- #1

Gotbread

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I have seen several DIY projects which successfully gathered heavy water

from normal water. For example Cody from codys lab used electrolysis

to "enrich" the water. This however is a messy process.

So i became curious, if this can be done easier by centrifugation.

Based on these data http://www1.lsbu.ac.uk/water/water_properties.html

around 1 in 6600 water molecules are heavy water (HDO). This would

have a density of ~1050kg/m³ compared to ~996kg/m³. This is not enough

to separate them under normal gravity but maybe this difference is enough

to be able to separate them in a centrifuge.

To get a feel for the forces needed, i want to calculate this. But here

is where i got stuck.

First, we assume a cylindrical centrifuge, spinning at a constant RPM.

We also assume that the system has reached a steady state so in the

frame of reference of the spinning liquid, nothing is moving. In that

frame, a fictitious force depending on the radius F(r) will act on the

liquid. Since the system is highly symmetric, it should be equivalent

to looking at only a 1D column along the radius.

In this steady state, the movement of particles due to the centrifugal

action and the movement due to diffusion will balance. Looking again at

the data table we find the diffusion coefficients of H2O and HDO, which

are (in SI) 2.299e-7 m²/s and 2.34e-7 m²/s respectively.

Here is my first confusion: the diffusion coefficient requires two

substances, is the second substance "normal water" (normal mixture of

H2O and HDO) ?

Second, to calculate the distribution, i am looking for a PDE i can

integrate numerically. I found the diffusion equation:

[tex]\frac{\partial \phi(r, t)}{\partial t} = \nabla \cdot \big[ D(r,t))\nabla \phi(r,t) \big][/tex]

with [itex]\phi[/itex] being the density and [itex]D[/itex] the collective diffusion coefficient.

(Can i assume the collective diffusion coefficient is the density weighted

average of the individual diffusion coefficients?)

Obviously, this equation does not include the radial force or the resultant

pressure.

I hope i can get around using the full navier-stokes equations, as they are

quite complicated. Is there a simpler form i can use? Essentially i am looking

for a 1D PDE.