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My question may be pretty basic, but I feel it is important to ask this as I've gone through several texts and none offer me the clarity I seek.

The question is: What is a fluid? What is flow? If we say that a fluid is something that flows, the next right question to ask would be what flow is. To my surprise and disappointment, there is no clear distinction between various definitions, which I present in the form of questions -

  1. Is a fluid simply something that can flow?
  2. Is a fluid, an object that can be continuously deformed, as a result of shear forces? (fluids can't sustain tangential stress)
  3. What is flow? Does it refer to the motion of fluid elements relative to one another, or does it refer to the motion of the fluid as a whole with respect to the container it is contained in? or, is it just the continuous sliding/deformation of fluid layers, which texts refer to as flow?

So, what properties really define a fluid? (Something that brings up a clear distinction between fluids and non-fluids)

A detailed explanation would be great. Thanks a lot.

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    $\begingroup$ Is traffic on the freeway a fluid? It can reasonably be thought of as a collection of many discrete particles that travel through a container over time, interacting with each other. I would imagine that some of the differential equations that model more conventional fluid flow apply to traffic and some do not. $\endgroup$ – Eric Lippert Mar 7 '18 at 18:29
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    $\begingroup$ Except drivers in traffic slow down at a bottleneck when they should speed up! $\endgroup$ – Tom B. Mar 7 '18 at 18:32
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    $\begingroup$ @TomB.: I'm not sure that's the best road safety advice I've ever heard ;-) $\endgroup$ – psmears Mar 7 '18 at 18:36
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    $\begingroup$ @Mauricio It definitely needs more explanation at the very least. Consider a segment of a pipeline through which a constant volume of fluid is flowing, the mass is not changing. $\endgroup$ – JimmyJames Mar 7 '18 at 19:58
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    $\begingroup$ @Eric: Indeed, there are continuum models of traffic flow (1, 2) based on the hyperbolic PDEs that describe compressible gas dynamics, though as you expected they differ in some significant ways -- most importantly, unlike gas molecules, cars should only be influenced by other cars in front of them, not behind. $\endgroup$ – Rahul Mar 8 '18 at 7:21
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There is no standard definition of the word fluid. It is a somewhat imprecise term used in various ways by different people.

Indeed, in real life there is no simple example of a fluid. There is a spectrum from superfluids at one end, through non-Newtonian fluids all the way to crystalline solids. I speak as an (ex) industrial colloid scientist who has spent many happy hours studying the flow properties of many vaguely fluid systems.

The practical definition widely used by colloid scientists is that a fluid is something that has a measurable viscosity. That is, if subject to a constant shear stress (typically in a rheometer) it has a constant strain rate (note that non-Newtonian fluids may take a long time to equilibrate to a constant strain rate).

The problem with this is that if you carry out your measurement for long enough even apparently solid materials like pitch will flow. I have heard rheologists claim that on a long enough timescale everything is fluid, though these claims tend to be reserved for the bar rather than in refereed publications. Where you draw the line between a fluid and a solid depends on the application and to an extent personal preference.

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    $\begingroup$ Oh, no! I wanted to comment with a link to the Wiki page of the pitch drop experiment, but then I saw that you had anticipated me :-( $\endgroup$ – valerio Mar 7 '18 at 17:24
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    $\begingroup$ Just curious, as you have some experience in the topic; would they consider a superfluid to have a "measurable viscosity"; even if in a perfect superfluid; that would be 0? (The naming might break down here; I could see the distinction becoming trivial/irrelevant when dealing with things at this complexity; it also may be such a niche field that you don't really know, but I'm just curious now) $\endgroup$ – JMac Mar 7 '18 at 17:27
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    $\begingroup$ @CarlWitthoft: And yet, gravity pulls ice like Ceres and rocks like the Earth into a sphere, into hydrostatic static equilibrium, just as if they were spheres of water suspended in an updraft (pulled together by surface tension, of course). It's a matter of perspective and scale; nature is rarely so considerate as to sort itself into neat, unequivocal categories for the benefit of strange apes like us. $\endgroup$ – Williham Totland Mar 7 '18 at 19:51
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    $\begingroup$ "I speak as an (ex) industrial colloid scientist who has spent many happy hours studying the flow properties of many vaguely fluid systems." - you probably didn't mean it that way, but I love the mental image there of a colloid scientist at happy hour, playing with mixed drinks and silly straws. $\endgroup$ – user2357112 Mar 8 '18 at 0:13
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    $\begingroup$ Some things aren't fluids on long time scales. They burn instead. (Opening the door for the philosophical question of whether a thing is still itself after it has burned and become a gas, which is fluid) $\endgroup$ – Cort Ammon Mar 8 '18 at 2:24
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Before Einstein's 1905 paper "Investigations on the Theory of the Brownian Movement" many physicists and even chemists didn't believe that molecules or atoms really existed. A fluid was considered a fundamental object. We now know that all fluids are really aggregations of particles. At temperatures above 0°C these particles are in constant chaotic motion. It is called Brownian motion after the botanist Robert Brown (born 1773) who, under a microscope, noticed a ceaseless movement of pollen grains in water. A fluid is said to be flowing if, in some reference frame, the particles' velocity vectors all have large components in the same direction. All the characteristics of the fluid, temperature, flow velocity, shear stress, viscosity, density, all are due to the motion of the particles. In some situations the particle nature of the fluid can be ignored. This is when the "fluid approximation" is valid. This approximation ignores viscosity and indeed any interactions between the particles. In other situations this approximation is not valid.

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Fluid is essentially a summary category for liquid + gas. And that makes sense, because an incompressible gas obeys the same equations of motion as a liquid. Hence, the term "fluid dynamics" applies to both. As one goes into greater detail, there surely are ambiguities; in particular we could discuss forever the difference between a liquid and a solid. Non-fluids are solids.

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