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sci.nanoparticle-diffusion-Einstein Calculator
Calculates nanoparticle diffusion coefficient from Einstein-Stokes equation: D = kT/(3πηd), and mean square displacement in solution. A 10 nm nanoparticle in water at 25 °C has D = 43 µm²/s — at room temperature, it diffuses its own diameter in ~1 µs.
Inputs
D Nm
Distance across a circle through its centre. Always confirm units match the rest of the calculation.
T K
Thermal state of the substance. Check whether the formula needs Celsius, Fahrenheit, or Kelvin (K = °C + 273.15).
Eta Mpas
Fluid resistance to flow. Water at 20°C: ~1 cP. Honey: 2,000–10,000 cP. Higher viscosity increases pumping power requirements.
Results
diffusion coefficient D (m²/s)
Sample size or count used in the calculation.
time to diffuse 100 nm (μs)
The computed duration or time value.
rms displacement in 1 ms (nm)
ISP (specific impulse) — rocket engine efficiency in seconds. Higher ISP means more thrust per kilogram of propellant consumed.
D = kT / (3πηd)
Reference formula or conversion factor shown for context.