Inside a spinning rotor, gaseous UF6 is thrown outward by the centrifugal force. Because the two isotopologues (²³⁵UF6 and ²³⁸UF6) differ in mass by only 3 amu out of ~352, the pressure of each species along the radius follows a Boltzmann-like barometric law:
p_i(r) = p_i(0) · exp[ M_i ω² r² / (2 R T) ]
Elementary separation factor (mass-based, wall-to-axis):
α₀ = exp[ (M₂ − M₁) ω² (r_wall² − r_axis²) / (2 R T) ]
where ω is the angular velocity, M₁ < M₂ the two molar masses, R the gas constant and T the temperature. The heavier ²³⁸UF6 is pushed slightly harder to the wall, so the light, ²³⁵U-enriched fraction accumulates near the axis. A single rotor gives only a tiny α₀ (a few tenths of a percent), so real plants pipe the light stream from each machine into the next as feed — a countercurrent internal circulation (driven by a temperature gradient and a scoop) multiplies the enrichment per machine several-fold, and cascading thousands of centrifuges in series/parallel compounds α₀ until weapons- or reactor-grade assay is reached.
- Peripheral speed — sets ω via v = ωr; separation grows with v², so centrifuge rotors are built from high-strength composites to spin as fast as physically survivable.
- Temperature — higher T randomizes molecular motion and reduces the radial separation (α₀ ∝ e^(1/T) term shrinks).
- Countercurrent flow — models the internal axial circulation that turns the modest single-pass α₀ into a larger effective per-machine enrichment.
- Cascade stages — chains machines so exit assay compounds stage-to-stage, exactly as a real enrichment cascade does; separative work (SWU) is the standard unit for a plant's total effort, independent of feed/product assay choice.
This is the physics behind uranium enrichment for both reactor fuel (~3–5% ²³⁵U) and, at far higher cascade depth, weapons-grade material — the same gas-centrifuge principle scaled very differently.