Enter the viscosity, terminal velocity, and density difference into the calculator to determine the Stokes radius of a particle in a fluid. The calculator helps in estimating the size of a spherical particle based on its settling velocity.

Stokes Radius Formula

The following formula is used to calculate the Stokes radius of a particle in a fluid:

r = √((9 * η * v) / (2 * g * (ρp - ρf)))

Variables:

  • r is the Stokes radius (m)
  • η is the dynamic viscosity of the fluid (Pa·s)
  • v is the terminal velocity of the particle (m/s)
  • g is the acceleration due to gravity (9.81 m/s²)
  • ρp is the density of the particle (kg/m³)
  • ρf is the density of the fluid (kg/m³)
  • ρp – ρf is the density difference between the particle and the fluid (kg/m³)

To calculate the Stokes radius, take the square root of the product of 9 times the dynamic viscosity of the fluid times the terminal velocity of the particle, divided by 2 times the acceleration due to gravity times the density difference between the particle and the fluid.

What is Stokes Radius?

Stokes radius is a measure of the effective size of a particle as it moves through a fluid. It is derived from Stokes’ law, which describes the force of viscosity on a spherical object moving through a fluid. The radius is particularly useful in fields such as sedimentology, hydrology, and biochemistry for understanding particle dynamics in a fluid medium.

How to Calculate Stokes Radius?

The following steps outline how to calculate the Stokes Radius:

  1. First, determine the dynamic viscosity of the fluid (η) in Pascal-seconds (Pa·s).
  2. Next, determine the terminal velocity of the particle (v) in meters per second (m/s).
  3. Next, determine the density difference between the particle and the fluid (ρp – ρf) in kilograms per cubic meter (kg/m³).
  4. Next, gather the formula from above.
  5. Finally, calculate the Stokes Radius (r) in meters (m).
  6. After inserting the variables and calculating the result, check your answer with the calculator above.

Example Problem:

Use the following variables as an example problem to test your knowledge.

dynamic viscosity of the fluid (η) = 0.001 Pa·s

terminal velocity of the particle (v) = 0.02 m/s

density difference between the particle and the fluid (ρp – ρf) = 2000 kg/m³