Microfluidic Mixing Length Calculator

Calculate the mixing length and Péclet number for laminar-flow microfluidic mixers. Estimate how much channel length you need for diffusive mixing in T-junctions and similar geometries.

Channel & Flow Parameters

Channel width (µm)

Channel height (µm)

Flow rate (µL/min)

Diffusion coefficient (m²/s)

Current: 4.25 × 10⁻10 m²/s

Small molecules & dyes

Proteins

Macromolecules & particles

Results

Mixing Length (T-mixer)

39.216 mm

Péclet number: 784.31

Flow regime:

Convection-dominated (Pe > 100)

Parameter	Value
Cross-section area	5000 µm²
Average velocity	3333.33 µm/s
Péclet number	784.31
Mixing length	39.216 mm
Mixing time	11.765 s
Diffusion time (full width)	11.765 s

Suggestion:With Pe > 100, convection dominates and passive mixing is slow. Consider active mixing (electrokinetic, electrowetting) or passive designs with enhanced surface area (herringbone, staggered array, Dean flow in curved channels).

Disclaimer: This calculator uses idealized laminar-flow theory for rectangular channels. Real devices may have 3D effects, non-ideal geometries, and dead zones. Always validate with experiments or computational fluid dynamics (CFD).

About Mixing in Microfluidics

In laminar microfluidic flows, fluids move in parallel layers with little turbulent disruption. When two streams meet at a T-junction, mixing relies entirely on diffusion across the interface—not on turbulent eddies like in macroscale flows. The distance over which mixing occurs is called the mixing length.

The Pécelt Number

The dimensionless Péclet (Pe) number compares convection to diffusion:

Pe = v × w / D

where v is the average flow velocity, w is the characteristic length (channel width), and Dis the diffusion coefficient. When Pe >> 1, convection dominates; when Pe << 1, diffusion is fast relative to flow.

Mixing Length for T-Mixers

For a T-mixer with side-by-side laminar streams, the mixing length scales as:

L_mix ≈ v × w² / (2D) = Pe × w / 2

This is the downstream distance required for molecular diffusion to homogenize the two streams. For high Pe, this distance can become impractically long.

Strategies to Reduce Mixing Length

Decrease channel width or height: Smaller characteristic lengths dramatically reduce mixing distance.
Reduce flow rate: Lower velocities favor diffusion over convection.
Herringbone (staggered array) mixers: Angled grooves create chaotic advection, increasing interfacial area without turbulence.
Split-and-recombine (SAR): Divide, rearrange, and recombine streams multiple times to exponentially reduce unmixed regions.
Dean flow in curved channels: Weak secondary flows from curvature enhance mixing without active inputs.
Active mixing: Electrokinetic forcing, electrowetting, or acoustic actuation can stir fluids at high Péclet numbers.

Microfluidic Relevance

Mixing is a fundamental operation in microfluidic analytics, chemical synthesis, and cell assays. For example:

Droplet formation: Fast mixing of two immiscible phases creates stable emulsions.
Protein binding assays: Rapid mixing of antigen and antibody reduces assay times.
Reaction kinetics: Precise control of mixing timescales enables study of transient intermediates.
Cell biology: Delivering stimuli (drugs, oxygen, signaling molecules) to cells requires well-mixed streams.

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