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Re: Centrifuge (was: Just So Stories)



How do we decide what is and what is not an explanation?

By whether it makes correct predictions!!!!!!!!!!!

Yes.

But a qualitaltive explanation could not be expected to produce
a quantitative prediction. Why should it provide answers to
all possible questions?

The tentative model I am trying to promote does predict that
the rate of settling should increase when the angular velocity
incresaes. Perhaps it was not clear that "THIS EXPLAINS "
refered to the model and not the zig-zag paths (which are parts
of the model). I tried to make it clear in the new version, as
shown at the end. I do not thing that the description is only
an empty worthless strory. I hope it can be turned into a good
strory for a first physics course, in a high school or college.

But I am old enough to know that authors nearly always like
what they compose. I am waiting for more comments.
Ludwik Kowalski
*****************************************
John Denker wrote:

Trying to be polite, I wrote an understatement:
thermal zig-zagging is not "the" explanation.

At 04:19 PM 11/3/00 -0500, Ludwik Kowalski wrote:

How do we decide what is and what is not an explanation?

By whether it makes correct predictions!!!!!!!!!!!

Since polite understatement didn't communicate the point, here it is with
kid-gloves removed:

-- The zig-zag theory predicts the wrong dependence on temperature.
-- The zig-zag theory predicts the wrong dependence on viscosity.
-- The zig-zag theory predicts the wrong dependence on particle size.
-- The zig-zag theory predicts the wrong dependence on particle mass.

-- It succeeds only in postdicting one bit, namely that small particles
qualitatively settle out faster.

Therefore, although it purports to be a scientific explanation, it is not
anything of the sort. Rather, it is what we call a "Just So Story".
*) How the small particles settle slowly.
*) How the camel got his hump.
*) How the leopard got his spots.
*) et cetera; see
http://www2.shore.net/~mogget/justso.htm

*******************************************
A slightly modified version :

..... 1) Begin by explaining "settling" of mud particles
suspended in a stationary tube. Two forces acting on a single
particle can immediately be identified, weight and buoyancy.
If there were nothing else then the particle would be moving
vertically down with a constant acceleration. Water resistance
is like friction and it would result in a progressive decrease
of acceleration (terminal v = constant).

But there is something else. Thermal agitation creates a
force which fluctuates randomly and results in Brownian
motion. The significance of randomness depends on the
size of a particle; the net random force becomes negligible
for large particles, such as rocks.

Thus only very large particles travel down along straight
lines. Slightly smaller particles also travel down vertically
but their terminal velocities (assuming the vessel is deep)
are slightly smaller. Very small particles, on the other hand,
fall down along zig-zag trajectories. We are interested in
rapid precipitation of very small particles. Trajectories of
particles whose masses are smaller are longer. On that
basis we expect larger particles to settle sooner than
smaller particles. Lower layers are indeed composed of
mostly larger particles than upper layers.

2) It is well known that the process of separating larger
particles from smaller can be speeded up by rotating a
tube. How can this be explained? Suppose that a closed
tube with muddy water is positioned horizontally. Then
we start rotating it about a vertical axis with the constant
angular velocity w. By doing this we are creating "artificial
gravity", a centrifugal force directed away from the center
of rotation. [One may elaborate on this or one can present
it as a well known experimental fact.]

The centrifugal force (m*r*w^2) is proportional to the
mass of particles. This is very significant. If there were
no other forces then particles would move horizontally
with progressively increasing acceleration. This could
be compared with a coin sliding along a radial groove
on a rotating platform. But other forces (weight, water
resistance and thermal) are present. In a centrifuge we
can ignore weight when m*r*w^2 >> mg.

The settling of mud particles in a rapidly rotating tube is
thus conceptually similar to the settling due to real vertical
gravity. But here we have a possibility of increasing the
speed of settling by increasing w.

3) The next step is to create a good quantitative problem
based on the preparatory description. I do not know how
to do this. So let me stop. Is the above explanation
correct? Is it acceptable? I hope somebody will actually
formulate the problem in the way which it can be presented
to students; perhaps as a replacement of the present version
for the 6th edition. I know that at least one person from
Serway's team is a PHYS-L-er.