An elastocapillary model of wood-fibre collapse

Abstract

An elastocapillary model for drying-induced collapse is proposed. We consider a circular elastic membrane with a hole at the centre that is deformed by the capillary pressure of simply and doubly connected menisci. The membrane overlays a cylindrical cavity with rigid walls, trapping a prescribed volume of water. This geometry may be suitable for studying structural failures and stiction in micro-electromechanical systems during wet etching, where capillary surfaces experience catastrophic transitions. The dry state is determined using the dihedral-angle and volume-turning-point stability criteria. Open and collapsed conformations are predicted from the scaled hole radius, cavity aspect ratio, meniscus contact angle with the membrane and cavity walls, and an elastocapillary number measuring the membrane stretching rigidity relative to the water surface tension. For a given scaled hole radius and cavity aspect ratio, there is a critical elastocapillary number above which the system does not collapse upon drying. The critical elastocapillary number is weakly influenced by the contact angle over a wide range of the scaled hole radius, thus indicating a limitation of surface hydrophobization for controlling the dry-state conformation. The model is applied to the drying of wood fibres above the fibre saturation point, determining the conditions leading to collapse.