LAUSR

A cellulose sponge is a mundane porous medium composed of numerous microporous cellulose sheets surrounding macroscale voids. Here, we quantify the capillary rise dynamics of non-aqueous liquids in a sponge using a combination of experiment and theory. Although the classical law of Washburn is obeyed in the early stages, the wet front propagation is no longer diffusive in the late stages and follows a power law, $h\sim t^{1/4}$ , with $h$ and $t$ being the capillary rise height and time respectively. The transition of the power law is a consequence of the peculiar heterogeneous pore structure of cellulose sponges. The permeability and driving pressure change at the rise height above which the macro voids can no longer be filled completely due to significant effects of gravity. We rationalize the $t^{1/4}$ law by considering liquid flows along the corners of macro voids driven by capillary pressure of microscale wall pores.