The Stokes radius is a measure of the size of a spherical particle in a fluid, based on its terminal velocity in the fluid. It is particularly useful in fields such as biology, chemistry, and fluid dynamics for understanding particle behavior and interactions.

## Formula

The Stokes radius (rrr) can be calculated using the formula:

r=9⋅η⋅v2⋅g⋅(ρp−ρf)r = \sqrt{\frac{9 \cdot \eta \cdot v}{2 \cdot g \cdot (\rho_p – \rho_f)}}r=2⋅g⋅(ρp−ρf)9⋅η⋅v

where:

- rrr is the Stokes radius (meters)
- η\etaη is the viscosity of the fluid (Pa·s)
- vvv is the terminal velocity of the particle (m/s)
- ggg is the acceleration due to gravity (9.81 m/s²)
- ρp\rho_pρp is the density of the particle (kg/m³)
- ρf\rho_fρf is the density of the fluid (kg/m³)

## How to Use

To use the Stokes Radius Calculator:

- Enter the viscosity of the fluid in Pascal-seconds (Pa·s).
- Enter the terminal velocity of the particle in meters per second (m/s).
- Enter the density difference between the particle and the fluid in kilograms per cubic meter (kg/m³).
- Click the “Calculate” button.
- The Stokes radius of the particle will be calculated and displayed in meters (m).

## Example

Suppose we have a particle in a fluid with the following properties:

- Viscosity = 0.002 Pa·s
- Terminal velocity = 0.1 m/s
- Density difference = 50 kg/m³

Using the calculator:

- Enter 0.002 for viscosity.
- Enter 0.1 for terminal velocity.
- Enter 50 for density difference.
- Click “Calculate.”
- The Stokes radius will be calculated as approximately 0.018 meters.

## FAQs

**What is the Stokes radius?**- The Stokes radius is the radius of a spherical particle in a fluid, calculated based on its terminal velocity and fluid properties.

**Why is the Stokes radius important?**- It helps in determining the size of particles in suspension and understanding their behavior in fluids.

**Can the Stokes radius be used for non-spherical particles?**- The Stokes radius formula assumes spherical particles. For non-spherical particles, different calculations or models may be required.

**What are the units of Stokes radius?**- Stokes radius is measured in meters (m).

**How does density difference affect the Stokes radius?**- A greater density difference between the particle and the fluid results in a larger Stokes radius.

**Is the Stokes radius the same as hydrodynamic radius?**- No, they are different. Hydrodynamic radius considers the overall size of a particle’s diffusion in a fluid, whereas Stokes radius specifically calculates size based on terminal velocity.

**Can Stokes radius be used in biological sciences?**- Yes, it is commonly used to determine the size of macromolecules and particles in biological fluids.

**What is the significance of the terminal velocity in Stokes radius calculation?**- Terminal velocity indicates the speed at which a particle falls through a fluid under gravity, crucial for determining its Stokes radius.

**Does the calculator account for all factors influencing particle size in fluids?**- The calculator focuses on the basic parameters required for Stokes radius calculation. For specific applications, additional factors may need consideration.

**Can Stokes radius be experimentally measured?**- Yes, experimental methods involve observing the behavior of particles in fluid flow and relating it to their properties and terminal velocities.

## Conclusion

The Stokes Radius Calculator provides a straightforward method for determining the size of particles in fluids based on their terminal velocities and fluid properties. By using the formula and inputting the relevant data, users can quickly obtain the Stokes radius, facilitating research and analysis in various scientific disciplines.