On the termination of an emerging droplet from a capillary tube over a flat surface by a wetting slug: A one-dimensional quasistatic model and CFD analysis

The problem of ejection of a droplet from a pore opening into a reservoir appears in many fields including pharmaceutical, food, chemical, and several other industries. In this work, we are interested in investigating the onset of dislodgment of such an emerging droplet. A one-dimensional model is developed that describes the dynamics of this process under quasistatic assumptions. Fluid inertia, the dynamic nature of the contact angle, as well as the entrance and exit hydrodynamic effects are ignored. Fluid inertia may be important at the very early stage of the displacement process, after which its effect diminishes. It is hypothesized that the emerging droplet will dislodge the surface when the two contact lines associated with the two interfaces meet. The forces acting on this system include external pressures, viscous and capillary forces. The flow rate is influenced by the capillary pressure of the emerging nonwetting fluid when the advancing interface reaches the exit of the tube and starts to develop, then by the two interfaces when the wetting fluid starts to displace the wetting one. At the onset of dislodgment, the capillary pressure across the two interfaces equalizes. A computational fluid dynamics (CFD) study has been conducted to confirm the stated hypothesis and to provide a framework for the validation and verification of the developed model. The CFD model depicts the whole spectrum of processes involved from the start of injection of the nonwetting fluid towards the ejection of the droplet. The model, however, only considers the system when the wetting fluid starts to emerge from the exit of the tube into the reservoir. Comparisons between the model and the CFD analysis show a good match, which builds confidence in the modeling approach. Interesting results are obtained, particularly when the interfaces reach the exit of the tube.