Re: Centrifuge

[John Denker <jsd@MONMOUTH.COM>]

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.