I just learned about this method to grow hydroponics with no power - no pumps. Pretty neat. Best for small plants like lettuce.
Here is a link that might be useful: MHP Gardener shows Kratky method
If you search this forum, you'll find where it has been discussed how much nutrient you need per plant to grow lettuce in that manner.
I like that the youtube video also linked to the original research paper.
Notice in the video, he said that it was winter when he was doing the trial. I think the no-aeration method would only work in cold weather, or at least his results would be not nearly so similar if he had tried the experiment in summer. Aeration becomes more important as reservoir temperature goes up. That's one of the many difficulties of trying to use off-grid hydro to feed starving people in a hot place like Africa. The hot weather requires aeration, which requires energy, and if they had energy, they wouldn't be starving in the first place.
If you want an off grid hydro system, I would just use a flood n drain system. make sure the medium will hold enough moisture that only one or two waterings are needed daily and simply use muscle power to flood the trays.
I'm pretty sure the thread I suggested the OP look up involved someone in Thailand using an unaerated raft. If memory serves me, no aeration is pretty standard in that kind of system, but I think it requires lettuce. Something about there roots being better adapted to it.
The video was posted Nov. 5, and was probably shot the previous week. The location is Virgina, so it's not 'winter' growing season. Kratky himself worked at the University of Hawaii. The point of the system is that aeration comes not from the nutrient solution, but from the roots left hanging in the humid air as the solution level goes down.