Fishy Spaghetti Explanation

Cecil's Columns/Staff Reports
101

But all of this just invites the question: How is toothpaste squeezed out of a tube? What’s happening at the molecular level?

Well, in the toothpaste case, the tube is filled with a single substance, there’s only room for a certain amount of said substance, and when you squeeze the tube, there’s room for less of the substance, so all the molecules making up the substance pushing against each other and against the walls of the tube tend to push some of the substance’s molecules out of the tube. Easy squeezy.

Now what about the Spaghetti case? To give the parallel answer would have to entail saying that the molecules of spaghetti and air are, together, pushing some spaghetti molecules out of the higher-pressure area. (And the rest of the spaghetti gets dragged along with it.)

Okay, but, this doesn’t answer the question Cecil is addressing in his column! Of course some combination of molecules of air and spaghetti are doing something which adds up to the movement we’re discussing. The question is, how that happens at the molecular level. In the toothpaste case, it’s easy to imagine. There’s a single substance, no relevant internal structure to it. But it’s not easy to imagine in the spaghetti case. There are two substances, with a boundary between them. What are the molecules of air doing to the molecules of spaghetti? When the spaghettie molecules right at the mouth are pushed into the mouth, are they pushed by air molecules, by spaghetti molecules, or both? How are they so pushed? If they are pushed by spaghetti molecules, where does the kinetic energy mouthwards of the pushing spaghetti molecules come from, if the pressure on most of the spaghetti is directed perpendicular to its surface rather than directed mouthwards? If the spaghetti molecules near the mouth are pushed by the air, then where does this kinetic energy mouthwards comefrom, considering that all of the air, whatever its pressure, is nevertheless just as likely to push in one direction as it is another? If the spaghetti molecules near the mouth are pushed by both air and spaghetti, then we just have both problems to solve.

Thinking about it like a toothpaste tube is helpful, probably, but I haven’t figured out how it helps. The differences between the toothpaste situation and the spaghetti situation confound my intuitions, and the very point of Cecil’s colomn was to attempt to address these very confounded intuitions. The toothpaste analogy fails to address those confounded intuitions.

-FrL-

102

Frylock, I think it goes something like this:

  • The air pushes the atoms of spaghetti closer towards the central axis of the spaghetti strand
  • When the spaghetti atoms are closer together they repel and try to spread back out, but this spreading back out is impeded by the continued pressure of the air molecules, except in the direction of the mouth where there are fewer air molecules.
  • So now they spread out towards the mouth, giving the strand an overall momentum towards the mouth. Eventually their kinetic energy carries the spreading too far, and they pull back together. But they pull back together while maintaining this overall mouthward momentum – that is, the strand shrinks in the direction of the mouth.

The key I think is that the bonds between spaghetti particles work sort of like springs – there’s a natural (equilibrium) separation between them, and if they get too far apart they pull back together, and if they get too close together they push further apart. This is true of any rigid solid I think – that’s why solids maintain their shape.

Under the pressure of squeezing I think toothpaste is more like a high-viscosity liquid. That is, the particles of toothpaste can actually move relative to each other without being snapped back to their equilibrium position, which is why the overall shape of the toothpaste changes, whereas the overall shape of the spaghetti does not (it stretches and squishes a little, but in the end it’s still shaped like the strand you started with).

103

Frylock, I will assume you’ve read my very first post; post number 5. If you haven’t, go back and read it.

Now, what air pressure does is create an internal stress within an object. Everywhere within an object. Think of a little cube, sitting out in the atmosphere. It’s got air pressure on top and bottom, so it’s being squashed in that direction. It’s also got pressure on left and right, and on back and front, so it’s being squashed in all directions.

Moreover, all that stress is being transmitted everywhere within the object. That means every molecule is pushing against its neighbors, equally in every direction. Or, to put it another way, the molecules of spaghetti are pushing at each other just as hard as the molecules of air are pushing on the spaghetti, in every direction.

