1. What is the Diffusion Constant?

The diffusion constant (D) quantifies how quickly particles diffuse through a medium at a given temperature. It's a fundamental parameter in understanding Brownian motion and transport phenomena in physics, chemistry, and biology.

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 of the fluid (Pa·s)
• \( r \) — Radius of the spherical particle (m)

Explanation: The equation relates the diffusion constant to temperature, viscosity, and particle size, showing that smaller particles diffuse faster in less viscous media at higher temperatures.

3. Importance of Diffusion Constant

Details: The diffusion constant is crucial for understanding processes like chemical reactions, biological transport, material science, and environmental processes. It helps predict how quickly molecules will spread in a given medium.

4. Using the Calculator

Tips: Enter temperature in Kelvin, viscosity in Pascal-seconds (Pa·s), and particle radius in meters. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for diffusion constants?
A: In water at room temperature, small molecules have D ≈ 10⁻⁹ m²/s, while larger molecules like proteins have D ≈ 10⁻¹¹ m²/s.

Q2: What are the limitations of the Stokes-Einstein equation?
A: It assumes spherical particles, continuum fluid, no particle-particle interactions, and no-slip boundary conditions.

Q3: How does temperature affect diffusion?
A: Diffusion increases with temperature (D ∝ T) as higher thermal energy drives more vigorous particle motion.

Q4: What's the difference between D and the diffusion rate?
A: D is a material property, while diffusion rate depends on D and the concentration gradient (Fick's first law).

Q5: Can this be used for gases?
A: The equation is primarily for liquids. Gas diffusion is better described by kinetic theory equations.