Calculator Inputs
Example Data Table
| Scenario | Inputs | Output D (m²/s) | Notes |
|---|---|---|---|
| Fick (membrane) | J = 1.2×10⁻⁶ mol/(m²·s), |dC/dx| = 400 mol/m⁴ | 3.0×10⁻⁹ | D = J/|dC/dx| |
| Stokes (nanoparticle) | T = 298.15 K, η = 1 cP, r = 1 nm | 2.18×10⁻¹⁰ | Thermal diffusion in liquid |
| MSD (tracking) | MSD = 2.5 µm², d = 2, t = 30 s | 2.08×10⁻¹⁴ | D = MSD/(2·d·t) |
Formula Used
1) Fick’s first law (steady state)
For one-dimensional diffusion, molar flux is J = −D·(dC/dx). Using magnitudes, D = J / |dC/dx|.
2) Stokes–Einstein (Brownian diffusion)
For spherical particles in a Newtonian fluid, D = kB·T / (6π·η·r), where kB is Boltzmann’s constant.
3) Mean-square displacement (single-particle tracking)
In d dimensions, MSD = 2·d·D·t. Rearranged: D = MSD / (2·d·t).
4) Porous correction (effective diffusivity)
A common engineering approximation is Deff = D·(ε/τ), using porosity ε and tortuosity τ.
5) Arrhenius temperature scaling
If diffusion follows an activation barrier, ln(D2/D1) = −Ea/R·(1/T2 − 1/T1). This helps normalize results between temperatures.
How to Use This Calculator
- Select the method that matches your measurements (flux, particle tracking, or viscosity-based).
- Enter values with their units; the calculator converts them internally to SI.
- Optionally add porosity and tortuosity to estimate an effective diffusivity.
- To compare temperatures, provide activation energy and a target temperature.
- Click calculate to see results above, then export CSV or PDF.
Always verify inputs; real systems may behave differently experimentally.
Professional Article: Interpreting Mass Diffusivity
1) Why diffusivity matters in chemical systems
Mass diffusivity links microscopic motion to macroscopic transport. It governs membrane separation, drug release, corrosion, crystallization, and reactor selectivity. A reliable D helps you estimate time-to-mix, boundary-layer resistance, and concentration profiles before running expensive experiments.
2) Typical ranges you should expect
Order-of-magnitude checks prevent unit mistakes. In gases at ambient conditions, many small molecules have D around 10⁻⁵ m²/s. In liquids, solutes often fall near 10⁻¹⁰ to 10⁻⁹ m²/s. In viscous media and polymers, effective values can drop below 10⁻¹² m²/s. For electrolytes, ion pairing and hydration can shift these ranges noticeably.
3) Choosing a method that matches your measurements
Use Fick’s law when you measured flux and a concentration gradient across a known path length. Use Stokes–Einstein when the species behaves like a Brownian particle in a Newtonian fluid and you know viscosity and hydrodynamic size. Use MSD when you have particle trajectories or imaging-derived displacements.
4) Unit discipline: where errors usually happen
Diffusivity has units of area per time. The calculator converts inputs to SI to reduce mismatches, but gradients are a frequent trap: if concentration is mol/m³, then dC/dx is mol/m⁴. Also confirm whether a size input is radius, not diameter.
5) Temperature effects and activation energy
Diffusion often accelerates with temperature. With Arrhenius scaling, a moderate activation energy (for example 20–60 kJ/mol) can change D by multiples over a 20–40 °C shift. Normalizing D to a target temperature improves comparisons across runs and datasets.
6) Porous media: turning D into Deff
In catalysts, electrodes, and packed beds, tortuous pores slow transport. A common approximation is Deff = D·(ε/τ). Higher porosity increases the accessible cross-section, while higher tortuosity increases path length. This correction is a practical first pass for design calculations.
7) Data quality checks for experimental workflows
Prefer steady-state gradients for Fick’s law, stable viscosity for Stokes–Einstein, and sufficiently long tracks for MSD. Repeat measurements to quantify spread, and document temperature, solvent composition, and ionic strength. When D changes unexpectedly, re-check calibration and sample preparation.
8) Reporting results for audits and reproducibility
Exporting a consistent record supports lab notebooks, QA reviews, and process validation. Report D in both m²/s and cm²/s, list the method used, and include key inputs and assumptions. This calculator’s CSV and PDF outputs make that documentation fast and standardized.
FAQs
1) What does mass diffusivity represent?
It is a proportionality constant that relates concentration gradients to diffusive flux. Larger values mean faster spreading of a species through a phase under the same driving gradient.
2) Which method should I select?
Pick Fick’s law for measured flux and gradient. Choose Stokes–Einstein for temperature, viscosity, and particle size in a fluid. Use MSD when you have displacement versus time from tracking or microscopy.
3) Why do I get an unusually large or small D?
Outliers usually come from unit mistakes, wrong length scale for gradients, or using diameter instead of radius. Compare your value with expected ranges for gases, liquids, and polymers before trusting the result.
4) What is the difference between D and Deff?
D is the intrinsic diffusivity in the fluid phase. Deff accounts for porous restrictions using porosity and tortuosity, reflecting slower net transport through winding, partially blocked paths.
5) Is Stokes–Einstein always valid?
It works best for spherical particles in Newtonian fluids at low Reynolds number. Strong interactions, non-spherical shapes, crowded environments, or non-Newtonian fluids can cause deviations from the simple prediction.
6) How should I use Arrhenius scaling?
Provide an activation energy and a target temperature to scale a reference diffusivity to new conditions. This is useful for comparing experiments run at different temperatures or for normalizing literature values.
7) What units are recommended for reporting?
m²/s is the SI standard and is preferred for modeling. cm²/s is common in older literature. Reporting both, along with method and conditions, makes results easier to interpret across disciplines.
Export, verify, and report diffusivity results with full confidence.