Elastocapillary imbibition

When a wetting liquid invades a porous medium or a capillary tube, the penetration or imbibition speed is known to decrease as the square root of time. We examine the capillary filling of a gap between flexible sheets and demonstrate that the pressure-induced inward deflection of the sheets leads to a non-monotonic behavior of the speed of the invading meniscus until eventually the flow is blocked. A model based on lubrication theory is formulated as a non-linear free-boundary problem, which is solved numerically using finite-difference methods. Good agreement is obtained with our experiments. At early times the deformation of the sheets is insignificant, and the penetration speed is unaffected. At later times, as the penetration distance approaches the elastocapillary length, the deformation becomes appreciable and the flow accelerates. Shortly thereafter, the gap at the airliquid interface goes to zero, and the flow necessarily stops. The length of the sheets above which imbibition will cause them to coalesce is determined and is found to be in good agreement with that predicted via scaling arguments. Biological applications of this transient wetting of flexible boundaries are discussed.