Tilting prevents the collapse of flexible sheets during imbibition

We study the imbibition of a wetting liquid between flexible sheets that are fixed in both ends. The liquid flow contracts sheets that are soft and forms a narrow neck that slows down the filling of the channel. Below a threshold stiffness, the sheets collapse and imbibition stops. Using the finite difference method, we solve the lubrication equation coupled with slender body deformation, and find that the meniscus motion has two regimes. Before reaching halfway, it advances faster than in traditional imbibition in stiff sheets. After, it slows down as the sheets contract and increase the hydraulic resistance of the channel. We propose a formula for the filling time in the asymptotic limit prior to collapse. In microfluidics, collapsing of flexible channels is a concern encountered in several applications. We show that tilting the initially parallel sheets cures this problem, and fills the channel in a short duration.