of the wedge. Our model is in good agreement with numerical calculations of the surface energy minimisation of static droplets deformed by gravity. Beyond the statics, we put forward a Lagrangian description of the droplet dynamics. We focus on the overdamped limit, where the driving capillary force is balanced by the frictional forces arising from the bulk hydrodynamics, the corner flow near the contact lines and the contact-line friction. Our results provide a theoretical framework to describe the motion of partially wetting liquids in confinement, and can be used to gain further understanding on the relative importance of dissipative processes that span from microscopic to macroscopic length scales.