How do you determine the coefficient of friction between
two materials? When you add a fluid for lubrication between the two
materials, how do you determine the amount of fluid to add?
Well, you can measure it. You press down on one material with
another with a given normal force and then measure the force required
to (a) start motion parallel to the interface, to measure static
friction, and (b) continue motion parallel to the interface, to
measure dynamic friction.
If your surfaces are of a relatively standard shape and material,
then it is likely the measurement has been done before, and you can
look the numbers up. What exactly are you after? Detailed
engineering specifications? The generic physics of friction? Your
first question is not so easy to pin down. . .
Ideally I believe you want as thin a film as possible. Think of it
this way: your purpose is to allow motion of one surface without
wasting energy in applying force to immediately adjacent surface.
Solid surfaces stick to one another because microscopic roughness
``catches,'' like two pieces of sandpaper facing each other. So you
put a liquid in between, which keeps the surfaces farther apart than
the microscopic protrusions protrude, and which deforms when the
protrusions move through it. If your layer is thick enough that the
protrusions do not catch, then your energy loss is through the
stirring up of the fluid, which heats it (pointlessly). This heating
will be more if the fluid is thick (viscous) than if it is thin. But
your fluid will stay in a rough, moving, crack under pressure better
if it is viscous. So you can only use a low-viscosity lubricant if
you have a thin crack. But if you have a thin crack, you need to have
better machining of your solid surfaces, so the protrusions are
smaller and a thinner layer keeps them apart.
Hence I think the thickness of a lubrication film is among other
things a compromise between the expense of high-quality machining and
the design goal of low friction. The study of the optimal solutions
comprises the field of tribology, a large and hairy subject.
If you mean: how do you determine microscopically the coefficient
of friction, the answer is no one can do that at present. Check back
in twenty years.
Caveat emptor: this is not my field!
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Update: June 2012