E. Rame, ON AN APPROXIMATE MODEL FOR THE SHAPE OF A LIQUID-AIR INTERFACE RECEDING IN A CAPILLARY-TUBE, Journal of Fluid Mechanics, 342, 1997, pp. 87-96
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.