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Re: Centrifuge



The centrifuge problem quoted in an earlier message
was criticized. But an attempt to include a biology-
related problem should be appreciated, as emphasized
by John (see below). Furthermore, drill and practice
is part of learning. Deeper understanding often comes
after a lot of mechanical "plugging and chugging".
Not all brains work in the same way. (The "love and
marriage" analogy comes to my mind.)

In that spirit it is useful to create an explanation of the
centrifuge for an introductory course. Let me try to
make a step in that direction. Perhaps we can produce
something good together. Feel free to grab chunks of
my writing and improve it.

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; other particles fall down along zig-zag trajectories.
This explains why larger particles settle sooner than
smaller particles. Lower layers are composed mostly of
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. 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.
Ludwik Kowalski

John Denker wrote:

At 09:36 PM 11/2/00 -0500, Ludwik Kowalski wrote:
>
Perhaps the physics of the centrifuge cannot be made
meaningful in the first physics course

That's quite an over-reaction.

I already told students why I do not like the centrifuge
problem; I plan to discuss the above sliding-coin problem
next week.

Taken together, recent postings suggest a hypothesis, namely that confusion
between merry-go-round geometry and lab-centrifuge geometry led to
misunderstanding of the Serway & Faughn centrifuge question and
inappropriate complaints against it.

Yes, I know that it is also a plug-and-chug
problem. But it is more appropriate for my class. Once
they understand this problem they will have some very
vague idea about what is going on in a centrifuge.

It is generally considered good pedagogy to deal with the simpler cases
first. Serway & Faughn evidently decided to start with a simple case where
only one radius need be considered. That seems reasonable to me.

It's not at all clear that there would be any advantage to starting with
the full-blown merry-go-round, wherein we have a centrifugal FIELD with a
direction and magnitude that changes from point to point. Non-physics
majors aren't particularly fond of vector fields.

There is also an argument that one should prepare students for real-life
jobs. Exposing students to the idea of centrifugal fractionation of blood
is a Good Thing if you ask me -- vastly more real than coins sliding on
merry-go-rounds.

But alas, given this real-world situation, the calculation that S&F choose
to do is unnecessarily hokey.

At 11:06 AM 11/3/00 +1100, Brian McInnes wrote:
can someone explain to me where the value of 4E-11 N for the
magnitude of the force came from. My cynical mind does not accept
that it is an experimentally measured value;

Brian's cynicism is right on target. The force number has obviously been
cooked.

What is the physics involved?
(1) Why don't the blood corpuscles settle out when the blood is
sitting in test tube?

They do. As I hinted in previous messages, red blood cells settle out just
fine under 1G conditions; the centrifuge only speeds up the process. The
field that S&F envision (14000 G) will make RBCs settle out real fast!

From this we conclude that the homework question should have said
"desired" rather than "required". Picky picky.

BTW I'm surprised nobody has yet mentioned buoyancy. The non-mention of
buoyancy is another sign that the problem is hokey.

Brian also asked:
What are the forces on any corpuscle balancing the gravitational force on it?

In general, the main dynamical factors include:
* Buoyancy
* Brownian motion / diffusion / equipartition
* Interparticle electrostatics
* Applied fields (E, G, ...)
* Friction / viscosity

Look up "colloid" in your favorite physics text or encyclopedia. But note
that RBCs are not colloidally suspended in blood.

The physics details are interesting, but I think we don't need to go
there. Remember Ludwik said he _wanted_ a plug-in-the-numbers problem. My
gripe (and I think Brian's gripe) is that this is a hokey problem playing
dress-up in the clothing of a real situation. That's a shame, because
there are non-hokey calculations one could do in this situation. For example:

Scenario: blood fractionation.
For non-colloids, sedimentation rate is proportional to
acceleration field. (Stokes. Svedberg.)
To get the desired rate we need XXX Gs.
Sample is held in the centrifuge at r=15cm.
Calculate the desired rotation rate in RPM.

Note the absence of hokey references to particle mass and force.
Note the absence of details that would derail the unskilled student.