Deborah Number Calculator

Formula used

The Deborah number measures how long a material “remembers” deformation compared to how fast the process acts. It is defined as:

De = λ / t_c

If the characteristic time is not known directly, you can estimate it using a representative length scale and velocity:

t_c = L / V

How to use this calculator

1. Enter the relaxation time λ for your material and select its unit.
2. Select an input mode: enter t_c directly, or use L and V.
3. Fill in the remaining fields and press Calculate.
4. The result appears above the form, with an interpretation label.
5. Use the download buttons to export CSV or PDF reports.

Deborah number in real processes

1) Why Deborah number matters

The Deborah number (De) compares a material’s relaxation time λ to a process time t_c. It helps you decide whether a material behaves more like a fluid that quickly forgets deformation, or a viscoelastic material that retains stress and structure during the experiment.

2) Key inputs and typical ranges

In many lab and production settings, λ can vary from milliseconds to minutes. Polymer solutions may show λ around 0.01–10 s, while polymer melts and structured fluids can reach 10–100+ s depending on temperature and molecular weight. Faster processes shrink t_c, increasing De.

3) Where relaxation time data comes from

Relaxation time is often inferred from rheology: oscillatory shear tests, stress relaxation experiments, or fitting viscoelastic models. If you have a spectrum of times, use a representative value such as the longest dominant mode when estimating memory effects.

4) Selecting a characteristic time

The best t_c matches the physics of your process: the period of oscillation, the inverse shear rate, the residence time in a channel, or the time scale of deformation in a forming step. A careful choice makes De more predictive and easier to compare across studies.

5) Using length and velocity to estimate time

When timing is not explicit, this calculator supports t_c=L/V. Choose L as a meaningful length scale (gap, nozzle diameter, feature size), and V as the characteristic speed. For example, L=0.10 m and V=0.02 m/s gives t_c=5 s.

6) Interpreting low, moderate, and high values

As a rule of thumb, De<0.1 indicates flow-dominated behavior with limited elastic memory, while De>10 suggests elasticity-dominated behavior where stress persists over the process. Values between 0.1 and 10 often show mixed effects such as shear thinning, recoil, or time-dependent recovery.

7) Practical examples you can benchmark

If λ=0.5 s and t_c=2 s, then De=0.25 and elastic effects are mild. If λ=12 s and t_c=0.8 s, then De=15 and memory effects can dominate, affecting extrusion swell, ink leveling, or filament stability in printing.

8) Common pitfalls and quality checks

Keep units consistent, avoid zero or negative inputs, and ensure L and V represent the same region of the flow. If De changes drastically with small parameter tweaks, revisit your t_c definition. Use the download reports to document assumptions and inputs for repeatability.

FAQs

1) What does the Deborah number represent?

It compares relaxation time to process time. Small values indicate quick relaxation during the process, while large values indicate persistent stress and stronger elastic memory effects.

2) Which input mode should I use?

Use direct t_c when you know the observation or deformation time. Use L/V when you can estimate time from a representative length scale and velocity.

3) Is Deborah number dimensionless?

Yes. Both λ and t_c are times, so their ratio cancels units and yields a dimensionless number suited for comparing different systems.

4) What is a good threshold for “high” Deborah number?

A common rule is De>10 for strong memory effects. The exact boundary depends on material model and experiment, but this threshold is a practical screening guideline.

5) How should I choose the length scale L?

Pick a physical feature that controls deformation or transport, such as a gap height, nozzle diameter, channel width, or characteristic microstructure size relevant to your flow.

6) Why do my results change a lot with small input changes?

Because De is a ratio. If t_c is very small, tiny changes can shift De significantly. Re-check your chosen time scale and measurement uncertainty.

7) Can I use this for non-viscoelastic fluids?

For Newtonian fluids, λ is not meaningful, so De is not informative. The metric is most useful for materials with measurable relaxation or recovery behavior.