Capillary penetration in cells with periodical corrugations

In this work we present a theoretical study of the spontaneous capillary flow of a viscous liquid, developed in the gap between a couple of parallel corrugated plates (corrugated Hele-Shaw cell). The periodical corrugation of the interior walls of the plates is assumed as a sine-like pattern, transverse to the flow direction. Such a configuration may generate periodical gaps with a structure where zones of maximum and minimum closing occur. This is a simple idealization of typical micro and nano fabricated gaps used to mould polymers by capillarity. This model can also be useful to understand the capillary flow in naturally fractured reservoirs. By using lubrication theory we found that a very peculiar temporal flow is developed which could be of interest in improving our knowledge of this type of moulding.