Example data table
| Particle diameter (µm) | ρp (g/cm³) | ρf (g/cm³) | Viscosity (cP) | r0 → r1 (cm) | Speed (RPM) | Predicted time (min) |
|---|---|---|---|---|---|---|
| 1.0 | 1.05 | 1.00 | 1.0 | 6 → 10 | 10,000 | ≈ 5–6 |
| 0.5 | 1.10 | 1.00 | 1.2 | 5 → 9 | 12,000 | ≈ 8–10 |
| 2.0 | 2.50 | 1.00 | 1.0 | 6 → 12 | 6,000 | ≈ 1–2 |
Formula used
In a centrifuge, the terminal radial motion of a small spherical particle in the Stokes regime is modeled as:
- dr/dt = k·r
- k = (2/9) · rp2 · (ρp − ρf) · ω2 / μ
Integrating from start radius r0 to end radius r1 gives the sedimentation time:
t = ln(r1/r0) / k
How to use this calculator
- Choose a calculation mode (time, velocity, required RPM, or required diameter).
- Enter particle diameter, densities, and viscosity with your preferred units.
- Set r0 (start) and r1 (end) radii from your rotor geometry.
- Provide speed as RPM or RCF at the average radius.
- Click Calculate, then download CSV or PDF if needed.
Centrifuge settling versus gravity settling
Stokes settling in a centrifuge replaces gravity (g) with radial acceleration ω²r, so particles move outward faster toward the tube bottom. This calculator integrates that changing acceleration rather than assuming a constant field.
What drives the sedimentation constant k
The key coefficient is k = (2/9)·rp²·(ρp−ρf)·ω²/μ. A larger particle radius rp or higher speed ω increases k sharply, while higher viscosity μ slows motion. With ρp = 1.05 g/cm³ and ρf = 1.00 g/cm³, Δρ = 50 kg/m³; in glycerol-rich buffers μ can exceed 10 cP, making times roughly tenfold longer. For example, doubling diameter cuts time by about four.
Why start and end radii change the time
Radii matter through ln(r1/r0), using the natural logarithm. If your sample starts at r0 = 6 cm and pellets at r1 = 10 cm, ln(r1/r0) ≈ 0.511. Measure r0 at the meniscus and r1 at the pellet location; a longer travel distance increases ln(r1/r0) and time.
Interpreting RPM and RCF in protocols
Many protocols specify RCF rather than RPM. RCF depends on radius: RCF = 1.118×10⁻⁵·r(cm)·RPM². At 10,000 RPM and r = 8 cm, RCF ≈ 8,944×g. This tool converts RCF using the average radius r_avg = (r0+r1)/2 to match the integrated model. If you move to a different rotor with a larger radius, the same RPM produces a higher RCF.
When Stokes assumptions are most reliable
Stokes’ law assumes laminar flow around the particle and a spherical shape. A quick check is the particle Reynolds number; very small particles (sub‑10 µm) in water-like fluids typically remain in the Stokes regime at common microcentrifuge speeds, but aggregates can violate it. Crowded suspensions also settle more slowly due to hindered settling, so dilute samples match the model best.
Viscosity and temperature sensitivity
Temperature affects viscosity strongly. Water is about 1.0 cP near room temperature and roughly 0.7 cP around 37°C, so the same setup can run about 30% faster when warmed. If you enter μ in cP, the calculator converts to Pa·s (1 cP = 0.001 Pa·s). Always use the fluid’s viscosity at your actual run temperature.
Using results to tune your run
Use the outputs to tune protocols: time (r0→r1), velocity at r0/r1, and RCF at key radii. If the predicted time is too long, solve for required RPM, or estimate what minimum particle diameter will pellet within your available run time. If time looks unrealistically short, carefully recheck units, densities, and that r1 is greater than r0.
FAQs
1) What does this calculator actually predict?
It predicts terminal radial settling under Stokes drag, giving time to move from r0 to r1, plus velocities and RCF. It is best for small, spherical particles in dilute suspensions where laminar flow dominates.
2) Can I use it when particles are lighter than the fluid?
Not for outward pelleting. If ρp ≤ ρf, the density difference is zero or negative, so particles will not sediment outward by this model. Use a flotation or inward-migration model instead.
3) Should I enter RPM or RCF?
Use either. RPM is direct. If your protocol lists RCF, enter it and the tool converts using the average radius between r0 and r1, which matches the integrated radial formulation.
4) How do I choose r0 and r1?
Measure from the rotation axis. r0 is typically the sample meniscus radius at the start, and r1 is the expected pellet location near the tube bottom. r1 must be greater than r0.
5) Why might my observed pelleting time be longer?
Real samples can be non-spherical, aggregated, or concentrated, which increases drag and causes hindered settling. Temperature-dependent viscosity and rotor geometry differences also matter. Use measured μ and verify r0/r1 for your rotor.
6) Which viscosity should I use for buffers or mixtures?
Use the dynamic viscosity of the actual medium at run temperature. Water is about 1 cP near room temperature, but additives like sucrose or glycerol can raise μ several-fold, increasing predicted times proportionally.