Andrew Wells

Abstract:

We consider convective instability in a deep porous medium cooled from above with a linearised thermal exchange at the upper surface, thus determining the impact of using a Robin boundary condition, in contrast to previous previous studies using a Dirichlet boundary condition. With the linearised surface exchange, the thermal flux out of the porous layer depends linearly on the temperature difference between the effective temperature of a heat sink at the upper boundary and the temperature at the surface of the porous layer. The rate of this exchange is characterised by a dimensionless Biot number, Bi, determined by the effective thermal conductivity of exchange with the heat sink relative to the physical thermal conductivity of the porous layer. For a given temperature difference between the heat sink at the upper boundary and deep in the porous medium, we find that imperfectly cooled layers with finite Biot numbers are more stable to convective instabilities than perfectly cooled layers which have large, effectively infinite Biot numbers. Two regimes of behaviour were determined with contrasting stability behaviour and characteristic scales. When the Biot number is large the near-perfect heat transfer produces small corrections of order 1/Bi to the perfectly conducting behaviour found when the Biot number is infinite. In the insulating limit as the Biot number approaches zero, a different behaviour was found with significantly larger scales for the critical wavelength and depth of convection both scaling proportional to 1/ √ Bi

Abstract:

The physics of ice crystal growth from the liquid phase, especially in the presence of salt, has received much less attention than the growth of snow crystals from the vapor phase. The growth of so-called frazil ice by solidification of a supercooled aqueous salt solution is consistent with crystal growth in the basal plane being limited by the diffusive removal of the latent heat of solidification from the solid-liquid interface, while being limited by attachment kinetics in the perpendicular direction. This leads to the formation of approximately disk-shaped crystals with a low aspect ratio of thickness compared to radius, because radial growth is much faster than axial growth. We calculate numerically how fast disk-shaped crystals grow in both pure and binary melts, accounting for the comparatively slow axial growth, the effect of dissolved solute in the fluid phase, and the difference in thermal properties between solid and fluid phases. We identify the main physical mechanisms that control crystal growth and show that the diffusive removal of both the latent heat released and the salt rejected at the growing interface are significant. Our calculations demonstrate that certain previous parametrizations, based on scaling arguments, substantially underestimate crystal growth rates by a factor of order 10–100 for low aspect ratio disks, and we provide a parametrization for use in models of ice crystal growth in environmental settings.

Abstract:

We describe the results of experiments on mushy layers grown from aqueous ammonium chloride solution in normal, micro, and hyper gravity environments. In the fully developed chimney state, the chimney plume dynamics differ strikingly when conditions change from micro to hyper gravity. In microgravity, we find fully arrested plume motion and suppressed convection. As gravity exceeds Earth conditions, we observe a host of phenomena, ranging from arched plumes that undergo forced Rayleigh-Taylor instabilities to in-phase multiple plume oscillatory behavior. For the same initial solute concentrations and fixed boundary cooling temperatures, we find that, in runs of over two hours, the averaged effects of microgravity and hypergravity result in suppressed growth of the mushy layers, a phenomenon caused by a net enhancement of convective heat and solute transport from the liquid to the mushy layers. These behaviors are placed in the context of the theory of convecting mushy layers as studied under normal laboratory conditions. © 2012 American Institute of Physics.