Using a phase field model introduced by Kobayashi*, Olivier Abellan has shown that dendrites form as crystallization occurs within a porous material. To our knowledge, this is the first demonstration of this phenomenon. It could have important implications for stress development during freezing, as pressure is exerted by the ice on the surrounding pore walls. The animation above shows ice growing at a small undercooling from the bottom of the frame, where no dendrites have formed, owing to the magnitude and anisotropy of the surface energy. Once the ice enters the porous network, the solid matrix of the porous body acts as a heat sink and encourages the formation of dendrites. Since the diameter of each dendrite is much large than the pore size, the curvature of the tip of the dendrite is evidently controlled by heat flow, not surface energy.
These results are detailed in the Masters thesis of Olivier Abellan, and will be submitted for publication soon. This work was supported by NSF Grant CMS-0509986.
*R. Kobayashi, ”Modeling and numerical simulations of dendritic crystal growth”, Physica D,Vol. 63, p 410-423, 1993.