From Wikipedia Capillary Action
Thus for a 4 m diameter glass tube in lab conditions given above (radius 2 m), the water would rise an unnoticeable 0.007 mm. However, for a 4 cm diameter tube (radius 2 cm), the water would rise 0.7 mm, and for a 0.4 mm diameter tube (radius 0.2 mm ), the water would rise 70 mm.
My question is: if we were to sit a collection of such narrow walled tubes around the edge of a bowl of water, and bend the ends of the tubes over in towards the center of the container, what would stop a continual water drip back into the water from the tubes?
The narrower the tube, the greater the capillary action and it is possibly the introduction of the bend that would restrict further water flow and that may be the solution to this "paradox".
Obviously, a perpetual motion device is impossible, but I wonder, at what point does "something" prevent the drips returning to the bowl, or what other mechanism prevents contravention of thermodynamic laws.
Best Answer
The dripping would occur as you describe it, if the drip ends of your tube or tubes is low enough to let gravity overcome the capillary action. That is what prevents a perpetuum mobile: Just as the water from the container is sucked into the tubes, water from the opposite end is also sucked in. To remove it, you have to expend energy, the same (in steady state) as you gained from the liquid's attraction to the capillaries.