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Re: Centrifuge (was: Just So Stories)



At 10:21 AM 11/4/00 -0500, Ludwik Kowalski wrote:

> "small particles settle more slowly because of thermal
> zig-zagging".

This is not a quotation from what I wrote. In the last message
I agreed with you that zig-zagging is not an explanation. It is
part of a qualitative model which can be used to understand
settling of mud particles in a stationary container.

To me, there is no important distinction between "model used to understand"
and "explanation". The other qualifiers are similarly unimportant. That is:

-- An explanation based on wrong physics is a wrong explanation.
-- A model based on wrong physics is a wrong model.
-- A model where a significant _part_ is based on wrong physics is still
wrong.
-- A _qualitative_ model based on qualitatively wrong physics is
qualitatively wrong.

The point remains, as discussed earlier: we have here a model (or whatever
you want to call it) that makes grotesquely wrong predictions. I thought
we agreed that making wrong predictions was a bad thing.



A smaller particle subjected to Brownian kicks (during its fall) will
usually need more time to reach the bottom than a larger particle for
which kicks are relatively less important. Thermal kicks have practically
no effect on particles whose masses exceed a certain limit, such as one gram.

Could you share with us the formula that you evaluated in order to arrive
at the "one gram" value? Would you be surprised to find that (in practical
situations) the actual limit was twenty orders of magnitude less?

What is wrong with this?

Maybe I'm old-fashioned, but 20 orders of magnitude seems like a lot to me.

What kind of misconception I am going to implant by using this simple model.

It is a misconception to think that Brownian effects (which you mention
prominently) are more significant than Stokes-type effects (which you
declined to mention at all, even when prompted) for RBC sedimentation.

It is a misconception to think that sedimentation rated are dependent on
temperature (and independent of solvent properties) in the ways suggested
by the zig-zag model.

This is not my model; I do not remember where I saw it for the first time.

Recommendation: Check what you read!

The procedures for checking what you read are similar to the procedures for
checking what you write:
1) Do the dimensional analysis and check the scaling properties.
2) Check the limiting cases.
3) Check the order of magnitude for reasonability.
4) Check against whatever experimental data is available.
5) Check the sign and magnitude of the dependence on the independent
variables.
6) Check against whatever tried-and-true theoretical results are available.
... Can anybody think of additional suggestions?


True anecdote: When I read the zig-zag theory for the first time the other
day, my BS detector was immediately pegged. This was so obvious to me that
I have had a hard time trying to view the situation from the viewpoint
where it is not obvious. I won't inflict on you PbBA (proof by bold
assertion); that is, I won't just loudly assert that it is
obvious. (Obviousness is in the eye of the beholder.) Instead, I will try
to make objective physical arguments. Here is my attempt to reconstruct
the thought processes that caused my BS detector to go "boink":

Homework #1: Do you stir your tea? If so, why? Why not let the
tea-flavor molecules just diffuse out of the teabag? Could it be that
diffusion is really, really slow for particles the size of alkaloid
molecules? If it's slow for alkaloids, won't it be insanely slow for
something the size of a RBC?



Homework #2: From elementary kinetic theory (and experiment!) we know that
the density of the atmosphere falls off by a factor of 2 every 18000 feet
or so. Estimate the corresponding scale height for a "gas" of RBCs
dispersed in plasma. (Assume the plasma has been prevented from clotting
by warfarin or the like.)

Use this to make a qualitative statement about the relative importance of
thermal zig-zag effects in the 1G situation. Would you say that room
temperature is a really high temperature or a really low temperature for
sedimentation of RBCs, assuming a regular-sized sedimentation tube?

Hint: The details aren't important, but if it helps you may assume RBCs are
a few percent more dense than the solvent. I don't know the exact number,
but it must be at _least_ a few percent. Pure protein is about 1.5 (i.e.
150%), but the RBC might be a bit lighter because it has some water
inside. If anybody has a more-exact number, please let me know.


Exhortation: The foregoing are not difficult calculations. If you know a
little bit of physics you can do them in your head in less time than it
takes to read the question. You just need a few basic ideas
-- thermal velocity: depends on mass and temperature
-- mean free path: depends on density and cross section
-- mean free time: depends on velocity and MFP
-- random walk: progress proportional to number of steps taken
-- equipartition: probability depends on exp(energy/kT)

I carry a few numbers around in my head:
-- thermal velocity for nitrogen at room temperature (hint: speed of sound)
-- mean free path for nitrogen at atmospheric density
-- scale height of the atmosphere (hint: base of Class A airspace)
... and I would have had to guess at the size of a RBC, but that was given
in Ludwik's problem. So all I had to do is rescale things from air-density
to water-density, and rescale from N2 mass to RBC mass, and I knew what the
answer had to be.


The goal was to explain what happens in the centrifuge in
terms of what students already learned in seven chapters.
Explaining what happens in a stationary situation was
the first step. The next step was to introduce artificial gravity
which plays the essential role in rapid precipitation. The
model predicts (qualitatively) that precipitation is faster
when the angular velocity is larger.

Nothing in that goal-statement requires any consideration of particle
size. So for the Nth time I ask, why not restrict consideration to a
single uniform particle size? Keeping silent about
particle-size-dependence is vastly better than saying wrong things about it.


If for some reason you want to consider the effects of particle size, why
not do it right? The correct story is well known. Please read the
references I cited yesterday.

I hope that somebody
can go one step further and compose a qualitative problem
based on what happens in the centrifuge. Is this possible?
Is this desirable? Is it worth trying?


At 06:17 AM 11/3/00 -0500, I wrote a constructive 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.

... but I didn't receive any comments on it. I don't know how to be more
constructive.