= Solution
Melting raises <permeability of a porous medium>. An advancing protrusion therefore offers a less resistive path to hot liquid, attracting larger <Darcy flux> and receiving more heat. The resulting faster melting reinforces the protrusion: this is a <reactive infiltration instability>. A permeability decrease would reverse this feedback, while zero contrast gives no growth in this ideal model.
For positive contrast, the <growth rate> is proportional to transverse <wavenumber>, so \b[the model has no finite fastest-growing wavelength]. The <latent-to-sensible heat ratio> slows the front but supplies no short-wave cutoff. Finite thermal transport and a resolved melting zone can introduce a length scale; pore geometry eventually limits the continuum description. If interface curvature changes the equilibrium melting temperature through the <Gibbs--Thomson relation>, that can also oppose short-wave corrugations. The modified <dispersion relation> must include such effects before a preferred wavelength can be calculated; a length scale alone does not guarantee that every added mechanism selects one.
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