Fick's First Law Calculator
Enter diffusion coefficient and concentration gradient to compute the diffusion flux J = −D·(dc/dx).
Input Data
Results
At a glance:Fick's first law of diffusion: the molar flux J (amount per area per time) is proportional to the concentration gradient, J = −D·(dc/dx), where D is the diffusion coefficient (m²/s) and dc/dx the gradient of concentration. The minus sign means diffusion goes from high to low concentration (down the gradient). Fick's second law (∂c/∂t = D·∂²c/∂x²) describes how concentration evolves. D increases with temperature (Arrhenius) and is larger in gases than liquids or solids. Applications span semiconductor doping, drug release, lung gas exchange and corrosion.
Formula
Fick's first law: J = −D·(dc/dx)
Fick's second law: ∂c/∂t = D·∂²c/∂x²
$$J = -D \frac{\partial C}{\partial x}, \quad \frac{\partial C}{\partial t} = D \frac{\partial^2 C}{\partial x^2}$$How to Use
- Enter the diffusion coefficient D (m²/s).
- Enter the concentration gradient dc/dx (mol/m⁴).
- The calculator returns the flux J.
Case Studies
Oxygen through membrane
D = 2×10⁻⁹ m²/s, gradient = −1×10³ mol/m⁴.
J = −2e-9×(−1e3) = 2×10⁻⁶ mol/(m²·s).
Steady flux into lower-concentration side.
FAQ
Why the negative sign?
Diffusion carries material from high to low concentration, opposite to the gradient direction (which points toward increasing c). The negative sign gives a positive flux down-gradient.
What affects D?
Temperature (higher T → larger D), medium (gas > liquid > solid), and the diffusing species size. In gases D ~ 10⁻⁵ m²/s, liquids ~10⁻⁹, solids much smaller.
Related Tools
References
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.