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When I wash up plates and don't dry them right away and place on top of each other, they seem to stick together with a relatively high "force": i.e. when I try to pick the top plate hours later, the bottom plate sticks to the plate that I try to pick up to the point that it "beats" gravity.

  • What is the name of this effect?

  • Is it possible to calculate the strength of the binding force (i.e. per area of the plates?)

  • Is there any research on how various types of liquids (not just water) affect this sticking force? (would oil provide better or worse sticking?)

  • Is there an "optimal" thickness of the liquid between the two plates that maximizes the sticking?

Edit: As per the request in the comments, I attach a picture of the plates (regular porcelain plates).

PS: I did an experiment with cold water (as suggested in one of the answers below) and the plates still stick together very quickly. So it must be the water viscosity & surface tension & adhesion of water molecules (as per Niels's answer below), rather than "vacuum" seal created by cooling "hot" water).

enter image description here

enter image description here

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    $\begingroup$ Surface tension ... I guess.. $\endgroup$ – A Student 4ever Jan 24 at 13:36
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    $\begingroup$ It would be fun to try to separate them while they are submerged in water. My intuition says they will come off easily. $\endgroup$ – Rew Jan 25 at 9:26
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    $\begingroup$ Think of a suction cup. It's hard to pull it directly off but peel off a corner to break the vacuum and things get easier. Water does not compress very well but if you had enough strength to pull the plates directly apart then it would probably vaporize the water holding it together. $\endgroup$ – MonkeyZeus Jan 25 at 15:46
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    $\begingroup$ @Rew Indeed. You can do the same thing with gauge blocks. They stick together very strongly with a thin film of oil in air, but submerge them and they just fall apart. Because surface tension of oil around the edges where the gauge blocks meet (no oil remains between the gauge blocks since it is squeezed out). $\endgroup$ – DKNguyen Jan 25 at 22:57
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    $\begingroup$ There's an experiment you can perform that might give you a better sense of how this happens. Take a stiff cup or glass (be careful is you use glass glass) with a smooth rim. Fill it completely to the top with water such that the top of the water is above the rim. Take a paper towel and place it on a plate and wet it. Carefully place the plate on the cup and press down. If you got this all done right, you can then pick up the cup and invert it and air pressure will hold the plate and the water in the glass in place. $\endgroup$ – JimmyJames Jan 26 at 16:27
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There is a very nice answer by Niels Nielsen, I feel I need to add some detail about the sticking mechanism:

  1. The Van der Waals force is not only responsible for giving water molecules the ability to stick together, it is also responsible for giving water molecules the ability to stick to other surfaces. Contrary to popular belief, there are multiple types of Van der Waals forces. Now in your case the Van der Waals force (one type) gives the ability on one side to water molecules to stick to one of the plate's surfaces, and for water molecules to stick together (another type of the Van der Waals), and then on the other side to stick to the other plate's surface. And there you have it, the effect is like the two plates stick. The Van der Waals force is commonly accepted to be based on electromagnetism, so we are back to the EM force dominating over gravity at short distances. If you have a single wet plate, and hold it up, you can see that not all water falls off of it, the Van der Waals force keeps some of the water stick to the plate (you can see it commonly referred to as surface tension). The EM force dominates over gravity in this case.

of the molecule will orient itself with the extremely negative side of another molecule.

Explanation of van der Waals force

  1. When you have two wet plates, and push them together, the water gets inbetween squished and the surface area increases extremely, and the Van der Waals force seems to be extremely strong against gravity, if you have two plastic plates, they might not even separate if you only hold the top one. Of course in your case, if you use heavy ceramic plates, the Van der Waals force becomes inferior and gravity takes over and the bottom plate separates from the top. By the way, this is how geckos stick to surfaces (including other electrostatic forces).

the gecko's amazing climbing ability depends on weak molecular attractive forces called van der Waals forces,

https://www.eurekalert.org/pub_releases/2002-08/lcc-sph082202.php

Although direct charge measurements clearly demonstrate that the contribution of CE-driven electrostatic interactions in gecko adhesion is dominant, it should be noted that, along with electrostatic forces, van der Waals (vdW) and capillary forces could also contribute to the measured adhesion forces [7,9,24];

https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4233685/

You can see phrases where they use surface tension and it is correct. I just wanted to make sure that the underlying mechanism (Van der Waals) and the fundamental force (EM) at work is clear.

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This has turned out to be a very interesting question indeed. Based on all the good comments I will amend my answer here. There are (at least) two parts to this problem. One is why the plates stick together in the first place and the other is the exact mechanism by which the adhesion between them is broken when you pry them apart. My original answer dealt with what makes them stick together (the adhesion mechanism) but there's a lot of interesting physics having to do with what happens when you do pull hard enough to separate the plates. There are a number of simple and fun experiments that could be done to put some light on what's going on here. First, you could repeat the experiment with the plates immersed in water so any effects having to do with wet/dewet dynamics are eliminated. Second, you can do the experiment in air but with detergent-spiked water, to greatly reduce surface tension effects. Third, you could perform the experiment with transparent glass plates or better yet sheets of flat glass and record what happens with a digital camera as they are separated. I now return you to the regularly-scheduled program.

