Microfluidic Flow Rate Calculator
Rectangular Channel
Circular Channel (Tubing)
Units: mPa·s (cP). Water ≈ 0.89 at 25°C
mbar
psi
Pa
atm
mm
cm
m
Units: Micrometers (μm)
Units: Micrometers (μm)
Calculation Results
Flow Rate (μL/min):
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Flow Rate (mL/hr):
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Hydraulic Resistance:
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Understanding Microfluidic Flow Rates
In the field of microfluidics, precise control of fluid flow is paramount for applications ranging from Lab-on-a-Chip (LOC) devices to organ-on-chip simulations. Because flow in these micron-scale channels is almost exclusively laminar, the relationship between pressure drop and flow rate can be determined using basic fluid dynamics principles derived from the Navier-Stokes equations.
The Physics: Poiseuille's Law
This calculator relies on the Hagen-Poiseuille equation for circular channels and the infinite plate approximation (with correction factors) for rectangular channels. The flow is assumed to be laminar (low Reynolds number), steady, and fully developed with a Newtonian fluid.
For Rectangular Channels:
Most microfluidic chips, fabricated via soft lithography or etching, have rectangular cross-sections. The flow rate ($Q$) is calculated using:
$Q \approx \frac{h^3 w \Delta P}{12 \mu L} \left[1 – 0.630 \frac{h}{w}\right]$
Where $h$ is the smaller dimension (height), $w$ is the larger dimension (width), $\Delta P$ is the pressure drop, $\mu$ is dynamic viscosity, and $L$ is channel length.
For Circular Channels (Tubing):
This geometry applies to capillaries and connecting tubing. The calculation is exact:
$Q = \frac{\pi d^4 \Delta P}{128 \mu L}$
Key Variables Affecting Flow
- Channel Dimension (h or d): Flow rate scales with the fourth power of the diameter (or the cube of the height in rectangular channels). A small change in channel size drastically impacts flow.
- Viscosity ($\mu$): The resistance to flow is directly proportional to fluid viscosity. Water is ~0.89 mPa·s at 25°C, while blood plasma is ~1.2 mPa·s.
- Pressure Drop ($\Delta P$): Flow rate is linearly proportional to the pressure applied by syringe pumps or pressure controllers.
How to Use This Calculator
- Select Geometry: Choose "Rectangular" for microfluidic chips or "Circular" for tubing/capillaries.
- Input Fluid Properties: Enter the dynamic viscosity (default is water at 25°C).
- Set Dimensions: Input the channel length and cross-sectional dimensions in micrometers ($\mu m$).
- Apply Pressure: Enter the pressure drop across the channel in your preferred unit (mbar, psi, etc.).
This tool is essential for designing microfluidic circuits, predicting shear stress, and ensuring pumps are configured correctly for biological experiments.