Dynamic confinement controls the porous-to-free convection transition

Area of Science:

• Geophysics
• Fluid Dynamics
• Heat Transfer

Background:

• Convection in porous materials is crucial for heat transport in diverse systems, from planetary interiors to engineered devices.
• Existing theories adequately describe the onset of buoyancy-driven flow but lack a unified description for transitions to inertia-influenced and plume-like convection.
• A unified framework is needed to connect viscous, inertia-influenced, and bulk fluid-like convection states in porous media.

Purpose of the Study:

• Develop a confinement-based scaling framework to unify descriptions of heat transport in porous materials.
• Quantitatively bridge classical porous convection with laterally confined Rayleigh-Bénard systems.
• Establish a dynamic criterion for the emergence of unconfined convective behavior.

Main Methods:

• Developed a confinement-based scaling framework using a scale-ratio perspective.
• Recovered an effective confinement measure from the onset condition for systems lacking an obvious static scale-ratio.
• Embedded experimental and numerical datasets into a unified phase diagram of buoyant forcing and static confinement.

Main Results:

• The framework connects viscous, inertia-corrected, and plume-driven convection states.
• A characteristic pore length and dynamic criterion for unconfined behavior were defined.
• The study revealed a systematic progression of heat transport from viscous-dominated to plume-driven convection.

Conclusions:

• The developed framework delineates the limits of porous-continuum validity and clarifies when inertial corrections are relevant.
• It highlights the dynamical analogy between confined porous flows and Hele-Shaw configurations.
• The phase diagram serves as a practical diagnostic for selecting appropriate governing equations for geophysical and engineered porous systems.