Dynamic confinement controls the porous-to-free convection transition - Dario M. Schwendener; Jerome Noir; Jonas Latt; Christophe Coreixas; Xiang-Zhao Kong (Proceedings of the National Academy of Sciences, 2026)
Convection in porous materials governs heat transport across scales ranging from planetary subsurface systems to engineered cooling devices. While the onset of buoyancy-driven flow is well described by linear stability theory within a porous-continuum representation, the subsequent transition from viscous, matrix-dominated convection toward inertia-influenced and ultimately bulk fluid-like plume convection has lacked a unified description. Here we develop a confinement-based scaling framework that connects these flow states through a common scale-ratio perspective and quantitatively bridges classical porous convection with laterally confined Rayleigh–Bénard systems. Because random porous and fractured media do not admit an obvious static scale-ratio, we recover an effective confinement measure from the onset condition. This links permeability-based systems to the classical confinement framework and defines a characteristic pore length for natural convection. Comparing this pore length with the thermal boundary-layer thickness yields a dynamic criterion for the emergence of unconfined behavior. Embedding experimental and numerical porous–convection datasets into a unified phase diagram of buoyant forcing and static confinement reveals a systematic progression from viscous, drag-dominated heat transport to inertia-corrected flow and ultimately to plume-driven convection whose statistics approach those of unconfined fluids. The resulting framework delineates the limits of porous-continuum validity, clarifies when inertial corrections become relevant, and highlights the dynamical analogy between strongly confined porous flows and thin-gap Hele–Shaw configurations. By linking heat-transport scaling to static and dynamic length scales, the phase diagram provides a practical diagnostic for selecting appropriate governing equations across geophysical and engineered porous systems.