Of course fluids have been around for longer than we humans have. Our usual and historical encounters with fluids are at our, macroscopic, level. Although Democritus spoke of them, atoms were not the stuff of physical thought until Einstein’s 1905 paper explaining Brownian motion. This was the first proof of the actual physical existence of submicroscopic particles. In this paper Einstein showed that fluids were indeed collections of interacting particles. Before that, Mendeleev’s chart of the elements was only thought of as a formal bookkeeping method for chemists. The elegant mathematics of fluid mechanics was and is very attractive but now it had to be shoehorned into the reality of the existence of atoms and molecules. It is for this reason that fluid mechanics texts preface their treatment of fluids with the “fluid approximation,” i.e., that fluids are really made up of molecules and atoms but that this fact will be put aside. This approximation ignores particle-particle interactions and it ignores the interactions of fluid particles with solid surfaces. Viscosity, a macroscopic property, is introduced to account for these.
In keeping with the view before 1905, then, a fluid was defined as a substance that takes the shape of its container and that does not exhibit static shear strain, i.e., it does not deform statically. Of course vortices and whirlpools and their attendant distortions of the fluid’s surface were observed but these are dynamic strains. Except for viscosity, then, a fluid was approximately ideal. An ideal fluid is one in which there are no particle-particle interactions. The effects of particle-particle and interactions between the fluid particles and solid surfaces in the flow are supposedly accounted for by the introduction of the notion of viscosity. This keeps the fluid approximation intact. There still are problems, though, in explaining some fluid behaviors, for example consider Bernoulli’s principle.
The principle is illustrated by the behavior of a fluid in a Venturi tube. A gas at a fixed pressure in a large container is allowed to exit through a narrow tube. In this tube Bernoulli’s principle relates the velocity of the exiting fluid to the difference in pressure between the large container and exit tube. At the macroscopic level the force that accelerates the fluid from zero in the container to its exit tube velocity is due to the pressure difference between that of the container and the final pressure of the space into which the fluid flows. This is all fine until one considers the manometer that measures the pressure differences. The flow rate of a real, i.e., viscous fluid at the walls of the apparatus is zero. How, then, do the manometers work, since they are installed in the walls? How is it that they measure the flow rates? The problem is that the fluid approximation is not valid at the walls.
What is going on at the particle level? What the manometers are sensing is the pressure due to the collective effect of the components of the velocities of the particles normal to the wall. The orifice into the exit tube is a sorting mechanism. Evidently only those particles which are at the orifice and whose velocity vectors are directed into the tube contribute to the flow in the tube. The particles whose velocity vectors are not precisely normal to the area of the orifice will strike the wall of the exit tube. Within the exit tube, of course, there will be particle-particle collisions but the average motion of the molecules will be in the direction of the tube. The fact that energy is conserved is reflected in the fact that the collectively increased velocity of the particles in the direction of the tube’s axis is accompanied by lower velocity components normal to the walls than the average within the container from which they came. This is what the manometer senses. This is why the pressure of the fluid in the exit tube is lower than that of the container. The exit tube’s orifice is a selection mechanism, like Maxwell’s Dæmon.