When a set of identical plates is stacked together, their adjacent top and bottom surfaces fit together well with very little gap space between them. If we try to pull them apart, it is easy for air to flow into the gap and hence allow that gap to grow, and for the plates to come apart.

If there is water in that gap, and we try to pull them apart, several things happen: first, we have to retract the thin film of water into a glob in the center of the plate stack, and the viscosity of the water resists that deformation.

Second, the adhesion that the water molecules have for the surfaces of the plates makes the water want to stay in contact with those surfaces and not get sucked back into a glob. It takes work to de-wet the plate surfaces, and so work must be applied in order to pull the plates apart.

In essence, the water acts as a (lousy) glue, but a good enough glue to illustrate several of the properties of a good glue: 1) it has to develop a high viscosity after being put into a gap, and 2) it has to completely wet the surfaces of the gap before its viscosity starts climbing.

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    $\begingroup$ I would want to say a bit about air pressure here, and mention that the forces associated with it are surprisingly large. $\endgroup$ – Andrew Steane Jan 24 at 18:09
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    $\begingroup$ When you mention "viscosity", do you also imply "surface tension"? My gut feeling for this question would be "air pressure + surface tension". Apparently, olive oil has 56 times the viscosity of water (see here). I really don't think the two plates would stick 56 times as strongly with olive oil than with water. $\endgroup$ – Eric Duminil Jan 24 at 21:22
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    $\begingroup$ @AndrewSteane, hello and happy new year. regarding the air pressure issue, note that for any real-world pair of (imperfect) plates, the air pressure in the (small) gap between them will be equal to ambient and for slow separation rates of the plates will remain so. fast separation will necessarily invoke the nonvanishing viscosity of the air and then you will get a pressure drop across the gap length, and you will indeed be fighting against ambient air pressure in this particular case to prise the plates apart. $\endgroup$ – niels nielsen Jan 24 at 21:31
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    $\begingroup$ @JanStuller say the plate area is $0.01\,{\rm m}^2$, then the force on each side from air is 1000 newtons. So to separate the plates it is crucial to get either air or water in between the plates. So the reason we need the water to gather into a blob (given that it is not itself stretchable) is to let the air come in: it is the air pressure between the plates which counteracts the pressure from outside. The force you exert yourself is negligible by comparison. $\endgroup$ – Andrew Steane Jan 25 at 16:30
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    $\begingroup$ Re @AndrewSteane's comment, I think you'll find the force of air pressure is much stronger than the force of viscosity. To demonstrate this, you could try to do the math on it, but much easier and more convincingly, you can just push laterally on your plates to separate them. They will slide apart far easier than if you try to pry them. $\endgroup$ – R. Barrett Jan 25 at 18:49
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The other answers here offer a lot of explanations for general cases in physics, but there is another factor that should be considered in your specific example: suction.

If you wash your dishes with hot water, then you will naturally heat up the plates in the process. After stacking your plates, the air trapped between them will absorb some of that heat as the plates settle, expand as per the ideal gas law, and push some of the air out into the surrounding atmosphere.

After several hours of cooling, the air trapped between the plates will shrink, exerting less pressure on the plates. At that point, the surrounding air will tend to push the plates together, similar to a suction cup.

The 'release' of the two plates is the same effect you see when opening a new jar of jam; the "popping" of the lid is caused by the spring action being released as air is able to re-pressurize the container. The low-pressure state is caused by packing the contents while hot, and allowing the cooling to "suck" the lid down, forming an air-tight seal which keeps the food fresh for years.

Notably, this is an easily testable theory: next time you wash your plates, run them under cold water for a short time before drying. Leave them for the same amount of time, then attempt to separate them. If the plates are easier to separate, then the suction from the shrinking air is a significant factor. If they are not, then the suction is not a significant factor (or the plates weren't cooled enough).

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    $\begingroup$ Are plates smooth enough that they avoid air intruding along irregularities? Jam Jars use deformable rubber to form a vacuum-seal against the glass, held down by the screw action of the metal lid. I can generate a vacuum seal using a bowl, a small plate, wet food and a microwave, but I'm uncertain if two warm plates would form such a seal. $\endgroup$ – Yakk Jan 25 at 16:52
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    $\begingroup$ @Yakk One could posit that condensation forms a seal along the inner edge of the rim. $\endgroup$ – Daron Jan 25 at 21:33
  • $\begingroup$ @Daron Water gets pushed by the air; it won't stand up to air pressure. Rubber can. The MW case above has relatively rapid cooling; the tiny gap between the plate and bowl can't keep up, and the top-plate deforms, so it is possible. I don't know if the much smaller volume of air between two plates could deform the top plate enough to form a similar seal. $\endgroup$ – Yakk Jan 25 at 21:47
  • $\begingroup$ @Yakk "water gets pushed by air" The air around a circular plate is pushing inward on all sides. It has no where to go. $\endgroup$ – JimmyJames Jan 26 at 16:23
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    $\begingroup$ @Daron I think it's likely that the entire gap between the plates is full of water. Ages ago when I was working as a dishwasher, if you stacked wet pizza pie pans, they would be almost impossible to get apart. The only hope was to get on edge up a small bit and then they would come apart immediately. $\endgroup$ – JimmyJames Jan 26 at 16:40
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They don't stick together for all liquids

If you were to put a liquid with a large wetting angle (such as Hg which "beads" up), the plates will be pushed apart. For a liquid such as water that tends to spread on a plate, the forces become very large at small separations.

