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Assuming I have a homogeneous solution such as salt in water. My intuition tells me that gravity or centrifugal forces would affect sodium ions more than water molecules. Theoretically, if I could centrifuge salt water fast enough for the pulling forces to surpass the forces of the hydrogen bonds between salt and water, would I be able to seperate it? Or is there some theoretical reason for why no amount of centrifugal force would be able to split it up?

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The issue is that salt ions, while heavier than individual water molecules (they are after all an ion surrounded by coordinated molecules) are not much heavier, and the diffusion rate due to thermal motion is faster than the settling drift. Hence they do not pile up well at the bottom of the container. Most use of centrifuges in desalination are using them to drive salt water through osmotic filters instead.

Sedimentation equilibrium happens when a suspension of particles needs up in an equilibrium where the sedimentation rate equals the diffusion rate. The volume fraction of the particles is given by the Laplace-Perrin equation: $$\Phi(z)=\Phi_0 \exp\left(-\frac{4 \pi g \Delta \rho R^3}{3 k_B T} z \right)$$ Here $\Delta \rho$ is the density difference - in this case at most a few times, and $R$ the radius of the particle. Note that if $R$ is very small, then the fraction in the exponential becomes very small, and the concetration changes very slowly with $z$. A criterion is that if $\frac{3 k_B T}{4 \pi g \Delta \rho R^3} \gg R$ there will not really be any sedimentation since diffusion dominates. This seems likely here, unless the centrifuge can make $g$ very large.

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