Nanopore Flow Calculator
Flow rate through nanopores with slip correction.
About this calculator
This calculator applies the Hagen-Poiseuille equation — the standard model for slow, laminar (viscous) flow through a cylindrical channel — to estimate volumetric flow rate through a single nanopore, scaled by the fourth power of pore diameter: Q = πd⁴ΔP/(128ηL). Because flow scales with d⁴, small changes in pore diameter swing the result enormously, which is exactly why nanopore diameter is the dominant lever in real membrane and nanofluidic design. A slip-length correction factor, 1 + 8λ/d, is then applied on top of the no-slip result to account for hydrophobic pore walls (like carbon nanotubes) that let fluid slide rather than stick at the boundary — set slip length to zero for hydrophilic pores where the standard no-slip assumption holds. The calculator also reports average velocity, Reynolds number, and an estimated molecules-per-second throughput.
The Reynolds number is derived directly from your entered viscosity (Re = 1000·v·d/η), so it correctly reflects whatever fluid you're modeling — it's included specifically to confirm the laminar-flow assumption underlying Hagen-Poiseuille, and at the nanoscale it should always come out far below 1, with a much larger value signaling the model no longer applies. The molecules-per-second figure is different: it assumes the fluid is water regardless of the viscosity you entered, converting flow rate into a molecule count using water's molecular volume (~3.0×10⁻²⁹ m³) and density (1000 kg/m³). So if you're modeling a non-aqueous fluid, trust the flow rate, velocity, and Reynolds number outputs, but treat the molecules-per-second figure as approximate — or ignore it entirely.
Inputs
Results
Flow Rate (m³/s)
0
Slip Enhancement Factor
1
How to Use This Calculator
- Enter nanopore diameter (nm) and pore length (nm) for your membrane or synthetic nanopore.
- Set the applied pressure difference (Pa) and solution viscosity (mPa·s).
- Enter slip length (nm) — positive values indicate hydrophobic pore walls that enhance flow.
- Review volumetric flow rate (m³/s and fL/s), average velocity (m/s), slip enhancement factor, and Reynolds number.
- Reynolds numbers well below 1 confirm laminar Hagen-Poiseuille flow is valid for this calculation.
What each input means
- Pore Diameter (nm)
- Nanopore diameter.
- Pore Length (nm)
- Length of the nanopore channel.
- Pressure Difference (Pa)
- Driving pressure across the pore. 1 atm = 101325 Pa.
- Viscosity (mPa·s)
- Fluid viscosity. Water at 25°C = 0.89.
- Slip Length (nm)
- Hydrophobic slip. CNT: ~50 nm, hydrophilic: 0.
What each result means
- Flow Rate (m³/s)
- Volumetric flow through one pore.
- Flow Rate (fL/s)
- Flow in femtoliters per second.
- Avg. Velocity (m/s)
- Mean fluid velocity in the pore.
- Slip Enhancement Factor
- Flow increase from wall slip.
- Reynolds Number
- Re << 1 = laminar (expected at nanoscale).
- Molecules/s
- Water molecules passing through per second.
How this is calculated
Worked example, using the default values
- Identify Input Parameters4 parametersPore Diameter (nm) = 10, Pore Length (nm) = 100, Pressure Difference (Pa) = 100000, Viscosity (mPa·s) = 0.89 = 5 input(s) provided
- Calculate Flow RateFlow Rate = parseFloat(qSlip.toPrecision(4))2.758e-19 = 2.758e-19
- Calculate Slip Enhancement FactorSlip Enhancement Factor = 1 + 8 * lambda / d1 = 1
- Calculate Flow RateFlow Rate = parseFloat(qFemtoLitersPerSec.toPrecision(4))0.2758 = 0.2758
- Calculate Avg. VelocityAvg. Velocity = parseFloat(avgVelocity.toPrecision(4))0.003511 = 0.003511
Engine last updated . Checked against 3 independently-derived tests — how we verify calculators. Built by Paul Gunder, a software engineer, not a licensed financial, medical, or legal professional.
Frequently Asked Questions
Why does doubling the pore diameter increase flow by 16 times instead of 2 times?
Hagen-Poiseuille flow scales with the fourth power of diameter (Q = πd⁴ΔP/(128ηL)), so doubling d multiplies flow by 2⁴ = 16. That's why pore diameter is by far the dominant lever in this calculator's output — a small measurement error or fabrication variance in diameter swings the predicted flow rate far more than an equivalent error in pressure, viscosity, or pore length.
What does the slip length input actually change, and when should I set it to zero?
Slip length (λ) feeds into the enhancement factor 1 + 8λ/d, which multiplies the no-slip Hagen-Poiseuille flow rate upward to account for fluid sliding rather than sticking at hydrophobic pore walls, like carbon nanotube channels. Set it to zero for hydrophilic pores (most oxide or biological nanopores), where the standard no-slip boundary condition holds and the enhancement factor collapses to exactly 1.
Why does the Reynolds number matter here, and what should it look like?
The calculator computes Re = 1000·v·d/η directly from your entered viscosity and the derived velocity, specifically to check the laminar-flow assumption that Hagen-Poiseuille depends on. At nanopore scales it should come out far below 1; if you enter values that push Re toward or above 1, the laminar assumption is breaking down and the flow-rate result is no longer reliable.
Can I trust the molecules-per-second output if I'm not modeling water?
No — that figure always assumes the fluid is water, converting the flow rate to a molecule count using water's molecular volume (~3.0×10⁻²⁹ m³) regardless of what viscosity you entered. If you're modeling a non-aqueous fluid, rely on the flow rate, velocity, and Reynolds number outputs instead, since those correctly reflect your entered viscosity, and treat molecules-per-second as approximate or irrelevant.
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