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.
What the model assumes
Section titled “What the model assumes”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 five omissions that matter most
Section titled “The five omissions that matter most”Entrance length
Section titled “Entrance length”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 · DₕAt 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.
Bend and junction losses
Section titled “Bend and junction losses”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.
Secondary flows
Section titled “Secondary flows”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.
Any concentration field
Section titled “Any concentration field”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.
Multiphase behaviour
Section titled “Multiphase behaviour”No interfacial tension, no wetting, no droplets, no bubbles. See Droplet generation.
How wrong is it?
Section titled “How wrong is it?”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.
When you need CFD
Section titled “When you need CFD”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.
What the app says
Section titled “What the app says”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.
- Pressure drop and Hagen–Poiseuille
- Fluid dynamics — using the tab
- Fluid property tables