And that means that the “pressure” force near your lips is the same, whether you have a long piece of spaghetti there, or a very short stubby one.

And, if you “suck”, the air pressure in your mouth decreases; so do the internal stresses in the spaghetti in your mouth; so does the “pressure” force near you lips on the inside. The larger force on the outside remains, and drives the spaghetti inwards.

*****************’
The toothpaste analogy may or may not be helpful; it’s just another way of showing how external air pressure turns into internal stress. If you find in confusing, ignore it. Not all analogies work for everyone.

Speaking of which, the energy issue is probably something of a red herring. The energy driving the spaghetti clearly comes from somewhere, but it starts with your cheeks, which pump air out of your mouth, which creates an opportunity for the potential energy in the air to convert into kinetic energy of the spaghetti, blah blah blah, but I suspect that’s more confusing to look at it that way than just balance the forces.

104

Maybe the toothpaste analogy works for some people, but the thing I don’t like about it is that the toothpaste undergoes a permanent change in its shape, whereas the spaghetti only undergoes temporary changes in its shape. (Of course it can bend, but I’m talking about stretching/squishing)

The idea that internal stresses are important is a good one, but like Cecil I initially dismissed the toothpaste analogy as irrelevant because spaghetti is more rigid than toothpaste, and because you can suck even more rigid objects like uncooked spaghetti.

Understanding that it’s an oscillatory stretching/squishing rather than a permanent distortion, it makes sense for rigid objects. With more rigid objects I think you’d just get a smaller amplitude of stetching/squishing oscillations, but with a higher frequency. So they’re still very suckable.

105

Same here. Your last post seemed plausible though–I try to think of the spaghetti as repeatedly stretching and springing back into shape.

-FrL-

106

I apologize if someone has covered this already, but I didn’t see any answer to zut’s question “how wide is area contributing most of the spaghetti-moving force?”.

I believe if you looked at it on a statistical molecular level, it would be on the order of the distance an average air molecule moves before striking another. The force would be greatest at the lips and decrease rapidly.

The idea that the air pressure is normal to the surface everywhere applies only at a macroscopic level.

107

At some particular time, one tiny piece of surface might get hit in one direction or another. But if each are equally likely, I’d think that averaged over time the force on even a microscopic piece of the surface is normal to the surface.

Anyway, the spacing between air molecules is on the order of nanometers at standard temperature and pressure, isn’t it? Even if there were a piece on that scale where the force wasn’t directed normal to the surface, I don’t think it would contribute significantly to the velocity of the strand.

I’m sticking with the idea that the motion is due to microscopic stretching and shrinking of the spaghetti due to the unequal pressure on the strand.

108

Oops, you’re absolutely correct, and furthermore, it’s explainable mathematically by perpendicular pressure vectors integrated over the surface (and the internal stresses induced by this).

Yes, I think you’re right.

109

Can someone tell Cecil to print a correction?

10 years after the fact, I know, but still…

-FrL-

110

I actually sent Cecil an e-mail a day or so ago basically summarizing the conclusions we’d come to in this thread. We’ll see if it leads to a correction…

111

I should point out that the intent of this question (which was never actually realized, but no matter) was to point out the implications of suggesting that the spaghetti was propelled by some statistically non-cancelled “sideways” pressure very near the lips. For example, if the area really was “on the order of the distance an average air molecule moves before striking another,” that’s only about 70 nm, which gives a very small area: not enough area to develop the required force. (What tim said, in other words)

Well, the poor quality of this answer has been noted before. Don’t hold your breath.

That’s actually pretty accurate, but the oscillatory nature isn’t really necessary to explain the spaghetti motion.

112

Yes, and after reflection I think I was wrong about that too; if anything the distance would probably have to be closer to the radius of a single molecule (i.e. the spaghetti molecules “touching” the lips would only be hit by air molecules from one side, in a simplified model).

