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The limits of analytical estimates

OpenChip’s flow numbers come from a one-dimensional network model. Each channel segment is a hydraulic resistance; the network is solved like a resistor network; per-segment quantities are derived from the resulting flows.

That is a good model. It is fast enough to update as you drag a node, it is transparent enough to check by hand, and for the question most people are asking — can my pump push this? — it is the right tool.

It is also not CFD, and the difference is worth understanding before you rely on a number.

Every one of these is genuinely assumed, and each fails somewhere:

Assumption Fails when
Fully developed laminar flow Near an inlet, or after a sharp change in section
Constant cross-section per sample Through a taper — sampled, so approximated
Newtonian fluid Blood at low shear, polymer solutions, cell suspensions
No-slip at the walls Essentially never fails at this scale
Perfect mixing at junctions Always — real junctions mix by diffusion like everything else
No entrance, bend or junction losses At every corner and every junction
Rigid channels Compliant tubing, thin-walled chips, high pressure
Single phase Droplet generators, anything with bubbles
Steady state During start-up, or with a pulsing pump

The velocity profile takes a distance to develop after an inlet or a change in section. The hydrodynamic entrance length is roughly

L_e ≈ 0.05 · Re · Dₕ

At Re ≈ 0.26 and Dₕ ≈ 0.6 mm, that is about 8 µm — utterly negligible.

This one you can usually ignore, and that is a genuine advantage of working at very low Re. It stops being negligible only if you push Re into the tens or hundreds.

Real flow loses pressure turning a corner and merging at a junction, beyond the straight-channel resistance of the same length. The model has none of this.

At low Re these losses are small relative to viscous drag along the channel — but they are not zero, and a serpentine with thirty-two corners accumulates them. The model under-predicts pressure drop on corner-heavy geometries.

Practically: treat a reported pressure on a serpentine or herringbone as a lower bound.

Dean vortices in a curved channel are not modelled. The spiral mixer relies on them entirely, and the Fluid tab will report its pressure drop and residence time correctly while saying nothing about the mixing that curvature buys.

The same applies to the herringbone: the model sees a channel with corners.

There is no species transport in the model at all. Junctions are assumed to mix perfectly and instantaneously, which is exactly wrong — real junctions mix by diffusion, over a length.

So the model cannot tell you whether your mixer mixes. It can tell you the residence time, and you can compare that against a diffusion time from Mixing without turbulence. That comparison is a decent design heuristic. It is not a prediction.

For a gradient generator, the model gives you the flow split, which is the thing that actually determines whether the concentration series is linear. That is the useful half.

No interfacial tension, no wetting, no droplets, no bubbles. See Droplet generation.

Roughly, for a typical straight-channel microfluidic design:

Quantity Confidence
Reynolds number Good — it is arithmetic on your geometry
Internal volume, residence time Good
Mean velocity Good
Pressure drop, straight channels Within ~10 % if your dimensions are right
Pressure drop, corner-heavy geometry Under-predicted, increasingly with corner count
Wall shear stress Order of magnitude
Heat exchange Right direction and magnitude, not a design margin
Mixing performance Not modelled
Droplet size Not modelled

The dominant error is usually not the model. It is that the channel you printed is not the channel you drew. A 0.05 mm dimensional error on a 0.4 mm channel changes the pressure drop by more than every modelling assumption on this page combined. Measure a printed part before blaming the arithmetic.

Reach for a real solver when:

  • You need a concentration field — how mixed, where, at what length.
  • You need a velocity or temperature profile across the channel, not a bulk average.
  • You are working with a non-Newtonian fluid and shear rates vary widely.
  • You are designing multiphase behaviour and need droplet size or breakup frequency.
  • Re is high enough that inertial effects matter — inertial focusing, recirculation behind a step.
  • The device’s performance depends on something at sub-channel scale — the floor ridges of a real staggered herringbone, for instance.

For everything else — will it print, will it fill, what pressure, how long does fluid spend in it, how much reagent will a run consume — this model answers the question and answers it in milliseconds.

The Fluid Dynamics tab carries this line on every view:

Estimates, not a full CFD simulation. A one-dimensional network model assuming fully developed laminar flow, perfect mixing at junctions, and no entrance or bend effects.

It is there on purpose. A number presented confidently and wrong is worse than no number.