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Is it possible to have a membrane that will not let a liquid through it at normal pressures due to gravity, but pass that liquid when substantially pressurised?

For instance, a few inches of water (say 0.1psi) would be blocked, but 100psi would pass through.

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I don't know about membranes, but it's easy enough to make a valve that will have that property. One possible design would look something like the valve on a pressure cooker, for example. – Nathaniel Mar 6 at 9:33
Yeah, it's a valve that I'm trying to replace because it occasionally leaks under the weight of water alone, plus I'd like the water to pass through distributed evenly across it's cross-sectional area, rather than being channelled or obstructed by some sort of valve flap. – jontyc Mar 6 at 9:45
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I think you'll struggle to find a membrane that behaves like a valve i.e. is either on or off. In the membranes used in reverse osmosis the flow rate is roughly proportional to pressure, so you require a lot of energy to get a high flow rate. – John Rennie Mar 6 at 10:22
I'm imagining a rubber membrane, with moderate thickness and many small puncture holes punched in it. The holes would be small enough to block flow, until pressure increase and the whole membrane swells and thins. Never seen anything like that, though. – kbelder Mar 6 at 22:10

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Such membranes do exist, like in reversed osmosis plants creating fresh water from sea water. Such plants use huge pressure to press fresh water through the membrane, and without pressure very little water will come through. If there are air on the other side of the membrane surface tension of the water in the pores might hold back all the water, if its not highly pressurized.

Membranes where pressure will expand the pores is well suited for your typical application. Puncture a balloon with a needle numerous times and attach it to the tap, this experiment might give you a clearer picture.

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A membrane with small pores and air on the other side could do the trick because you will have to overcome a capillary pressure. However, this is only going to work once. After that there will most likely be a wetting layer at the outside of the membrane which effectively reduces the capillary pressure drop over the membrane to 0. To make this work you need to dry the outside of the membrane every time, which is very impractical.

What I would suggest is to use something similar to an elastically deforming membrane like the one you find in beakers for small children You could use a small buffer region in the valve to make sure that the flow is somewhat even. Entirely even is not going to be possible, because you will most likely have flow rates that are low enough to have laminar flow such that your profile will be parabolic mouthpiece for children's beaker

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