[Atomic-S (OP)]

When a fluid flows through a well-polished pipe, is the rate of flow affected by the meniscus behavior of the materials; that is, whether the meniscus of the said fluid, when stationary in a vertical capillary composed of the pipe material, is positive or negative? (Note that this is a measure of the relative attraction of liquid molecules for each other as compared to their attraction to the pipe.)

[eric l]

Meniscus behaviour is created by the difference in interfacial tension (a.k.a. "surface tension") between liquid and air on one side, and between liquid and recipient on the other. 
The "surface tension" or "interfacial tension between liquid and air" is only important on the "free" surface, not in a filled pipe.
Provided the inner surface is not rough enough to create turbulence, I take it that the material of the pipe has little or no influence (and this is confirmed by experience) but I have no experimental data at hand.

[Atomic-S (OP)]

A cylindrical container filled with a solid (e.g., a shaft inside a pulley) resists the removal of the solid with a force which is dependent upon, among other things, the chemical substances involved. That is, there exists a coefficient of friction between the container and contents which depends upon the substances involved, which must have something to do with the way molecules of the one substance relate to molecules of the other. (I here assume the lack of complicating factors such as lubricant). If the system is heated to the point that the inside substance melts (let us assume that the outside substance melts at a higher temperature than the one being used), does this chemistry stop being effective on the way the inner substance moves within the outer? One would think not, unless the velocity difference between a fluid element and the surrounding container must inevitably approach zero as the distance from the element to the container wall approaches zero. Now it may be than if the melted substance has a low viscocity, this condition is closely approximated. But is it true in general? And if not, then some of the fluid flow would consist in the actual sliding of the fluid surface at the container surface, like solid-state friction. In such a case, the differences of chemistry presumably would affect the situation, and since friction and capillarity both relate to the relative attraction of molecules under given conditions, one  might suppose that they would be related.

[eric l]

I see your point, but you are reaching a complicated matter, and I tried to find some good links on the net, but failed so far.

It is all a matter of rheology, which could be translated as "the science of flow".

Basically, you have a perfect fluid, known in rheology as "Newtonian".  Newtonian flow through a pipe means that the speed at the pipe wall is zero, while the speed in the centre is maximum.  Depending on the source (handbook) the speed profile will be described either as parabolic in shape or as conical.
But with real life fluids, you are bound th have "Non-Newtonian" flow types such as

• plastic flow
• pseudo-plastic flow
• visco-elastic flow

Some of this flow types will result in "plug flow".  In extreme cases this means a rupture between the liquid and the pipe wall, and a flow like "a solid shaft pushed through a pulley" (to quote you).  In most cases however, you have a layer with a speed gradient between that solid shaft and the pulley, and the thickness of that layer depends mainly on the "yield stress" of the fluid.  ("Yield stress" by the way is the stress at which the product stops behaving like a solid and starts behaving like a fluid - e.g. the stress you have to apply for spreading butter over a slice of toast.)

Things like this are important in processes like extrusion of plastic (http://en.wikipedia.org/wiki/Plastics_extrusion).  There is laboratory equipment around for measuring such things, but to the best of my knowledge the dies used are always made from the same material.

I'll try to find more on the net, but there are good handbooks both on applied rheology and on extrusion of plastic.