Calculator
Use the method selector first. Then enter values in the active panel.
Plotly Graph
The graph updates after calculation and compares key inputs against the computed coefficient.
Example Data Table
| Case | Method | Primary Inputs | Calculated D | Interpretation |
|---|---|---|---|---|
| Lab Tracer A | Variance-Time | σ = 0.12, t = 15 | 0.000480 | Very low spreading |
| Membrane Test B | Flux-Gradient | J = 0.003, dC/dx = -0.75 | 0.004000 | Controlled transport |
| Column Flow C | Advection-Dispersion | Pe = 45, u = 0.09, L = 3.2 | 0.006400 | Moderate spreading |
Formula Used
1. Variance-Time Method: Use D = σ² / (2t). Here, σ is plume spread or standard deviation, and t is transport time.
2. Flux-Gradient Method: Use D = |J / (dC/dx)|. Here, J is mass flux, and dC/dx is concentration gradient.
3. Advection-Dispersion Method: Use D = uL / Pe. Here, u is average velocity, L is characteristic length, and Pe is Péclet number.
Choose a method that matches your experiment, model, or process data. Keep unit systems consistent before interpreting results.
How to Use This Calculator
- Select the method that matches your chemistry dataset.
- Enter the required values in the visible input boxes.
- Press the calculate button to generate the result.
- Review the dispersion coefficient and supporting indicators.
- Inspect the graph for a quick comparison view.
- Download the calculation summary as CSV or PDF.
Frequently Asked Questions
1. What does the dispersion coefficient describe?
It measures how quickly a substance spreads through a medium because of mixing, molecular motion, and transport effects. Higher values usually indicate stronger spreading.
2. Which method should I choose first?
Use the variance-time method for tracer spread data, the flux-gradient method for diffusion style measurements, and the advection-dispersion method when flow and Péclet values are known.
3. Why does the calculator use absolute value for flux-gradient results?
Flux and concentration gradients often carry opposite signs. Taking the absolute value keeps the reported coefficient positive and easier to compare across experiments.
4. What units should I enter?
Use one consistent unit system throughout the calculation. For example, if length is in meters and time is in seconds, dispersion will commonly appear in m²/s.
5. What is a good dispersion coefficient value?
There is no universal best value. Suitable ranges depend on the medium, solute, temperature, and transport conditions in your chemistry application.
6. Why is my Péclet number important?
The Péclet number compares advective transport to dispersive spreading. Large values often mean advection dominates, while smaller values suggest stronger dispersion influence.
7. Can I use this for column studies?
Yes. The calculator is useful for packed columns, tracer tests, membrane systems, and transport studies where dispersion estimates help interpret chemical movement.
8. Why export CSV or PDF?
Exports help with reporting, lab records, classroom work, and quick sharing. CSV supports spreadsheets, while PDF is useful for fixed summaries.