Dispensing nozzle

Implementation

The solver assembles the full axisymmetric Stokes strain terms with P2 velocity and P1 pressure on a body-fitted mesh.

Three nominal bore geometries are exported as STEP and STL. Raw nodal fields, pressure comparisons and input dimensions are included.

The virtual bench executes tolerance-corner FEM checks, pressure-envelope calculations, synthetic instrument fits, obstruction detection and a compliant dosing/shutoff model. The final operating decision is supplied as JSON.

Inputs and assumptions

• Isothermal Newtonian reference liquid: density 1000 kg/m3; viscosity 0.5 to 1.0 Pa s.
• Flow 10 to 30 mm3/s; 1 mm outlet diameter; 20 mm passage; 6500 Pa pump budget and 60 mm3 retained-volume limit.
• Nozzle walls are no-slip. Developed profiles bound the modeled passage; external fittings and supply lines are excluded.
• Combined system envelope: command at most 26.4 mm3/s at 0.5 to 1.0 Pa s with +/-0.01 mm bore radii, +/-0.1 mm outlet-land length, the declared 10 mm feed tube and bounded static meniscus. The original 30 mm3/s endpoint is comparison evidence, not an accepted combined-system operating point.

Results

Report figures (3)

Open the full report ↗

Verification

21 executed numerical/geometry checks pass, including six regression tests, pipe benchmark, three mesh levels and extended boundaries. Additional virtual bench: 14 verification checks; 243 tolerance/operating cases; 30 synthetic observations; four dosing cases. Original maximum-flow condition fails added system effects; computed bound 26.4 mm3/s.

python run.py

Project files

The ZIP contains the source, inputs, results, and instructions. These files are also available individually.

• Axisymmetric FEM solverflow.py · 5 KB
• Geometry and operating inputsinputs.json · 1 KB
• Selected nozzle STEPoutputs/cad/wide-inlet.step · 18 KB
• Selected fluid volume STEPoutputs/cad/wide-inlet-fluid.step · 10 KB
• Dimensioned section viewoutputs/section.svg · 43 KB
• Flow and viscosity sweepoutputs/operating-sweep.csv · 2 KB
• Mesh convergence resultsoutputs/mesh-study.csv · 2 KB
• Physical pressure-test procedurebench-test.md · 2 KB
• Selected operating envelopeoutputs/virtual-bench/selected-operating-envelope.json · 1 KB
• Completed virtual-bench verificationcompletion.json · 5 KB
• Virtual pressure and dosing bench sourcevirtual_bench.py · 23 KB
• Tolerance, instrument and dosing inputsvirtual-bench-inputs.json · 1 KB
• Virtual bench and acceptance reportoutputs/virtual-bench/report.html · 11 KB
• Acceptance outcomesoutputs/virtual-bench/acceptance-matrix.csv · 1 KB
• All 243 pressure-envelope casesoutputs/virtual-bench/tolerance-pressure-envelope.csv · 27 KB

Run locally

Python 3.12 / CadQuery 2.7.0 / scikit-fem 12.0.2 / NumPy 2.3.5 / SciPy 1.17.0 / Matplotlib 3.10.8

Extract the ZIP and open a terminal in the dispensing-nozzle folder. The README includes setup and usage details.

python -m pip install -r requirements.txt
python run.py
python test_flow.py

Limits

• Numerical reference study; no physical dispensing measurements were used.
• Stokes flow excludes inertia. The declared range stays below Re 0.1, but a different fluid or flow rate needs a new regime check.
• CAD uses nominal geometry. Materials, seals, threads, surface finish, tolerances and cleaning validation require a separate manufacturing release.
• Additional static meniscus and lumped compliance models cover pressure-head and shutoff sensitivities. They do not resolve droplet breakup, moving bubbles or physical contact angle.