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Nature's (disposable) water filter. As a plant physiologist I can say that this would probably work in removing bacteria, but only with certain types of wood. Oaks and other ring porous species have long, wide vessels that could let some bacteria/protozoans through. The researchers used Eastern white pine -- conifers have a different wood structure where water has to pass through a lot of the kind of pit membranes shown in the picture at the top of the article, so they would be the best bet. You'd want to watch for leakage around the tube-wood seal. I suspect the setup shown would be extremely slow and so you would want a gravity feed and some time on your hands or a squeeze system to speed it up. We use a similar set-up to measure the hydraulic conductivity of twig samples, only up to about 5mm in diameter, but with a 1 m head you get only a few drops a minute even with species with high conductivity. Shorter, fatter twig sections should work better than the opposite. I can't take it too seriously (yet) but it's an intriguing idea and I may play around with it just for fun.
PS: I took a look at the published article in PLOS ONE. It's by a group at MIT and very thorough. They specifically say that conifers should be used, and include a diagram showing how wood of other kinds of trees can let bacteria through. They used compressed nitrogen to drive water through the wood, at a pressure of about 5 psi, about what you'd get with 3.5 meters of hydraulic head (so you'd need a long piece of tubing to get that kind of pressure) to get a flow rate of a bit less than 5 ml/minute, so it would take over 3 hours to get a liter of water. Hmm -- clearly requires some tinkering.