Reynolds Number Calculator
Determine flow regime in microfluidic channels. Calculate the Reynolds number and Dean number for curved channels. Predict whether your flow is laminar, turbulent, or creeping.
Channel & Fluid Parameters
For spiral or serpentine channels. Leave blank for straight channels.
Result
| Parameter | Value |
|---|---|
| Channel width | 100 µm |
| Channel height | 50 µm |
| Flow rate | 10 µL/min |
| Density (ρ) | 998.2 kg/m³ |
| Dynamic viscosity (µ) | 0.001002 Pa·s |
| Hydraulic diameter (Dh) | 66.6667 µm |
| Average velocity (v) | 0.033333 m/s |
| Reynolds number (Re) | 2.2138 |
Understanding Reynolds Number in Microfluidics
The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in different fluid flow regimes. It compares the relative magnitude of inertial forces to viscous forces, making it the single most important number for understanding microfluidic flow behavior.
The Equation
where ρ is fluid density (kg/m³), v is average velocity (m/s), Dh is hydraulic diameter (m), and µ is dynamic viscosity (Pa·s).
Why Microfluidic Flows Are Almost Always Laminar
Most microfluidic applications operate at Re ≪ 100 because:
- Channels are tiny (10–500 µm), making Dh very small
- Flow rates are low (nL/min to µL/min) to conserve reagents and control dwell times
- Working fluids are typically water or oil, both with modest viscosity
The result: laminar flow dominates, enabling precise, predictable, and reproducible mixing and reaction control.
Implications for Mixing
In laminar flow, fluids mix only by diffusion, not by turbulent eddies. This means:
- Mixing time depends on the diffusion coefficient and channel dimensions
- Thin diffusion layers form at fluid interfaces
- Passive mixing structures (herringbone, staggered grooves) or active mixing (electrokinetic, acoustic) are often necessary
Dean Number for Curved Channels
In spiral or serpentine channels, Dean flow (secondary circulation) enhances mixing. The Dean number (De) quantifies this effect:
where Ris the radius of curvature. Higher Dean numbers indicate stronger secondary flows and better mixing in curved geometries. De > 50 typically enables significant mixing enhancement compared to straight channels.
Flow Regimes
- Re < 1 (Stokes/Creeping Flow): Viscous forces completely dominate. Motion is reversible and fully determined by pressure gradients.
- 1 ≤ Re ≤ 2300 (Laminar): Smooth flow in parallel layers. No mixing except by diffusion.
- Re > 2300 (Turbulent): Chaotic, three-dimensional flow with eddies. Rapid mixing but difficult to control.
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