113

I expect that the spaghetti surface molecules “most responsible for motion” are those that fall on (or near?) the intersection of the spaghetti surface with a cylinder formed by the lips and perpendicular to them.

114

Which gets us back to the beginning!

Y’know, I’m still a bit dissatisfied. The noodle case still seems fundamentally unlike that of a solid rod (piston) or of a liquid.
How about this:

[ul]
[li]Air pressure exerts a (normal!) force that compresses the noodle outside the mouth.[/li]
[li]The lack of air pressure inside the mouth permits a corresponding expansion of the noodle inside the mouth, relative to the part that is outside.[/li]
[li]So the expanding “shoulder” of the noodle around the inside of the lips is what actually pulls it in, the way an octopus pulls itself through a hole that seems much too small.[/li][/ul]

In this model, all the compressive energy required to suck the noodle is released as the shoulder expands. Fully expanded noodle farther inside the mouth does no work. It just lies there–it’s obviously not helping to pull any more in.

So it seems to make sense that the outside air molecules that matter most work against an area of noodle equal to and opposite the “shoulder” on the inside. All the other outside molecules simply back up those happy few who get to shove noodle into the breach, as it were.

This explanation allows the noodle to be considered distinctly different from, say, a hardened steel rod. Any minute compression/expansion differential in a solid object is probably much less effective than the simple piston force across its opposing faces. But, conveniently, a solid rod has opposing faces, while a noodle really, honestly speaking, does not.

The analogy to toothpaste also falls down in this case. But, as somebody mentioned already, toothpaste is fluid and/or inelastic and not really analogous to a noodle.

On the other hand, perhaps you could take the view that the noodle behaves like a solid near the lips, as far as its stiffness allows it to behave like a piston, and behaves like a liquid farther away, where air pressure pushes it up through the “straw” of its own surface tension.

And I thought this thread had run out. Oh well.

115

On the one hand, “surface molecules most responsible for motion” is somewhat meaningless, because you’re talking about hydrostatic air pressure which exists verywhere on the surface of the spaghetti, and the overall motion (or lack therof) is due to the sum of all the forces. Ignoring that, though, remember that pressure acts perpendicularly to the surface; it’s not exactly clear whether you are agreeing with that or proposing some form of “tangential pressure.”

I refer you back to my original post in this thread. If you look at a small section of spaghetti right at the entrance to the mouth, it has a larger force on it outside the mouth than it does inside. An unbalanced force causes acceleration. Acceleration causes motion.

Speculation about diameter increase is all well and good, but why is it even necessary?

116

For my own part, I want to know where the force is, and what it’s made of.

-FrL-

117

It’s throughout the spaghetti, and not really made of anything–it’s an intangible force. If you have specific followup questions, I’d be happy to answer them.

118

I think the part that makes myself and others uncomfortable is that, for a noodle, a force in one direction seems to produce acceleration in a different direction. Otherwise it really looks like you’re pushing on a rope.

There’s a pretty clear connection in the case of a solid object, or liquid sucked through a straw. But for the noodle case, I’m not good enough with math to find comfort in Maxwell’s equations, if they even apply. I turned to diameter change seeking a simple explanation that I can understand without resorting to either faith or hard work.

With the caveat, of course, that complex problems have simple, easy-to-understand, wrong answers.

119

Absolutely I’m agreeing with that; no tangential pressure necessary. The model(s) I’m proposing are thus:

  1. Simple model: the contribution from a patch of spaghetti surface falling on the intersection I spoke of in the quote above is equal to (air pressure)*cos(theta)dA where theta is the angle between the spaghetti surface and the plane tangential induced by the mouth hole opening.
  2. More complex model: as above, but blurring of the edges of the area of contribution due to inter-spaghetti-molecule-elasticity.
120

Or better, …sin(theta)…, where theta is the angle between the spaghetti surface and the axis of the cylinder I described earlier.