How To Calculate Diffusivity

Stokes-Einstein Equation:

\[ D = \frac{k T}{6 \pi \mu r} \]

Boltzmann Constant (k):

J/K

Temperature (T):

Viscosity (μ):

Pa·s

Radius (r):

Diffusivity (D):

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1. What is the Stokes-Einstein Equation?

The Stokes-Einstein equation relates the diffusivity of spherical particles through a liquid with low Reynolds number to temperature, viscosity, and particle radius. It provides a fundamental relationship in statistical mechanics and fluid dynamics.

2. How Does the Calculator Work?

The calculator uses the Stokes-Einstein equation:

\[ D = \frac{k T}{6 \pi \mu r} \]

Where:

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

Explanation: The equation describes how the diffusion coefficient depends on temperature and inversely on viscosity and particle size.

3. Importance of Diffusivity Calculation

Details: Diffusivity calculations are crucial for understanding mass transfer processes, predicting reaction rates, designing separation processes, and studying biological transport phenomena.

4. Using the Calculator

Tips: Enter temperature in Kelvin, viscosity in Pascal-seconds, and radius in meters. The Boltzmann constant is pre-filled with its standard value but can be adjusted if needed.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusivity?
A: Diffusivity values typically range from 10⁻⁹ to 10⁻¹¹ m²/s for small molecules in liquids, and even smaller for larger particles.

Q2: When is the Stokes-Einstein equation applicable?
A: The equation is valid for spherical particles in continuum fluids where the particle size is much larger than the solvent molecules.

Q3: What are the limitations of this equation?
A: The equation may not be accurate for very small particles, non-spherical particles, or in systems with significant particle-solvent interactions.

Q4: How does temperature affect diffusivity?
A: Diffusivity increases with temperature due to decreased viscosity and increased thermal energy of molecules.

Q5: Can this equation be used for gases?
A: While the Stokes-Einstein equation is primarily for liquids, similar principles apply to gases though different equations are typically used.