InterPore2026

From Darcy to inertia-dominated convection: the role of plume-scale confinement

19 May 2026, 14:05

15m

Oral Presentation (MS09) Pore-Scale Physics and Modeling MS09

Speaker

Dario Schwendener (ETH Zurich)

Description

Natural convection in porous materials governs heat transport across scales ranging from planetary subsurface convective systems to engineered cooling systems in micro-electronics.
While the onset of buoyancy-driven flow in such systems is well captured by linear stability analysis within a porous-continuum framework, the subsequent transition toward inertia-dominated and ultimately free Rayleigh–Bénard convection remains neither systematically quantified nor synthesized into a coherent phase map.

Here we combine high-resolution lattice Boltzmann simulations with experimental and numerical results from the literature to formulate a confinement-based scaling description of porous convection across regimes. The dimensionless confinement parameter $Λ=δ/b$, relates the dynamically emerging plume neck width, equivalent to the thermal boundary-layer thickness $δ$, to the characteristic pore spacing $b$.

In the strongly confined limit, a Churchill–Usagi-type interpolation captures both Darcy and Forchheimer asymptotic behaviour and accurately identifies the onset of inertia-dominated convection. As confinement weakens, a critical threshold $Λ_c$ marks the progressive breakdown of porous-continuum scaling: once thermal and velocity length scales fall below the representative pore size, the system transitions toward Rayleigh–Bénard-type dynamics. The resulting regime map links heat-transfer scaling to geometric confinement and porous Prandtl number, clarifying when Darcy–Forchheimer models remain valid and when unconfined plume-driven convection emerges.