On an approximate model for the shape of a liquid–air interface receding in a capillary tube

Abstract

A good approximation to modelling the shape of a liquid–air meniscus advancing or receding in a capillary tube of radius a can be constructed by balancing the curvature of the interface with the sum of a viscous stress valid near the contact line and a constant static pressure. This model has unique solutions for each value of the boundary condition, i.e. the dynamic contact angle. When the meniscus recedes at very small capillary numbers, the model predicts a critical receding velocity beyond which a liquid layer of the receding fluid (a liquid tail) develops along the solid (see figure 4). The length of the layer increases as the receding speed and the contact angle decrease. This layer regime is characterized by menisci whose macroscopic curvature is >1/a.