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Prince Rupert's Drops are glass objects created by dripping molten glass into cold water. While the outside of the drop quickly cools, the inside remains hot for a longer time. When it eventually cools, it shrinks, setting up very large compressive stresses on the surface.

courtesy of wikipedia

The result is a sort of toughened glass: you can hammer the drop head without damaging it, but a scratch on the tail leads to an explosive disintegration. Check out this video.

So, is it possible to build spherical Prince Rupert's drops? And if so, how? One example of an application is as a replacement for traditional ball bearing spheres. There will be improvements in wear resistance and maximum loads tolerable, and a glass sphere would cost less anyway.

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    $\begingroup$ I really wonder about effects of releasing one in freefall (no gravity) and then immersing it in water rapidly. $\endgroup$ – SF. Jan 26 '15 at 8:38
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    $\begingroup$ What would happen if, after forming the drop and letting it cool, you were to heat and melt away the tail - similar to how glass blowers finish pieces by melting away break marks. Would the change in internal tension cause it to shatter as if you'd broken the tail, or would it behave differently due to the relatively slow change in tension caused by heating rather than snapping it? $\endgroup$ – Tom Jun 7 '15 at 17:37
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    $\begingroup$ @SF: Without gravity, there is no freefall, and after releasing the object would just stay in place. $\endgroup$ – Olin Lathrop Jun 26 '15 at 20:07
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    $\begingroup$ @Tom: The glass within the tail of a PR drop is subject to a combination of tensile and sheer forces. Past some point on the tail the shear strength of the glass would be sufficient by itself to withstand the tensile forces, so melting away glass beyond that would likely have no effect. Closer to the head than that, the part of the glass which was no longer being pulled from the tail side would have insufficient shear strength to resist the pull from the head. As soon as one part near the outside fails, portions toward the head where the tension exceeds sheer strength by... $\endgroup$ – supercat Jan 1 '17 at 21:20
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    $\begingroup$ ...an even larger amount would also fail essentially instantly, causing the entire piece to explode. $\endgroup$ – supercat Jan 1 '17 at 21:22
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Prince Rupert's drops are an example of a tempered silica glass component: its surface has been cooled more rapidly than its interior. Tempering of glasses is important because it lends toughness to the glass, i.e. an ability to resist fracture under load, which explains why a drop can be hit with a hammer and survive. Silica glass, as is common with other ceramic materials, exhibits unstable crack propagation when its fracture strength is exceeded by its stress state. Unlike with most alloys, ceramics exhibit very little, or no, plastic deformation. When they reach their elastic limit they fracture. So if you stress a silica glass component too hard, it fractures rapidly and all at once.

A glass component may be tempered by cooling its exterior more rapidly than its interior so that there is a non-uniform residual stress distribution in the component. Specifically, because the exterior solidifies first, its density increases and volume decreases first, drawing material outward from the interior. Then, as the interior solidifies with less remaining material, it pulls inward on the exterior. The resulting stress state is tension in the interior and compression in the exterior.

Cracks only propagate when there is a tensile stress across the crack. If there is a residual compressive stress across the crack, it will remain closed unless stressed in tension. Because the compressive stress must be overcome before the crack opens, it takes a greater tensile stress to propagate a crack through a tempered glass component than an un-tempered component. If such a crack propagated past the neutral-stress surface between the exterior and interior of the component, the crack tip would be in tension due to the residual stress state of the interior. Such a crack would begin propagating in an unstable fashion as all of the residual stresses are released, resulting in an explosion of glass shards, as they all undergo elastic recovery from the non-uniform stress distribution.

From all of this, it should be apparent that a "perfectly" spherical, tempered glass component is theoretically possible, as it is only required that the exterior of the glass cools more rapidly than the interior to obtain the required non-uniform stress distribution, while maintaining the desired shape. A combination of gravity and viscosity are the cause of the tail in a traditional Prince Rupert's drop. Therefore, removing each of those components, such as with a drop formed in free-fall by free-surface surface-tension relaxation of a "floating" blob of glass, can result in a sphere of viscous glass. Relaxation may take a long time and the glass must be kept viscous the entire time. The next step is cooling the sphere rapidly without disturbing its shape, which is admittedly difficult. Spraying it with fluids would cause ripples in the surface, and submersion would require moving it infinitesimally slowly, which would cause the wrong kind of non-uniform stress distribution. Exposing it to the vacuum of space might be sufficient, but I haven't done any calculations of the radiated heat loss.

