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I have noticed a chain-like shape when milk is poured from a height into a cup.

The chain pattern repeats itself after some distance till it reaches the milk in the cup.

Any reason behind this? enter image description here

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  • $\begingroup$ Sorry: I can't resist saying this: of course there's a reason: it's encoded in the Navier-Stokes equations! Now that we've gotten that lame one out of the way, hopefully someone will give you a more helpful answer to this wonderful question. $\endgroup$ – Selene Routley May 23 '15 at 10:31
  • $\begingroup$ @iappmaker See physics.stackexchange.com/a/512344/155230 $\endgroup$ – AlphaLife Nov 8 '19 at 6:14
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    $\begingroup$ @ACuriousMind♦ This question is not a duplicate due to the reasons mentioned in the meta post below. $\endgroup$ – AlphaLife Nov 10 '19 at 7:45
  • $\begingroup$ physics.meta.stackexchange.com/a/12509 $\endgroup$ – AlphaLife Nov 10 '19 at 7:46
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    $\begingroup$ @EmilioPisanty Yes, I completely agree that they look similar; but they are not same! Chain formations and helical pattern formations are due to two different concepts; physics.meta.stackexchange.com/q/12508/155230 $\endgroup$ – AlphaLife Nov 12 '19 at 17:20
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My understanding is this. I invite a discussion on this answer.

While pouring the milk from the glass, Lets say "N" milk-molecules is reaching the air in the open space say "S". As the milk is more viscous fluid the milk-molecules are interested in coming as close to each other and hence it converges and hence the space in which the milk travels is reduced from "S" to "S1".

Though the space reduced from "S" to "S1" the volume of milk-molecules "N" which is getting out of Glass is going to remain same. Now the volume is same but the space for travel is reduced to "S1" hence the milk-molecules which is continuously coming out of glass tries to find the alternate way to travel. Thus it reaches (bulges in) the left and right side of the path. This is the new PATH-2. Now the milk-molecules which has come in PATH-2 has to undergo the same concept.

The above concept repeats and hence the chain like shape.

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The shape of the spout of your milk jug makes the milk from the edges flow towards the center - but as this means that the profile is trying to get narrower, the milk "has to go somewhere" and makes the jet wider in the other direction. However, surface tension is pulling back on the liquid (it would prefer the jet to be a perfect circle) so the liquid starts to be forced back. This can in principle happen a couple of times before instability tears the liquid apart.

This is a form of Rayleigh Instability - see for example this diagram:

enter image description here

from the corresponding wikipedia page

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  • $\begingroup$ Floris, I have seen the same effect while pouring the milk from different glass with different spout. Hence the effect is not because of the mouth of the glass. $\endgroup$ – iappmaker Apr 20 '15 at 4:17
  • $\begingroup$ My understanding is that the Plateu-Rayleigh-Taylor Instability explains why this pattern develops in a perfectly axial/azimuthal flow in a cylinder of water which moves with constant velocity and has no radial flows. It arises in delicate conditions. However I think the radial flows imparted at the lip of the container and the acceleration of the liquid as it falls, causing the column of water to narrow (continuity equation), make the PRTI effect redundant as an explanation here. $\endgroup$ – sammy gerbil Jan 11 '20 at 19:38

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