You wish to capture 3 mu m particles in a linear density gradient having a densi

Question

You wish to capture 3 mu m particles in a linear density gradient having a density of 1.12 g/cm^3 at the bottom and 1.00 at the top. You layer a thin particle suspension on the top of the 6 cm column of fluid with a viscosity of 1.0 cp and allow particles to settle at 1 g. (a) How long must you wait for the particles you want (density = 1.07 g/cm^3) to sediment to within 0.1 cm of their isopycnic level? Is it possible to determine the time required for particles to sediment to exactly their isopycnic level? (b) If instead of 1 g you use a centrifuge running at 800 rpm. and the top of the fluid is 5 cm from the center of rotation, how long must you centrifuge for the particles to move to within 0.1 cm of their isopycnic level?

Explanation / Answer

,

we can see that the particles we want have

the density

of 1.07 g/cm6^3

. However, the gradient has a density of 1.12 g/cm^3 at the bottom and

1.00 at the top. So when calculating the density of the medium 0

, we assume x as the distance from top to the aim distance where the density is 1.07 g/cm^3

0 =(1.00 +1.12 -1.07 /6 * x ) g/cm^3 =(1.00+0.02x) g/cm^3

when ro =1..07g/cm^3

, we get x=3.5cm

dx/dt =2a^2(r -ro) g /9 mu

dx/dt = 2 (0.5 *3* 10^-6 m) x [1.07-(1.00-0.02x)] g/cm^3 * 9.8 m/s^2 *10^6 cm^3/m^3/   

           9.1*1*10^-2 g/cms

=4.91x10^-6 x (7-2x) cm/s

Lmit 0-3.5   (7-2x) cm/s    =4.91 x10^-6 dt

T=1/2x4.91 x10^-6 ln0

We know ln0 is of no value, so it is impossible to determine the exact tim

.

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