Free Online Mixing Time Calculator | Impeller Blend Time & Reynolds

Vessel geometry

Tank diameter D0.50 m

Liquid height H0.75 m

Impeller diameter d0.18 m

Agitation

Impeller type

Agitation speed N150 rpm

RPM

No. of impellers1

qty

Fluid properties

Density ρ1000 kg/m³

kg/m³

Viscosity μ1.0 mPa·s

mPa·s

Aeration0.00 vvm

vvm

📊 Hydrodynamics & Blend Time Diagnostic Results LIVE SIMULATION

95% Blend Time (θ95)
—
seconds

Impeller Reynolds (Re)

—

dimensionless

Specific Power (P/V)

—

W/m³

Impeller Tip Speed (u_tip)

—

m/s

Total Agitation Power

—

Watts (W)

Vessel & Impeller Geometric Parameters

Working Volume V—

Aspect Ratio (H/D)—

Impeller to Tank Ratio (d/D)—

Power Number (Np)—

Tip Shear Stress Assessment—

Model Physics & Upstream Handoff

Nienow & Ruszkowski blend time model. Dynamically corrected for transitional flow regime (Re < 10⁴) and laminar regime (Re < 10). Multi-impeller staging correction: θ95 ∝ n^–0.5. Aeration drag penalty: ×(1 + 0.38 vvm).

UPSTREAM WORKFLOW HANDOFF ➔ STEP 4
Computed specific power dissipation (P/V) and agitation speed hand off directly into the Oxygen Mass Transfer (kLa) Predictor (Step 4).

📚 Stirred-Tank Mixing & Homogenization Blend Time (θ95) Guide Upstream Bioprocess • Step 3 of 7

Theoretical Principles & Engineering Fundamentals

Rapid homogenization in stirred bioreactors is essential to eliminate localized nutrient hot-spots, pH extremes near acid/base feed ports, and dissolved gas concentration gradients. 95% blend time ($ heta_{95}$) characterizes the time required for an injected tracer to reach $\pm 5\%$ homogenization throughout the vessel volume.

For fully baffled turbulent stirred tanks ($Re > 10^4$), dimensionless mixing time $N \cdot heta_{95}$ is governed by the Grenville correlation:

$$N imes heta_{95} = rac{5.2}{N_p^{1/3}} imes \left(rac{T}{D} ight)^2$$

Governing Equations & Mathematical Formulations

Grenville 95% Blend Time \theta_{95} = \frac{5.2}{N \times N_p^{1/3}} \times \left(\frac{T}{D}\right)^2

Estimates 95% homogenization time where $N_p$ is impeller power number, $T$ is tank diameter, and $D$ is impeller diameter.

Impeller Reynolds Number Re = \frac{\rho \times N \times D^2}{\mu}

Defines hydrodynamic flow regime: Laminar ($Re < 10$), Transitional ($10 \le Re \le 10^4$), Turbulent ($Re > 10^4$).

Impeller Pumping Rate Q = N_q \times N \times D^3

Volumetric flow circulating through the impeller swept volume, where $N_q$ is the flow number.

Industrial Benchmark Data & Parameter Reference

Impeller Style	Power Number (Np)	Flow Number (Nq)	Primary Flow Vector
Rushton Turbine (6-Blade Flat)	5.20	0.75	Radial (High Shear / Gas Dispersion)
Pitched Blade Turbine (4-Blade 45°)	1.27	0.79	Axial / Mixed Flow
Marine Propeller / Hydrofoil	0.35 – 0.55	0.55	Axial (High Pumping / Low Shear)
Maxflo / Elephant Ear	0.75	0.85	Axial (Biopharma Cell Culture)

Frequently Asked Questions (Bioprocess Engineering FAQ)

What is the typical mixing time for commercial 10,000L bioreactors?

While 5L benchtop bioreactors achieve $ heta_{95} < 5$ seconds, 10,000L to 20,000L vessels typically exhibit mixing times of 40 to 120 seconds due to fluid transit limitations.

How do baffles prevent vortex formation?

Standard fermenters utilize 4 vertical wall baffles with width $W = T/10$ to $T/12$, which break rotational swirl and convert angular momentum into vertical and radial recirculation loops.

Why does high mixing time trigger overflow metabolism?

Slow blend times cause concentrated substrate zones near feed pipes. Cells entering these zones experience localized glucose saturation, inducing Crabtree overflow metabolism and producing toxic acetate.

BioFlo Bioprocess Engineering Network

This calculator is maintained by the simulation engineers at BioFlo Bioprocess Engineering. We specialize in industrial bioreactor design, computational fluid dynamics (CFD) modeling, oxygen mass transfer optimization, and custom digital twin development for pharmaceutical fermentation plants.

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