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I just met with a very basic question.(Might even sound silly!) My textbook kinda says(not exactly), 'Whatever flows is a fluid'. That got me wondering because we are creating a whole category of matter just because they flow! So there must be some significance to 'flowing'. That further led me to ask why in the first place should we say liquids and gases "flow" and not "move"?! It seems to tell me that there should be a major difference between the physics of flow and movement. What is it?

PS:- I don't want the difference in meaning from a dictionary but a scientific difference. Please don't get too mathematical. I haven't acquired good mathematical skills YET.

Edit:- Okay. Since a comment below says "Movement is actually seldom defined very rigorously", I suppose I must refine my question here. Consider someone is saying that a box moves on a table as you applied a force on it. Now why is that person saying it 'moved' rather than it 'flowed', here? What is the difference between flow and movement in this case and how can we generalize the idea?

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The Wikipedia definition is as scientific as it gets in one sentence: "In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress". What about this aren't you happy with? –  leftaroundabout Jul 29 '14 at 15:17
that defines flowing ...alright. But what about movement and how is it different from flowing? –  VenkiPhy6 Jul 29 '14 at 15:18
"... that continually deforms ..." –  leftaroundabout Jul 29 '14 at 15:19
A point particle can move but it cannot flow. –  Alfred Centauri Jul 29 '14 at 15:20
@leftaroundabout movement - 'deformation for an instant' ? –  VenkiPhy6 Jul 29 '14 at 15:20

2 Answers 2

up vote 3 down vote accepted

In very basic terms, flow is movement with continuous deformation while regular old movement is without continuous deformation, but there could be discrete deformation I suppose.

Water will flow when spilled, it tumbles and rolls and breaks up and rejoins. But when you push a ball across the table, the ball stays together, moving rigidly. It could be a rubber ball, which will deform locally and may even stay deformed if it's inelastic, but as a whole, the object moves as one unit.

How an object moves and it's relation to shear stresses is what defines states of matter which I describe very simply in the linked answer. Flowing really implies movement with no fixed shape (apart from shape imposed by the boundaries, such as containers or channels) which distinguishes it from the movement of solids.

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okay..so movement with actual fixed shape - normal movement, movement without actual fixed shape - flow. Makes sense. But we consider a fluid flowing to have a fixed shape(psedo shape as opposed to actual shape) since in fluid dynamics(being part of continuum mechanics) we consider things(fuids) at a macroscopic scale only. Am I right here? –  VenkiPhy6 Jul 29 '14 at 15:46
okay...got a bit confused there! We only consider a fluid to have fixed volume in fluid dynamics though there actually isn't(?). BTW I suppose I should further ask questions about what shape actually is and get answers to understand this fully! Because even a cloth doesn't have fixed shape but it 'moves' right? But then i wouldn't trouble you with a '"shape"- elaborate' as that is out of scope to this post. So thanks! –  VenkiPhy6 Jul 29 '14 at 15:56
Okay I finally seem to get it. It would be easier to understand if we say since a solid retains it shape throughout the movement (as opposed to has fixed shape) it is said to 'move' while a fluid doesn't retain its shape and hence flows. (Ah! Deep exhalation At last!:-D ) –  VenkiPhy6 Jul 29 '14 at 16:11
@Venki Not to confuse you more, but "retains its shape throughout movement" isn't any more correct than "fixed shape" because deformation of any kind is neither retaining shape nor a fixed shape. Cloth is obviously a solid but it deforms quite a bit during motion. Although it is a bit more muddled than that since it's a collection of pure solids and not itself a pure solid (woven strands vs say an iron rod). –  tpg2114 Jul 29 '14 at 16:48
right @tpg2114 thanks! :-) –  VenkiPhy6 Jul 30 '14 at 13:36

I don't quite agree with tpg2114's answer.

For one thing, metals deform like clay and "flow" plastically when heated to sufficiently high temperatures. They are clearly in the solid state (have a well defined lattice structure, for instance) but quite easy to deform.

In fact, modern forming processes like extrusion use this principle to effect changes in the shape of metals. The strains can be very large, and the change in shape is permanent - characteristics shared with fluids.

From a continuum mechanics perspective, there is no difference between a "flow" and a "motion" - they are used interchangeably to denote the map $\chi$ in the following equation.

$$ \mathbf{x} = \chi(\mathbf{X},t) $$

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So you are saying that even though they have a fixed shape('well defined lattice structure'), amorphous solids(which is what you refer to when you say metals here, I suppose) 'flow' and hence tpg2114's answer is not so acceptable, right? But then amorphous solids aren't considered pure solids, are they? They are just super cooled liquids and hence fluids and hence flow! –  VenkiPhy6 Jul 31 '14 at 12:33
@Venki No no no. I mean crystalline, not amorphous. Polycrystalline metals (such as steel heated before working it) can experience very large strains. Look up superplasticity. Anyway, my principal objection to that answer is the fact that in describing deformation, there is no distinction between flow and motion. –  user_of_math Jul 31 '14 at 16:09

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