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When I cook spaghetti, they never tangle themselves so much to form knots, neither when in the boiling water nor when they're mixed with sauce.

Why is this so?

I experience this behaviour both with durum wheat flour spaghetti (stiffer and higher diameter, 2 mm when cooked) and rice noodles (thinner, 1mm when cooked, and more flexible). The length is the same, about 25 cm.

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    $\begingroup$ Is spaghetti flexible to knot even if you tried to on your own? Off the top of my head, I think it would rip before you could tie a knot. Then how could it knot spontaneously, if you can't even knot it purposely. Perhaps spaghetti arrives at configurations which could form a knot, but slip out of it—since it is unwilling to bend enough to ``secure'' the knot. This is my first thought, liked to hear back if you've ever tried—or will try. $\endgroup$
    – Novice C
    Mar 21, 2016 at 0:53
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    $\begingroup$ Friction, reptation, and breaking. Spaghetti tends to tangle more easily after it dries out (though actual knots are still rare), so are you asking about why friction is lower when spaghetti is wet? $\endgroup$
    – TLDR
    Mar 21, 2016 at 0:54
  • $\begingroup$ @NoviceC Yes, spaghetti are flexible enough to be "knottable" - I could tie a knot with them using my hands $\endgroup$
    – Marco
    Mar 21, 2016 at 0:56
  • $\begingroup$ @Couchyam No, I'm not asking why friction is lower when spaghetti are wet (it's pretty obvious to me that being wet implies less friction). What I'm wondering is, why I don't see spaghetti making knots, given that the low friction and the high flexibility wouldn't prevent it. $\endgroup$
    – Marco
    Mar 21, 2016 at 1:02

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One reason you might expect to see few if any 'knots' in a pot of cooking noodles is that without external stirring (and assuming the noodles are dilute), the motion of each noodle strand is determined only by currents of the boiling water. Since noodle strands are relatively massive and aren't very stretchy, the response of the noodle to changes in the flow field can be quite slow. The velocity profile of boiling water tends to form cycles that transport heat from the region nearest to the stove up to the surface. These cycles might cause groups of noodles to twist around each other, but couldn't carry any individual noodles into a knotted configuration. On smaller scales (of order the persistence length), fluctuations in the velocity profile would tend to cancel over extended segments of noodle. However, if you also stir the noodles directly, then you can artificially make knots with long spaghetti strands (and maybe measure how long they persist). For a dilute strand, I would expect the lifetime of simple knots to depend strongly on how long the spaghetti has been cooked. As mentioned in the comments, the stiffness of spaghetti will tend to favor the elimination of curvature over time. Once the total curvature in the spaghetti gets below a certain threshold, it is impossible for knots to exist. A simple threshold value for total curvature is given by the total curvature of a circle (or more accurately, a closed loop with a single fold defect, that acts like a hinge). You can analytically estimate the lifetime of a spaghetti knot by solving for the flow of curvature density along the spaghetti as a function of time, with local sources that represent the effect of the fluid flow. Very roughly, I would expect this to be similar to a diffusion equation with a continuous source, representing the twisting motion of the boiling fluid.

Now that we've discussed the behavior of a single noodle in response to the flow field generated by boiling water, let's consider the effect of many-noodle interactions. At high densities, interactions between noodles become important (and the effect of noodles on the velocity field). When the separation between noodles is of order the persistence length, one might expect the noodles to behave somewhat like a liquid crystal, favoring alignment between adjacent strands. You can then group together clusters of parallel noodles, and think of each cluster as an "effective noodle" on larger scales. In the rescaled system, there is some distribution of binding stiffness among effective noodles, but it's reasonable to expect a longer effective persistence length than before on average. "Effective noodles" can be grouped together again, leading to "effective effective noodles" at even larger scales. If the order persists up to the scale of the typical noodle length, then knotting will knot occur spontaneously. However, if you tied a spaghetti strand in a knot and placed it in a dense pile, then many-spaghetti interactions will cause the knot to have a longer life-time than it would have in the dilute phase. The rate at which curvature density 'diffuses' along a preknotted noodle is controlled by the friction, inertia, and density of neighboring strands.

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