ON AN APPROXIMATE MODEL FOR THE SHAPE OF A LIQUID-AIR INTERFACE RECEDING IN A CAPILLARY-TUBE

A good approximation to modelling the shape of a liquid-air meniscus a dvancing or receding in a capillary tube of radius alpha can be constr ucted by balancing the curvature of the interface with the sum of a vi scous stress valid near the contact line and a constant static pressur e. This model has unique solutions for each value of the boundary cond ition, i.e. the dynamic contact angle. When the meniscus recedes at ve ry small capillary numbers, the model predicts a critical receding vel ocity beyond which a liquid layer of the receding fluid (a liquid tail ) develops along the solid (see figure 4). The length of the layer inc reases as the receding speed and the contact angle decrease. This laye r regime is characterized by menisci whose macroscopic curvature is > 1/alpha.