A reduced-order nonlinear thermo–fluid model of pressure-driven extraction in a moka pot

Abstract

We present a reduced-order, fully dimensionless thermo–fluid model describing pressure-driven extraction in a moka pot. The system is formulated as a minimal set of coupled nonlinear ordinary differential equations capturing heating, vapor-pressure generation, and threshold-driven flow through a porous medium. The model exhibits distinct dynamical regimes governed by a small number of physically interpretable dimensionless parameters, including delayed extraction, smooth extraction, and rapid-flow behavior arising from nonlinear feedback. The model is calibrated and quantitatively validated against digitized experimental measurements of pressure and cumulative extraction, while the temperature evolution provides an independent experimental assessment of the thermal scaling of the reduced model. Despite its simplicity, the model captures the essential thermo–fluid coupling responsible for self-regulating extraction dynamics in confined systems and provides a transparent framework for analyzing threshold-driven flow phenomena.