Re: Centrifuge

[brian whatcott <inet@INTELLISYS.NET>]

At 12:49 11/2/00 -0500, you wrote:
> Problem #21 from College Physics of Serway& Faughn
> (5th edition, page 211) asks students to calculate v when
> m, R and F=(m*v^2)/R are given. The answer one gets
> (150 rev/s) is the same as that shown in the book. Note
> that R is "the radius of the centrifuge".
>
> The problem defines F as "the force required to make
> it [particle of mass m] settle out of the plasma". Most
> blood particles are initially at r<R.
> .
> Since v=w*r one has F=m*r*w^2. At a constant w
> F increases when r increases. Does this mean that
> particles at r<R will not settle at 150 rev/sec?
>
> What is a better way to formulate the centrifuge
> problem in a non-calculus physics course?
> Ludwik Kowalski


I find a hypothetical but operational approach works
for me on this one.
Spinning a mass on a string, I find that for a certain
rotation rate, I feel a certain force at the string
restraint.
Doubling the string length, the force doubles.
Doubling the rotation rate, the force grows to four times
its previous value.
 If I streamline the peripheral mass, the effort needed to
spin it is reduced, so I (correctly) deduce that spinning
in a vacuum would also be easier.
In the cultural imperative urge for more, bigger, faster;
I try to make the string very long, but I see that the
string now breaks at a certain speed, so I am at a 'speed of
centrifuge' barrier.
What am I to do?

I have a bright idea: halve the string length (half the force)
but double the rotation rate. Now the force is doubled
as a result of multiplying the two parameters: 1/2 X 4 = 2

But wait a moment: we hit the strength of string constraint
at some critical length and speed, did we not?
 Yes indeed - so now we progess to a solid wheel with
a few little pockets for test tubes.
 This design (as it turns out) has the happy property that it
only bursts at some rotational rate reasonably
inverse-proportional to its diameter.

So halving its diameter allows us to spin it at twice the speed.

And in pursuit of the ultimate, I end up with a tiny rotor
which can spin in vacuum at a truly phenomenal rate - several
 thousand turns a second.

Did I mention the other reason for the vacuum?
 No, but I should have.

Seperations with centrifugal methods are a matter of making
buoyant particles go one way, and denser particles go the other.
 The spin multiplies these effects - that's the whole point -
and temperature always varies buoyancy and density - so we
have to take every precaution to stop stray heating.
That means no air friction. That means a vacuum for our
record attempts.

This is what *I* call a 'Just-So' story. Useless for plug-n-chug,
helpful for physical insight. I know which approach I would have
 preferred.

Hypothetical problem 1:
describe a formulation relating centrifuge rotor speed,
 diameter and force.

Hypothetical problem 2:
A blood sample seperates to the desired degree when spun on
a radius = 10cm at 150 rpm in 3 minutes.
Redesign the rotor system to seperate blood in 10 seconds,
given the critical speed & diameter for duralumin is 16 cm
and 60,000rpm.  Minimize the rotor volume.


brian whatcott <inet@intellisys.net>  Altus OK
                Eureka!