How to simulate differential sedimentation — stokes settling, size selectivity, svedberg

Four centrifuges run side by side on the same medium so the **d² law is visible as a result rather than asserted**: 20, 50 and 100 nm protein particles at 200,000 × g, plus a 10.24 nm particle at 250,000 × g. `centrifuge` is sized by **Sigma theory**, `Σ = Q/(2 v_g)`, where `v_g` is the g-amplified Stokes settling velocity `v = d²(ρ_p − ρ_m)g/(18η)`. So the reported `sigma_m2` carries the settling velocity, recoverable as `v = Q_liquid/(2Σ)`. Against the closed form the solver agrees to machine precision (relative difference 0 to 4e-16), which makes this a check of the tool and not just a demonstration of it. What it shows: **v(20 nm) = 1.53e-3 cm/s**; the 100 nm particle settles **exactly 4×** faster than the 50 nm one, since velocity goes as the square of diameter and every other term cancels; and the 250,000 × g branch is sized so its velocity is 5e-4 cm/s, giving a sedimentation coefficient **s = v/ω²r = 20.4 S** — the Svedberg range real proteins occupy (catalase 11.3 S, ribosome ~70 S). **Bounded, and the bound matters.** This is terminal Stokes velocity at constant field: no wall, no concentration gradient, no Boycott effect, and no hindered settling. Run the 50 and 100 nm particles for 30 minutes and the arithmetic says they separate by 51 cm, which no rotor can deliver — both pellet against the tube bottom first, the 100 nm one in about four minutes. The *ratio* is robust; the distance is what the formula says rather than what a centrifuge does. It is also the reference wiring for a solids flowsheet: the particles arrive as their own `phase: "solid"` feed with a flat `solids` payload, wired **directly** to the centrifuge. Declaring them `liquid` or `mixed`, or routing them through a mixer first, leaves the unit with no solid-phase inlet and the solve fails.

Frequently asked questions

What does the Differential sedimentation — Stokes settling, size selectivity, Svedberg model simulate?

Four centrifuges run side by side on the same medium so the **d² law is visible as a result rather than asserted**: 20, 50 and 100 nm protein particles at 200,000 × g, plus a 10.24 nm particle at 250,000 × g. `centrifuge` is sized by **Sigma theory**, `Σ = Q/(2 v_g)`, where `v_g` is the g-amplified Stokes settling velocity `v = d²(ρ_p − ρ_m)g/(18η)`. So the reported `sigma_m2` carries the settling velocity, recoverable as `v = Q_liquid/(2Σ)`. Against the closed form the solver agrees to machine precision (relative difference 0 to 4e-16), which makes this a check of the tool and not just a demonstration of it. What it shows: **v(20 nm) = 1.53e-3 cm/s**; the 100 nm particle settles **exactly 4×** faster than the 50 nm one, since velocity goes as the square of diameter and every other term cancels; and the 250,000 × g branch is sized so its velocity is 5e-4 cm/s, giving a sedimentation coefficient **s = v/ω²r = 20.4 S** — the Svedberg range real proteins occupy (catalase 11.3 S, ribosome ~70 S). **Bounded, and the bound matters.** This is terminal Stokes velocity at constant field: no wall, no concentration gradient, no Boycott effect, and no hindered settling. Run the 50 and 100 nm particles for 30 minutes and the arithmetic says they separate by 51 cm, which no rotor can deliver — both pellet against the tube bottom first, the 100 nm one in about four minutes. The *ratio* is robust; the distance is what the formula says rather than what a centrifuge does. It is also the reference wiring for a solids flowsheet: the particles arrive as their own `phase: "solid"` feed with a flat `solids` payload, wired **directly** to the centrifuge. Declaring them `liquid` or `mixed`, or routing them through a mixer first, leaves the unit with no solid-phase inlet and the solve fails.

Which thermodynamic method does it use?

The PENG-ROBINSON property package, over water — already selected. You can switch the method on the canvas before running.

Which unit operations are in the flowsheet?

It chains 4× CF P23. Every block is a real, solvable unit operation you can reconfigure, add to, or remove.

Do I need to install software or buy a license?

No. Differential sedimentation — Stokes settling, size selectivity, Svedberg runs entirely in your browser on MaximaLabs — free, no install, no license. Open the model to load it live and run the deterministic solver.