The desired setup would likely be a radiation oven in the vacuum of space, with a blob of glass floating in it, with no relative velocity. The oven melts the glass, which relaxes into a sphere. The oven is turned off, the door is opened and the oven moves rapidly away from the sphere. The sphere emits radiation, cooling the surface more rapidly than the interior (or so we hope), and the glass is tempered, resulting in a Prince Rupert's Space Drop.

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    $\begingroup$ A key aspect of tempering glass is that the mass of glass inside a tempered portion of a piece must be smaller than if the piece was simply annealed. In PR drop, when the outside of the big part of the drop contracts, the tail will provide a path by which molten glass can flow out; the tail will then solidify before the inside of the drop, thus preventing the glass from flowing back in as the drop cools. If one were to heat all the glass well above the annealing point, quickly cool the exterior to the just above the annealing point, moderately quickly cool it to just below... $\endgroup$ – supercat Jan 1 '17 at 21:11
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    $\begingroup$ ...the annealing point, and then cooled it from there relatively slowly so as to prevent the glass from cracking, one could end up with glass that was somewhat tempered, but not as strong as a Prince Pupert's drop since the cooling exterior wouldn't be able to "squeeze out" glass from the interior. $\endgroup$ – supercat Jan 1 '17 at 21:13
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    $\begingroup$ I am a bit sceptical about your vacuum hypothesis. I think even in glass, heat transfer by convection beats heat transfer by radiation. $\endgroup$ – Tomáš Zato Jun 21 at 13:02
  • $\begingroup$ An interesting point. In microgravity, if we assume the glass is allowed to reach thermal equilibrium with the oven, then the driving force for convection would have be a radial pressure gradient. It would all hinge on how fast an outer shell of highly viscous glass would form due to radiation, compared with the formation of convective flows. I imagine that would be entirely dominated by the size of the drop. Larger drops would have time for convective flows to set up (like with the iron catastrophe in the Earth's formation), smaller drops perhaps not as much. I wish I had time to model it! $\endgroup$ – wwarriner Jun 21 at 17:47
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I think the tail forms as a result of how the glass is dropped. In the video, the molten glass separates from the rest of the lump and stretches - like Silly Putty or molten mozzarella cheese. I expect that you could at least shorten the tail by cutting the gooey glass - but there's a possibility that the result would explode on cooling, as suggested in nivag's comment.

Sufficiently spherical glass balls would be pretty difficult. Maybe it could be done using the shot tower concept, or some kind of molding method.

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It was stated previously that a "perfect" sphere cannot exist in terms of engineering or manufacturing, but ignoring trivialities, let's answer the question. A Prince Rupert's drop is such that molten glass is viscous enough to droop off your rod and into a bucket of water, causing the glass to cool rapidly enough to create high amounts of internal tension, which causes the famed effect of making an unbreakable teardrop.

Even if you were to spin the rod quickly so as to not have a long tail, some thin dragging would still exist and make a tail. It may be small, but it would still be there. If you were interested in making it more spherical, you might think to shave off the tail end, but as you know, a single nick or disturbance to the tail end results in a solid glass explosion.

Let's say you spun the rod in a way (in a magical world) so that there was no tail. Then you wouldn't have a Prince Rupert's drop!

The answer to your question is no, it is not possible to make a spherical Prince Rupert's drop because either the glass would explode, or you simple don't have the drop you were looking for.

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What about this. Create the drop as usual, but use the hottest water you can in order to slow the creation of the stresses which of course will still occur. Here's the critical step...... decrease the depth of the water with experimentation and finally, release the drop right at the water surface which should, to some extent, reduce the length of the tail or practically eliminate it. The drop will fall at a much reduced rate considering the semi-weightless condition in the water. Another thing to consider would be to snip the drop just before it drops. By snipping the drop just before it drops, the tail, which cools much quicker than the head, is practically eliminated and so the head with its internal stresses are not threatened by the brittle tail.

