Research
Photon-pressure-driven seepage in porous media
A novel cross-domain prediction from automated equation coupling. The composite couples Darcy’s law for porous-media flow with radiation-pressure momentum deposition from absorbed photon flux.
The prediction
In a horizontal porous medium saturated with an absorbing fluid:
where k is permeability, α is the absorption coefficient, I is beam intensity, μ is dynamic viscosity, and c is the speed of light.
At representative parameters (k = 10−12 m², α = 103 m−1, I = 109 W/m², μ = 10−3 Pa·s): u ≈ 3.3 × 10−6 m/s (~12 mm/hour).
Why this is novel
A systematic prior-art search (12 queries across Web, arXiv, and Google Scholar) found zero direct hits on this specific coupling. The acoustic analog (acoustic-streaming-driven pore flow) is well-published in J. Fluid Mech. and PMC (2018). The optical-in-bulk-fluid case is published (Leonhardt, Phys. Rev. A 90, 033801, 2014). But the specific gap — optical/electromagnetic momentum → pore-fluid flow in porous media — remains unfilled.
The gap exists because the two parent communities (porous-media hydraulicists and radiation-pressure physicists) do not cite each other’s journals. This is Mechanism A (cross-community isolation) from the hequ.ai novelty pathway.
Verification
| Check | Result |
|---|---|
| A — symbolic canonicalization | rational normalization → zero |
| B — property-based testing | 200 stratified samples, all within 10−10 tolerance |
| C — mpmath 50-digit cross-CAS | 3.33564×10−6, rel_err = 0 |
| Board formula | matches local formula exactly |
| Board citations | Darcy 1856, Ashkin 1970, Jackson §6.7, Bear Ch 5 |
Falsification conditions
- Steady flux in a horizontal dyed porous sample must scale linearly with beam intensity (u ∝ I) after controlling for thermal buoyancy.
- Measured velocity at the stated parameters must be within an order of magnitude of 3.3 × 10−6 m/s.
- No prior peer-reviewed publication formalizing this specific coupling exists.
Distinguishing signature
The prediction is independent of pore-fluid density ρ, unlike gravity-driven Darcy flow where u ∝ ρg. Varying fluid density while holding viscosity constant should not change the photon-pressure-driven seepage velocity. This decoupling provides a clean experimental control.
“Board is not a CAS” side contribution
On the Arrhenius+Fick Damköhler composite, the AI board’s numerical estimate was 7.24 × 109 while the true value is 725.4 — a 107-fold error that the local-CAS protocol caught by design. LLMs provide formulas and citations; SymPy + mpmath provide numbers.
Provenance
- Descriptor schema frozen before proposal (SHA-256:
5b1af167...b4cd3633) - Candidate generated by the AI review board (OpenAI GPT-5, Mechanism B) during novelty-generation brief v1
- Sympy-verified before composite authored (Rule A9)
- Phase 13 verification: all four checks passed
- Source: github.com/makau-ai/hequ
Verified composite catalog
| # | Composite | Parents | Transducer | Novelty |
|---|---|---|---|---|
| 1 | Simple harmonic oscillator | Newton II + Hooke | identity | textbook |
| 2 | Work = force × distance | Newton II + Work-Energy | identity | textbook |
| 3 | Soret thermodiffusion | Fourier + Fick | Onsager sT | textbook |
| 4 | DC motor steady-state | Newton II + Ohm | gyrator K | textbook |
| 5 | Damköhler regime | Arrhenius + Fick | compound Da | textbook |
| 6 | Photon-pressure seepage | Darcy + RadPress | mobility k/μ | NOVEL |