Nuclear Fuel Cycle

Principle

From kinetic theory, when a gas is in thermal equilibrium, all molecules have the same average kinetic energy:

$E = \frac{1}{2}mv^2 = kT$

This means that lighter molecules move faster than heavier ones. Since $^{235}$UF₆ (mass 349 amu) is lighter than $^{238}$UF₆ (mass 352 amu), $^{235}$UF₆ molecules have a slightly higher average velocity.

Now consider UF₆ gas in a container separated by a porous membrane (with pore sizes on the order of ~10 nanometres, similar to the mean free path of a UF₆ molecule). The faster $^{235}$UF₆ molecules will statistically strike the membrane more frequently and therefore diffuse through at a slightly higher rate than $^{238}$UF₆ molecules.

The gas on the far side of the membrane is therefore slightly enriched in $^{235}$U.

Separation Factor

The maximum theoretical separation factor for gaseous diffusion is:

$\alpha_{\text{max}} = \sqrt{\frac{M_{\text{heavy}}}{M_{\text{light}}}} = \sqrt{\frac{352}{349}} \approx 1.0043$

This is an extremely small separation factor. In practice, real separation factors are even smaller than this theoretical maximum.

Cascade Arrangement

Because the separation factor per stage is so small, it is necessary to connect a very large number of diffusion stages in series to form a cascade:

• The enriched stream from each stage feeds the next stage; the depleted stream is recycled back.
• To achieve 3-5% enrichment from natural uranium, approximately 1,000 stages are required.
• Since only about half the gas diffuses through the membrane at each stage, the product mass decreases progressively, requiring smaller units at the top of the cascade.

Drawbacks of Gaseous Diffusion

• Enormous capital cost and physical size
• Extremely high energy consumption — the George Besse diffusion plant in France required the output of almost three nuclear reactors to power it
• Now considered obsolete for new construction; the last major diffusion plant (George Besse I in France) closed in 2012