Surface tension / atmospheric pressure formulas?

[Endy0816]

Anyone know a formula for how big a hole can be yet still keep water suspended in an otherwise sealed vessel, factoring in surface tension and atmospheric pressure?

[Enthalpy]

The books I've seen made the simple calculation. Problem, I have seen no experiment report telling "the books were right", and unfortunately it often happens that authors put some model or theory and imagine that Nature has to follow it.

That is, if T is the liquid's tension and h the local height along a drop at the outlet, T*(d²h/dx²+d²h/dy²) gives you the maximum pressure difference, and it relates to the drop's radius. But I expect that the hole's material matters too, at least by restricting the angle of the drop where it exits the hole, hence the possible drop's radius. The shape beyond the hole must matter too, and definitely how far the exit is wetted. If a big area beyond the exit is wetted, the hole has no effect - which suggests the process isn't reliable or demands a special shape.

Frankly, if this question has any sort of consequence, I'd search for experimental data or make measurements by myself.

[Endy0816]

17 hours ago, Enthalpy said:

The books I've seen made the simple calculation. Problem, I have seen no experiment report telling "the books were right", and unfortunately it often happens that authors put some model or theory and imagine that Nature has to follow it.

That is, if T is the liquid's tension and h the local height along a drop at the outlet, T*(d²h/dx²+d²h/dy²) gives you the maximum pressure difference, and it relates to the drop's radius. But I expect that the hole's material matters too, at least by restricting the angle of the drop where it exits the hole, hence the possible drop's radius. The shape beyond the hole must matter too, and definitely how far the exit is wetted. If a big area beyond the exit is wetted, the hole has no effect - which suggests the process isn't reliable or demands a special shape.

Frankly, if this question has any sort of consequence, I'd search for experimental data or make measurements by myself.

Thank you.

About what I was afraid of. Had some idea to apply the concept to create a suspended water aquarium, where larger holes would look better.

Does seem like should be more to it. You'd think the polarity would matter along with hole shape and roughness.

[studiot]

Droplets also have a habit of falling in time.

So I suspect you also need to factor time into this as the water will eventually run out of any hole big enough to be visible.

[Endy0816]

23 hours ago, studiot said:

Droplets also have a habit of falling in time.

So I suspect you also need to factor time into this as the water will eventually run out of any hole big enough to be visible.

I was thinking to reset periodically. Making up for lost water and expelling air that enters.

In theory could just break the vacuum for a second and release some of the water. Use the falling water to bring clean water in.

Still need to test what happens if something falls into one of the holes from the inside. Be embarrassing if brought down by fish poop.

[Enthalpy]

On 1/18/2020 at 7:14 PM, Endy0816 said:

Had some idea to apply the concept to create a suspended water aquarium, where larger holes would look better.

Maybe I imagine your proposal wrongly, but as soon as water wets a larger surface below the hole, the capillary action is lost. Only the lower face acts then, as inefficiently as the same face without the hole.

If many drops joint, you also lose the benefit of a droplet with small radius. Together, they make a big drop with small curvature, where the surface tension is inefficient.

Or if you prefer, surface tension acts on surfaces while gravity acts on masses hence volumes. Surface tension works better on small scale, like droplets or capillary tubes. You can cheat a bit with fragmented surfaces, like a wick or a sponge.

[Endy0816]

8 hours ago, Enthalpy said:

Maybe I imagine your proposal wrongly, but as soon as water wets a larger surface below the hole, the capillary action is lost. Only the lower face acts then, as inefficiently as the same face without the hole.

If many drops joint, you also lose the benefit of a droplet with small radius. Together, they make a big drop with small curvature, where the surface tension is inefficient.

Or if you prefer, surface tension acts on surfaces while gravity acts on masses hence volumes. Surface tension works better on small scale, like droplets or capillary tubes. You can cheat a bit with fragmented surfaces, like a wick or a sponge.

If you can excuse my artistic skill, would look something the depiction below(with suitable valves and hydrolocks for care and maintenance).

Did see some of what you were talking about while filling the test model(cup). Seemed to depend on how it was being filled so not a huge issue.

[Enthalpy]

Got it thanks to the drawing.

Definitely possible. Make the exit of the tubes and their surroundings hydrophobic, that's vital. If not, water wetting beyond the exit would flow without stopping. Something should prevent items like fingers to touch the tubes' exit, or water would flow permanently.

Some fish species may accept altitude, for instance the ones living in Titicaca. But as far as possible, I'd try to avoid the underpressure, as it introduces one failure mode more and complicates operations. Just tubes thin enough should suffice. Check how high water climbs in capillaries, this tells you how deep water can be in your aquarium. 0.1m or 0.2m seem feasible.

I hope the aquarium is static? In a boat, a plane, a van... water could become higher at one side, increasing the pressure.

[Endy0816]

6 hours ago, Enthalpy said:

Got it thanks to the drawing.

Definitely possible. Make the exit of the tubes and their surroundings hydrophobic, that's vital. If not, water wetting beyond the exit would flow without stopping. Something should prevent items like fingers to touch the tubes' exit, or water would flow permanently.

Some fish species may accept altitude, for instance the ones living in Titicaca. But as far as possible, I'd try to avoid the underpressure, as it introduces one failure mode more and complicates operations. Just tubes thin enough should suffice. Check how high water climbs in capillaries, this tells you how deep water can be in your aquarium. 0.1m or 0.2m seem feasible.

I hope the aquarium is static? In a boat, a plane, a van... water could become higher at one side, increasing the pressure.

Will do. I have some supplies coming so I can make a better test model.

Was going to check on what fish might work best as well later. Ones that go to surface for air are definitely out, but not sure about effects of low pressures you mention or lack of a normal tank bottom. Once I'm further along on the design of the tank, there are some marine biologists I can ask.

May just go with a wholly static display instead. Perhaps some floating pumice stones and artificial plants in the top portion.

I'm planning to mount it up on a wall, possibly above a door way or arch for the best experience. Definitely not in anything moving lol.

Edited January 27, 2020 by Endy0816