Critical Capillary Number of Interfacial Film Displacement in a   Capillary Tube
  The role of surface tension and wettability in the dynamics of air-liquid interfaces during immiscible fluid displacement flows in capillary tube driven by pressure has been investigated. The contact angle and capillary number drive the force wetting processes which is controlled by the balance between the capillary and the viscous lubrication forces. The dynamic wetting condition with the critical capillary number is studied analytically and validated experimentally, which demonstrates that the critical capillary number is associated with the contact angle, slip length and capillary radius. 
Changfei Yan and Huihe Qiu
physics.flu-dyn