The Diffusion Coefficient Calculator is a scientific tool that calculates the rate at which molecules or particles spread in a medium over time. It is essential in fields such as chemical engineering, environmental science, materials science, and biology to understand molecular transport phenomena.
This calculator quickly computes the diffusion coefficient (D) based on measurable parameters, eliminating complex manual calculations and enabling engineers and researchers to optimize processes effectively.
The diffusion coefficient (D) quantifies how fast a substance spreads in another substance due to molecular motion. It is expressed in units of m²/s and depends on factors like temperature, pressure, medium viscosity, and particle size.
Understanding diffusion is key for processes like gas separation, drug delivery, pollutant transport, and heat and mass transfer.
The diffusion coefficient depends on the type of medium and the model used. Common formulas include:
1. For gases (Chapman-Enskog Equation):
D_AB = (0.001858 * T^1.5) / (P * σ_AB^2 * Ω_D) * sqrt(1/M_A + 1/M_B)
Where:
D_AB = diffusion coefficient of gas A in B (m²/s)
T = temperature (K)
P = pressure (atm)
σ_AB = collision diameter (Å)
Ω_D = collision integral (dimensionless)
M_A, M_B = molar masses of gases (g/mol)
2. For liquids (Stokes-Einstein Equation):
D = (k_B * T) / (6 * π * η * r)
Where:
k_B = Boltzmann constant (1.380649 × 10⁻²³ J/K)
T = absolute temperature (K)
η = dynamic viscosity of the liquid (Pa·s)
r = radius of the diffusing particle (m)
Highlighted Formula for Better User Experience:
D = (k_B × T) / (6 × π × η × r) [For liquid diffusion]
This frame makes the formula clearly visible to users.Example: Calculate the diffusion coefficient of a small molecule in water at 298 K, with:
Viscosity (η) = 0.001 Pa·s
Particle radius (r) = 1 × 10⁻⁹ m
Step 1: Use Stokes-Einstein equation
D = (1.380649 × 10⁻²³ × 298) / (6 × π × 0.001 × 1 × 10⁻⁹)
Step 2: Calculate
D ≈ 2.18 × 10⁻¹⁰ m²/s
Result: The diffusion coefficient is approximately 2.18 × 10⁻¹⁰ m²/s.