Bioreactor Mixing Time Calculator
Enter practical tank, impeller, fluid, and process values. The calculator estimates mixing time, Reynolds number, power draw, pumping flow, circulation time, and useful beginner guidance.
Example Data Table
| Case | Tank Diameter | Impeller Diameter | RPM | Viscosity | Expected Mixing Behavior |
|---|---|---|---|---|---|
| Small seed bioreactor | 0.60 m | 0.20 m | 220 | 1.0 cP | Fast turbulent mixing |
| Pilot fermenter | 1.20 m | 0.40 m | 180 | 1.2 cP | Balanced process mixing |
| Viscous broth | 1.50 m | 0.45 m | 120 | 25 cP | Slower transitional mixing |
| Aerated culture | 2.00 m | 0.65 m | 140 | 2.0 cP | Needs gas penalty review |
Formula Used
Impeller speed: N = RPM / 60
Reynolds number: Re = ρ × N × D² / μ
Power draw: P = Np × ρ × N³ × D⁵ × number of impellers × efficiency
Power per volume: P/V = power draw / working volume
Pumping flow: Q = Nq × N × D³ × number of impellers
Estimated mixing time:
tm = [K × (T/D)² × √(H/T) × baffle factor × gas penalty × viscosity penalty / √impellers] / N × safety factor
This is an educational empirical estimate. Real bioreactors need validation with tracer tests, conductivity tests, dissolved oxygen response, scale-down studies, and process-specific acceptance limits.
How to Use This Calculator
- Enter tank diameter and liquid height in meters.
- Add working volume in liters, or leave it blank.
- Enter impeller diameter, speed, power number, and flow number.
- Add broth density and viscosity.
- Select baffle condition, aeration penalty, and homogeneity target.
- Press the calculate button.
- Review mixing time, power, Reynolds number, and design note.
- Download the result as CSV or PDF for records.
Beginner Guide to Bioreactor Mixing Time
What Mixing Time Means
Mixing time is the time needed to make a tank nearly uniform after a change. That change may be a feed pulse, pH correction, antifoam addition, salt addition, or tracer injection. In a bioreactor, poor mixing can create zones. These zones may have different pH, oxygen, nutrients, or temperature. Cells can feel stress before sensors show it.
Why It Matters
Good mixing supports stable growth. It helps oxygen transfer. It spreads nutrients. It reduces local overdose during feeding. It also protects product quality. A short mixing time is not always best. Very high speed may damage shear sensitive cells. It may also increase foam, heat, and power cost.
Simple Idea Behind the Calculation
The calculator starts with tank geometry. It compares tank diameter with impeller diameter. A larger tank or smaller impeller usually increases mixing time. Speed then becomes important. Faster rotation lowers the time, but only within safe limits. The Reynolds number helps identify the flow condition. Water-like broth often reaches turbulent flow. Thick broth may stay transitional or laminar.
Power and Flow
Power number estimates the energy sent into the liquid. Flow number estimates how much liquid the impeller moves. These values depend on impeller type. Rushton turbines, pitched blade turbines, hydrofoils, and marine impellers behave differently. Use supplier data when available. Default values are only starting points.
Scale-Up Warning
A small flask or bench tank does not copy perfectly into a production vessel. Mixing time changes with geometry, impeller count, liquid height, gas rate, and viscosity. During scale-up, compare mixing time with oxygen transfer, tip speed, power per volume, heat removal, and shear limits. Use this page for early screening. Confirm important decisions with experiments.
Practical Use
Try a base case first. Then change one input at a time. Increase speed slowly. Try more impellers for tall tanks. Review baffles if swirling appears. Add a higher gas penalty for aerated runs. Use the safety factor when uncertainty is high. This method keeps the calculation simple, while still giving useful engineering direction.
FAQs
1. What is bioreactor mixing time?
It is the time required for liquid conditions to become nearly uniform after a feed, tracer, acid, base, or nutrient addition.
2. Is this calculator suitable for beginners?
Yes. It uses simple inputs and gives practical results. It also includes advanced factors for baffles, aeration, viscosity, and safety.
3. What Reynolds number should I expect?
Water-like broths often reach turbulent flow. Thick broths may become transitional or laminar, which usually increases mixing time.
4. Why does viscosity increase mixing time?
Higher viscosity resists motion. The impeller moves liquid less effectively, so concentration and temperature differences disappear more slowly.
5. Why are baffles important?
Baffles reduce swirling and improve top-to-bottom circulation. Poor baffling can create a vortex and increase practical mixing time.
6. Does aeration change mixing time?
Yes. Gas can reduce effective pumping and change power draw. Use a gas penalty when the culture is strongly aerated.
7. Can I use this for scale-up?
You can use it for early estimates. Final scale-up should include tracer tests, oxygen transfer checks, shear review, and process validation.
8. What safety factor should I use?
Use 1.10 to 1.30 for normal uncertainty. Use a higher value for unusual geometry, foaming, viscous broth, or limited test data.