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Re: centrifuge exercises



Ludwik Kowalski wrote:

.... Use mud in water (instead of blood) and
assume that all particles, big a small, are spherical. A uniform
initial distribution of radii, from 0.0001 to 0.01 cm is probably
acceptable for a simple typical centrifuge problem. To simplify
we can also assume that all particles are made from aluminum
and are initially at 1 mm below the surface (to avoid surface
tension complications). For example, 20 grams of water and
0.02 grams of Al in a 25 cm tube. First stationary (vertical),
then in very fast horizontal (horizontal).

I did the easy part (stationary tube) using the formula for
terminal velocity derived in Serway and Faughn (p 293).

vt=((2*r^2*g)/(9*eta))*(ro1-ro2)

where eta=1e-3 (viscosity of water at 20 C), g=9.8,
ro1=2700 (Al) and ro2=1000 (water). For very small
particles (r<0.1 mm) terminal velocity is reached over
very short distance and the time to cover 25 cm is
practically equal to 0.25/vt. It is inversely proportional
to r^2.

The results are:

r=0.1 mm --> time=6.75 seconds
r=0.01 mm --> time =675 secends
r=0.001 mm --> t=18.75 hrs
r=0.0001 mm --> t=1875 hrs = 78 days
r=0.00001 mm --> 21 years, etc.

I do not know why there were no numerical problem
on this at the end of Chapter 9. S&F usually provide
problems on everything covered. These numbers
look reasonable to me. But I must admit, I have no
experience with rates of sedimentation.

Can somebody go one step further and show by how
much these times are reduces at 100 rev/sec ?
Ludwik Kowalski