Mixing Time in Bioreactor Calculator

Calculation setup

Choose a method, then enter vessel and process data.

Show advanced inputs

Calculation method

Target homogeneity (%)

Estimated uncertainty (±%)

Dimensionless method

Dimensionless mixing time, N·tₘ

Use a value matching the chosen impeller, geometry, regime, and homogeneity target.

Pumping and turnover method

Required tank turnovers

Power-density correlation

Power source

Measured shaft power

Power unit

Correlation coefficient, K

Tank diameter exponent, a

Power-density exponent, b

Experimental tracer analysis

Tracer data: time, reading

Import CSV or text

Final-value tolerance (±%)

Required stable duration (s)

Minimum stable samples

Initial value source

Manual initial value

Final value source

Manual final value

Sensor location

Tracer measurement

Scale-up comparison

Scale-up criterion

Custom speed exponent

Reference mixing time (s)

Reference working volume

Target working volume

Reference tank diameter

Target tank diameter

Reference impeller diameter

Target impeller diameter

Reference impeller speed

Mixing-time tank exponent

Mixing-time power exponent

Reference density

Target density

Reference viscosity

Target viscosity

Vessel and operating conditions

Total vessel volume

Working liquid volume

Volume unit

Tank internal diameter

Liquid height

Length unit

Bottom shape

Number of baffles

Baffle width

Draft tube

Process mode

Impeller and agitation

Impeller type

Impeller diameter

Rotational speed

Speed unit

Impeller stages

Bottom clearance

Impeller stage spacing

Power number, Np

Pumping number, NQ

Flow direction

Blade count

Blade angle (degrees)

Fluid properties and rheology

Fluid density

Density unit

Dynamic viscosity

Viscosity unit

Temperature (°C)

Rheology model

Consistency index

Flow behaviour index

Solids concentration (%)

Biomass concentration (g/L)

Aeration and correction factors

Operating condition

Gas flow rate

Gas-flow unit

Sparger type

Gassed power factor

Gassed pumping factor

Overall user correction factor

Gravity (m/s²)

Formula used

Dimensionless method: tₘ = (N·tₘ) / N Pumping method: Q = NQ·N·D³ and tₘ = K·V / Q Power method: P = Np·ρ·N³·D⁵ and tₘ = K·Tᵃ·(P/V)ᵇ Reynolds number: Re = ρ·N·D² / μ Tip speed: u = π·D·N Froude number: Fr = N²·D / g Superficial gas velocity: ug = Qg / A

How to use this calculator

Select the method matching your available data.
Choose consistent units for volume, length, speed, density, and viscosity.
Enter vessel, impeller, fluid, and aeration conditions.
Use advanced mode for corrections, rheology, scale-up, and tracer controls.
Review every warning before using the result for design decisions.
Export the result table, chart, and assumptions for documentation.

Example data

Example	Volume	Tank	Impeller	Speed	Suggested method
Lab stirred tank	10 L	0.22 m	0.075 m hydrofoil	300 rpm	Dimensionless
Pilot bioreactor	100 L	0.50 m	0.17 m pitched blade	180 rpm	Pumping
Production vessel	1,000 L	1.00 m	0.35 m hydrofoil	120 rpm	Power density
Tracer test	Measured	Measured	Installed	Recorded	Tracer data

Saved calculation history

Date	Method	Mixing time	Status
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Frequently asked questions

What is mixing time in a bioreactor?

It is the time needed for a measurable addition to become sufficiently uniform throughout the liquid.

How is mixing time measured?

A tracer is added, then sensors track conductivity, pH, colour, fluorescence, temperature, or concentration until readings stabilise.

What does 95% mixing mean?

It usually means the measured signal has entered a band representing five percent deviation from its final value.

How does impeller speed affect mixing time?

Higher speed generally increases pumping and turbulence, but the final relationship depends on flow regime and vessel geometry.

How does viscosity affect mixing?

Higher viscosity reduces turbulence and circulation, often increasing mixing time and changing the valid impeller correlation.

Why does aeration change mixing time?

Gas can reduce effective power and pumping, alter circulation loops, and create impeller loading or flooding conditions.

What is dimensionless mixing time?

It is the product of rotational speed and mixing time, allowing comparison across speeds under similar hydrodynamic conditions.

How does impeller diameter affect mixing?

Diameter strongly affects pumping and power because these terms contain the third and fifth powers of impeller diameter.

What differs between mixing and turnover time?

Turnover time describes one theoretical vessel-volume circulation, while mixing time may require several circulations and local dispersion.

Which scale-up criterion should be used?

Choose the criterion protecting the most important process limitation, then review shear, power, oxygen transfer, and circulation together.

Why can experimental and calculated results differ?

Probe position, tracer injection, vessel internals, gas holdup, rheology, dead zones, and correlation limits can shift results.

Engineering note: This tool provides screening estimates, not equipment certification. Confirm correlations with vendor data, pilot tests, or validated computational and experimental studies before final design.