Hi David,
Thank you so much for that link! The discussion on real poles and the low-pass source code is exactly the bridge we need. You hit the nail on the head—the fluid dynamics of this incompressible liquid mirror audio dataflow perfectly.
Your link helps us model the 'charging' phase beautifully, where the biochar matrix acts like the time-domain ramp of a [lop~] filter.
Reflecting on your advice, I've been thinking about how to model the 'reset/restart' phase, which is highly asymmetrical. When the check valve snaps open, the sudden backpressure and directional flow shift feel less like a simple low-pass and more like a band-pass filter experiencing heavy asymmetrical clipping. The water hammer acts like a massive initial resonant peak that forcefully clears the system before the loop clips and resets.
I realize now we can model this entire cycle in Pd using [delwrite~] and [delread~] for the matrix time-delay, fed through the sigpack diode object to handle the non-linear threshold switching. This should let us fully simulate fluidic astable switching!
We would love to synthesize these behaviors to test a complete mathematical model of the physics. We’ve also just opened a second issue on our GitHub to design a way to cross-couple two of these modules (180^{\circ }) out-of-phase (like a two-phase AC generator) to eliminate the reset dead-time entirely.
If you or anyone else wants to explore the logic layout, our primary hub is here: https://github.com/MeshTent/Passive-fluidic-micro-hydro/issues/2.
Massive thanks for pointing us in the right direction!

Hello Pd Community,We have built and tested a passive macro-scale fluidic relaxation oscillator designed to harvest low-flow water sources for micro-hydro power. Prototype 1 successfully generated 20mW continuously for 3 days.

The architecture behaves exactly like a hardware dataflow patch or an electronic RCL circuit, but using pure fluid dynamics:Input (DC Source): Constant-pressure header tank (Mariotte bottle principle).Timing Loop (RC Network): A compost/biochar matrix acting as a fluidic resistor/capacitor, creating a phase lag as it saturates.Switch (Threshold Gate): A one-way check valve that snaps open when backpressure clears a distinct threshold.Impulse (Inductive Kickback): A hydraulic ram effect that uses fluid inertia to force a reset/drain of the biochar matrix, looping the system.

The Ask: Because this community deeply understands dataflow logic, feedback loops, and oscillation mechanics, we are looking for conceptual feedback on how to mathematically model or optimize the phase lag of the wicking matrix to prevent premature switching.Note: This is an open-source project permanently registered under a CC BY-NC 4.0 license for public, humanitarian, and non-commercial use only.Our active peer-review thread and documentation is hosted on GitHub here:

https://github.com/MeshTent/Passive-fluidic-micro-hydro/tree/main

Thank you so much to anyone , who can give this time !