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In the book "Vectors, Tensors, and the Basic Equations of Fluid Mechanics" by Rutherford Aris I read the following:

If the fluid is such that the torques within it arise only as the moments of direct forces we shall call it nonpolar. A polar fluid is one that is capable of transmitting stress couples and being subjected to body torques, as in polyatomic and certain non-Newtonian fluids.

Can someone help me understand this? Say by giving me another definition of polar and nonpolar fluids.


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I would say that the use of "polar" in this book is not common to most scientists today, and that under this definition you may safely assume that in almost all circumstances you are dealing with a 'NONpolar' fluid. –  Greg P Dec 30 '10 at 3:31
This use of "polar" is not "uncommon", its simply scandalous! Misusing a established wording is a sign of narrow-mindedness of the writer. –  Georg May 23 '11 at 8:51
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4 Answers

A polar fluid is just a fluid where the constituent molecules have a polarization -- it could be a fluid of molecules that have a magnetic spin moment, or something like H2O where each individual molecule has a nonzero electric dipole -- and at the macroscopic level, as you average over all of the microscopic moments, you get a net polarization for the whole fluid.

I'm no expert on fluid mechanics, but I imagine the polarization somehow couples to the stress tensor in a way that generates torques in whatever equations of motion the author is interested in.

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This is certainly what most people understand by polar vs. nonpolar fluid (i.e. water is polar an oil is non-polar). But it is not clear to me that the author of the book is talking about the same thing. –  Greg P Dec 30 '10 at 2:34
In fact, from looking at this book on Google Books, I am fairly certain that the author is not talking about the usual distinction between polar and non-polar fluids familiar, say, to chemists. On page 123 he says that polar fluids have an asymmetric stress tensor. I don't know of an example of this, but I don't think it applies to a classic polar fluid such as water! –  Greg P Dec 30 '10 at 3:22
I haven't got to pg.123 yet, but one gets the feeling that these are standard terms from the way the author uses them. I also don't think that water should be considered polar, so this is not the usual distinction between polar and non-polar fluids that chemists use. –  becko Dec 30 '10 at 5:47
On the other hand, I think it has to do with the fact that the molecules can store angular momentum internally that doesn't show up macroscopically. But I'm not sure. A confirmation would be helpful. –  becko Dec 30 '10 at 5:49
I think the problem with water is that while water molecules are polar, a macroscopic amount of water will not have a spontaneous polarization, since all of the dipoles are randomly oriented. It's possible what the author means is something like a ferromagnetic or ferroelectric fluid, that is spontaneously polarized. –  wsc Dec 30 '10 at 6:12
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It is about the stress tensor; it is almost always assumed that it is symmetric to satisfy angular momentum conservation. Yet, there are some fluids capable of creating rotation from squeezing (like those spintops with pistons) and thus have some antisymmetric part in their stress tensors.
Aris just calls those fluids polar, what is pretty correct but makes confusion with electromagnetic properties -- I believe that "fluid with non-symmetric stress" or "couple stress" are better keywords.

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Can you elaborate on "those spintops with pistons"? Are they a real thing or a weird model? ;-) –  Greg P Dec 30 '10 at 15:18
@GregP After consulting Wikipedia I think I should have written spintops with augers. But this is a real toy. –  mbq Dec 30 '10 at 18:01
what page in wikipedia? can you give a link? –  becko Dec 30 '10 at 18:10
en.wikipedia.org/wiki/Top –  mbq Dec 30 '10 at 18:29
I always though that having antisymmetric tensor for a fluid means the fluid have some inner (molecular) angular momentum. That is though the liquid doesn't move it can have an angular momentum. Is this right? BTW having an antisymmetric tensor and linear material equations leads to the notion of the third viscosity. –  Yrogirg Aug 15 '12 at 13:24
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This is an old Post, but no, water is not a polar fluid. What the author means is that the fluid stress tensor is anisotropic, as was pointed out earlier.

Take for example the classical description of a fluid, under any shear stress the material must continually flow or deform. A polar fluid does not behave this way, it can withstand shear stress. A number of fluids do behave this way, viscoelastic and bingham plastic fluids can withstand shear stress. Cement paste, for example, which is typically a Bingham plastic must first reach a yield stress before it will flow.

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Aris' use of polar is broader than the chemical/electromagnetic usage cited above, but his use may, strictly speaking, include that case as well. The distinction is mainly one of scale. In a polar fluid such as water, the polar nature comes from the molecules themselves, as opposed to, say, long polymer chains or a magnetizable suspended particles. (To cite another, very different example, a suspension of tiny pear-shaped particles, or even micro-organisms, in a gravitational field would also be polar.) If the polar nature is confined to the molecular level, as for water, then the effects at the meso/macro-scopic scales are mainly confined to that substances chemical and physical properties (viscosity, thermal conductivity, melting/boiling point, and the nature of the liquid state itself) and are not apparent as non-symmetric stresses. On the other hand, if the polar nature of the fluid is due to larger particles (or long chain molecules) then there can be non-symmetric stresses and, because the particles can transmit these stresses to the surrounding carrier fluid, the flows of this fluid will exhibit non-Newtonian flow characteristics. So: I don't think Aris had (molecularly) polar fluids in mind, but I do think he had in mind certain suspensions (i.e. ferrofluids and MR fluids) and polymer fluids. To me what is interesting is whether a polar suspension could be used effectively as a "model system" to examine the nature of molecular polar fluids, such as water.

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