Why doesn't this capillary action generator work? So I was doing a bit of reading.
Apparently the obstacle to generating energy from the forces driving capillary action is breaking the surface tension at the top of a capillary tube. It is just impossible to get the water to fall to drive a generator, getting it out of the top of the tube requires more energy than you would generate.
Or is it?
 
Here's the deal. The horizontal tube rests on the edge of the vertical tube, held down against it by the attached weight when there is no water in it.
So, the horizontal tube is touching, disrupting, the meniscus that will form at the top of the vertical tube. Water will begin to flow down the small horizontal tube by capillary action. This is especially certain if the horizontal tube is much smaller so that its diameter is less than the height of the meniscus.
At certain point, the weight of water in the horizontal tube causes it to rotate, breaking the surface tension at the meniscus, and allowing water to pour out of the lower end of the horizontal tube.
Then the tube rotates back to horizontal.
Rinse and repeat.
And in case you think it might be complicated by the horizontal tube touching the water, this works even simpler if you reduce the size of the horizontal tube such that it never could touch the reservoir.
 A: As you've indicated in your title, the correct question is "why doesn't this work". The system, as described would continue to produce energy indefinitely without any being added to it (perpetual motion, violation of conservation of energy...) . So you can be sure there's a problem.
I believe that part of the trouble here is in the assumption that the horizontal tube will allow the water to leave after it tilts down. If the capillary forces involved are sufficient to draw water up, there's no reason to think that they would not be sufficient to retain the water when the tube is rotated. 
If you were to build such a device, it would probably work as described until the tube rotated down. The water would stay inside and the system would just stop.
A: https://en.wikipedia.org/wiki/Perpetual_motion#Apparent_perpetual_motion_machines

This is a fancy capillary bowl and the same force that pushes the water upwards will prevent the droplet at the top of the tube from flowing through the oscillating tube.
If you gave initial energy enough to break the droplets, the friction of the moving pipe with the droplets will stop it since the cohesive energy of the "meniscus" is the same amount of energy that what a droplet dropped from the tube to the reservoir has.
A: I think if the radius is long enough then the velocity achieved may be high enough to overcome the surface forces. The concept would require the pivot to the left with spring return or similar.
Technically it would not violate conservation of energy unless work was harnessed from the perpetual motion.
A: What If.... 
You design a special wick, say maybe microscopic 3d printed that started out wide at the base with many absorption layers and got narrow as it went up, would it in theory be possible to get water to rise 100+ feet in the air using the capillary effect?  Isn't this basically how trees do it?
Then you could design many of these and put them all in a system where all the water they collect from a central reservoir buried in the ground collects in a second reservoir elevated in the air in the center of all the wicks.
Using that, assuming you can get water in it fast enough, you then funnel that water through a 1/2 pipe or something like that down 90 feet.  If you need more water build more 100 foot tall wick systems (artificial trees basically).
If you get enough PSI doing that you could run a small hydro generator to generate power.  if the pressure is enough to run more than one you could split the pipe at the bottom into 2 or more generators.
The exhaust water going straight back into the bottom reservoir.
If it's not enough volume to run the generators 24/7, then build the elevated reservoir big enough to store 12+ hours of collected water.  Then supplement with solar and use the stored water to generate electricity during the night?
If this is possible then most houses could already do it, assuming they are tall enough.  The water tank for the upper reservoir could reside in the attic.  the reservoir for the wicks could be the houses sump pump/french drain system.  Then you could design all of the siding on the house to act as wicks to bring the water into the attic reservoir.  Then generate power by letting it fall back to the french drain system through a small diameter pipe.
Additionally, with a properly designed attic you could use all the heat generated during the summer to pressure the upper reservoir and ramp up power output.
Imo, this isn't a system of perpetual motion, it's merely transforming energy from one form to another.
For reference: https://phys.org/news/2018-05-capillary-harnessed.html
A: Capillary action is a workable principle provided differences in the altitude of the water, the destination for the water must typically have lower altitude, see: https://www.youtube.com/watch?v=-tT-EJNZVqI
Your method depends on the idea that water could be sealed periodically within the upper tube in a manner similar to baffling or Tesla Valves.
Resistance to the capillary action could be created using the properties of shallow slope. It would have to be specially designed. It seems if capillary action could draw it along an upward curve. A strainer-type attachment might be used to allow pressure retention.
In the past, cumulative effects like cumulative weight of water in the tube has been used to create mechanical effects, for example, with the dominoes of increasing heights.
https://www.youtube.com/watch?v=YyCzDpkQs0U
If the functionality is similar to sponge devices it is thought it will not work because of oddities in pressure differences. Still, this device may be more clever than a sponge device, and sponge devices are already very clever.
Sponge experiments:
https://www.youtube.com/shorts/y6BQN3zEJeA
https://www.youtube.com/watch?v=Luf6MJkqIE0&t=32s