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    $\begingroup$ Actually, the tail forms in the air before the drop hits the water. $\endgroup$ – Timothy Aug 5 '16 at 14:06
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Perhaps you could form a spheroid of molten glass in free fall, then quench it with a cold gas.

I suggest a cold gas instead of a liquid because you can't "drop" it into a liquid in free fall, and splashing it with a liquid rapidly enough to quick-freeze the exterior would probably involve asymmetric forces that would distort the sphere, whereas a gas would exert equal pressure on all sides. It would have to be some very cold gas! I don't know whether a heavy gas like argon increase thermal conduction, or something like hydrogen or helium might work better.

The tail doesn't seem like a necessary feature. Seems to me it's formed before the quench by the viscosity of the dripping glass, not the passage through the water. The tail isn't rapidly extruded from the blob of rapidly cooling glass; it's already present, formed by gravitation / stretching before the quench, and just cools in that tail shape.

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    $\begingroup$ lead balls are made with this techniqe. $\endgroup$ – joojaa Jun 28 '15 at 5:44
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It's not a perfect sphere but as close as I've gotten.

Suspend in heated jet, then drop. Done.

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You have to control the temperate carefully, too hot and it flies apart.

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    $\begingroup$ Can you describe how it behaves compared to a typical drop with a long tail? Can you show any images or video of the end result? $\endgroup$ – Air Aug 18 '15 at 23:27
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Well forget the "perfect" sphere, but I don't see why it couldn't be made in any shape. You just have to cool the outside fast. I seem to recall that pyrex is made this way, with built in stresses.. but I couldn't find a link. This may be helpful.

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    $\begingroup$ well "perfect" as in "suitable for ball bearings". My doubts come from the tail, that seems to be a key component, and seem not to be avoidable. $\endgroup$ – Vladimir Cravero Jan 21 '15 at 17:52
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    $\begingroup$ I see you are in Italy, here in the US McMaster-Carr lists a number of glass balls, some in ball bearings, some made out of Silicon Nitride ceramic. There should be something similar where you are. (The tail is just from how it's made... for a sphere you'd need a mold or something.) $\endgroup$ – George Herold Jan 21 '15 at 18:04
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After the outside of a Prince Rupert drop solidifies, it will quickly contract. During this process, if there is nowhere for the glass inside to go this will cause the outside to be under significant tension, virtually guaranteeing that it will crack (crackle-glass is formed by quenching an entire glass piece briefly; the exterior layer will crack immediately, but if all the cracked glass pieces are in contact with glass that is still molten the overall piece will remain intact). While it's possible to cool glass slowly enough to prevent cracking, reducing the peak tensile load sufficiently to prevent cracking will also reduce the amount by which such a load can be shifted toward being compressive.

This difficulty may be overcome by lowering the glass relatively slowly into the water (the tail is still attached to the rod from which it came). Doing this will mean that while part of the outside of the glass has solidified and is contracting, the liquid glass in the middle will, during most of this contraction, have a continuous path of liquid glass which extends out of the water.

At some point the glass entering the water will be so thin that it's no longer possible for liquid glass to flow through the center, but by the time that happens the larger portions of the glass will have contracted almost as much as they're going to, so the amount of liquid glass that would still need to be displaced to avoid creating tension will be pretty small, and so the amount of tension created by an inability to displace any more liquid glass from the interior will be likewise small. If the region of the glass which is thick enough to allow liquid flow through the center overlaps the region that's thin enough to avoid breaking when it cools, the drop may be cooled to room temperature without premature failure. A uniform spherical blob, however, would have nowhere to displace the interior liquid to avoid having the pressure of that liquid fracture the exterior.

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No tail in zero gravity. As long as the material is maintained in a heated environment you would have a "near perfect" sphere as long as pressure and temperature and absence of gravity is constant. Cooling would result in similar uniform stresses to the Rupert"s Drop although the effect of the tail would be missing. Any distortion would result in a "flaw" and impact the uniform stress and the Rupert's Drop effect would not exist. In a perfect idea, you'd end up with a "yourname" sphere.

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protected by hazzey Sep 29 '15 at 1:44

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