1. What is the Stokes-Einstein Equation?

The Stokes-Einstein equation relates the diffusion coefficient of spherical particles through a liquid with low Reynolds number to temperature, viscosity, and particle radius. It's fundamental in understanding Brownian motion and particle dynamics in fluids.

2. How Does the Calculator Work?

The calculator uses the Stokes-Einstein equation:

Where:

• \( D \) — Diffusion coefficient (m²/s)
• \( k \) — Boltzmann constant (1.380649 × 10⁻²³ J/K)
• \( T \) — Absolute temperature (K)
• \( \eta \) — Dynamic viscosity (Pa·s)
• \( r \) — Radius of spherical particle (m)

Explanation: The equation describes how particles diffuse through fluids, with larger particles diffusing more slowly and higher temperatures increasing diffusion rates.

3. Importance of Diffusion Coefficient

Details: The diffusion coefficient is crucial in many scientific fields including chemistry, physics, biology, and engineering. It helps predict how substances will spread in solutions, which is vital for processes like drug delivery, chemical reactions, and material science.

4. Using the Calculator

Tips: Enter temperature in Kelvin, viscosity in Pascal-seconds, and radius in meters. All values must be positive. For best results, use SI units as specified.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusion coefficients?
A: Diffusion coefficients typically range from 10⁻⁹ to 10⁻¹¹ m²/s for small molecules in liquids at room temperature.

Q2: What are the limitations of the Stokes-Einstein equation?
A: It assumes spherical particles, dilute solutions, and no particle-particle interactions. It may not be accurate for very small particles or in complex fluids.

Q3: How does temperature affect diffusion?
A: Diffusion increases with temperature as molecules have higher kinetic energy, overcoming viscous drag more easily.

Q4: What is the significance of the Boltzmann constant?
A: The Boltzmann constant relates the average kinetic energy of particles to the temperature of the system.

Q5: Can this equation be used for gases?
A: While the equation is primarily for liquids, similar principles apply to gases though different equations may be more appropriate.