Drop propulsion in tapered tubes

Authors: P. Renvoisé, J. W. M. Bush, M. Prakash, and D. Quéré

Link: https://iopscience.iop.org/article/10.1209/0295-5075/86/64003

DOI: https://doi.org/10.1209/0295-5075/86/64003

Abstract: We present the results of a combined experimental and theoretical investigation of the motion of wetting droplets in tapered capillary tubes. We demonstrate that drops may move spontaneously towards the tapered end owing to the Laplace pressure gradient established along their length. The influence of gravity on this spontaneous motion is examined by studying drop motion along a tilted tube with its tapered end pointing upwards. Provided the tube taper varies, an equilibrium height may be achieved in which the capillary force is balanced by the drop's weight. We deduce the family of tube shapes that support a stable equilibrium.

Additional Information:

Take a small pool of water and dip a fine glass capillary. Voila! the water rises up almost as if something is pulling it up (and something is pulling it up). This experiment was done and basically understood in the 1600's. But now take a conical capillary. Put a drop of water and watch what happens. The drop will spontaneously move towards the narrow end due to the LaPlace pressure gradient generated due to the taper. Though this is such a simple geometrical configuration, fluid flow in a tapered tube is non-trivial. Here we derive a stability criteria for tapered tubes of all shapes and form.