The force depends on the surface tension of the liquid, the wetting angle at the plate, the volume of the liquid, and the separation of the plates.

This can be worked out from capillary theory with the calculus of variations:

Here is a paper that shows the capillary force between two plates as a function of how well the liquid "wets" the plates: https://www.sciencedirect.com/science/article/abs/pii/0001616088903288

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  • $\begingroup$ Thank you for the additional answer & insights. Just for my clarity: is "adhesion of water molecules to the plate surface" the same thing as "surface tension" in this context? Because surface tension is usually described as "The property of the surface of a liquid that allows it to resist an external force, due to the cohesive nature of its molecules." So I am not sure whether "surface tension" in this context refers to the resistance of the water molecules due to their adhesion to each other, or their adhesion to each other and also the surface of the plates ? $\endgroup$ – Jan Stuller Jan 26 at 11:09
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    $\begingroup$ Thank you for your kind words. Surface tension is the energy associated with surface area. It is the (practically) work that is done to increase surface area of a fluid. In the case of plates, there are three surface tensions that matter: the one between the liquid and the plate, the liquid and the air, the air and the plate. Surface tension is a macroscopic quantity: its microscopic origins are in the bonding energies near the surfaces, and their entropies. In other words, we measure the force with equipment that averages over many molecular interactions. $\endgroup$ – Craig Carter Jan 26 at 12:00
  • $\begingroup$ Thank you. So I gather from your answer that "Surface tension" in this context would refer to the work required to "to retract the thin film of water into a blob in the center of the plate stack" + eventually separate the water molecules in this blob from the plate surfaces. Am I understanding this correctly? PS: I spent one year at MIT (2015-2016, I did Master of Finance at Sloan, but I took 24 graduate units of course 6: (6.436 & 6.265): I'd say that it was easily one of the best years of my life :). Great place for curious minds :) $\endgroup$ – Jan Stuller Jan 26 at 12:08
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    $\begingroup$ Very close: the work would be the surface tensions multiplied by the total change in the surface areas. (In my experience, students tend to like MIT, but only after they’ve been away for a few years...) $\endgroup$ – Craig Carter Jan 26 at 12:12
  • $\begingroup$ I loved every day whilst I was there (perhaps because I knew it'd only last one year), even the P-set struggles :). And I love the memories still. $\endgroup$ – Jan Stuller Jan 26 at 12:22
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This process is apparently called wringing. From Wikipedia:

Because of their ultraflat surfaces, when wrung, gauge blocks adhere to each other tightly. Properly wrung blocks may withstand a 300 N (67 lbf) pull. While the exact mechanism that causes wringing is unknown, it is believed to be a combination of:

  • Air pressure applies pressure between the blocks because the air is squeezed out of the joint
  • Surface tension from oil and water vapor that is present between the blocks
  • Molecular attraction that occurs when two very flat surfaces are brought into contact; this force causes gauge blocks to adhere even without surface lubricants, and in a vacuum

It is believed that the last two sources are the most significant. There is no magnetism involved.

Note that this theory applies to extremely flat surfaces ("The minimum conditions for wringability are a surface finish of 1 microinch (0.025 μm)").

In case of less perfect objects (e.g. dinner plates), the two first sources (air pressure & surface tension) will be the most significant.

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    $\begingroup$ No, this isn't wringing since that requires ultraflat surfaces, which isn't the case for plates. In a normal home I don't think there is anything that is flat enough for wringing, remember that we talk about flat on a molecular scale. Per the wikipedia article "The minimum conditions for wringability are a surface finish of 1 microinch (0.025 μm) AA or better, and a flatness of at least 5 μin (0.13 μm)" $\endgroup$ – Polygorial Jan 24 at 23:25
  • $\begingroup$ @Polygorial thanks for the correct observation. Could that mean that the 3 above reasons are still valid, just with different relative importances? The third one is probably close to 0% for less than perfect plates. $\endgroup$ – Eric Duminil Jan 25 at 2:25
  • $\begingroup$ Cody's Lab tested the first bullet point $\endgroup$ – noslenkwah Jan 25 at 14:48
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    $\begingroup$ I've noticed this effect with a glass cutting board (its rubber feet have all fallen off) on a linoleum counter. After rinsing it, it slides easily, but it's hard to lift. $\endgroup$ – Barmar Jan 25 at 15:51
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    $\begingroup$ @EricDuminil - He found no evidence that suction plays any role in keeping the blocks together. If there is indeed a suction force acting, but not detected in his experiment, it is certainly not the dominant force keeping them together. $\endgroup$ – noslenkwah Jan 25 at 23:31

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