Freeze fracturing of elastic porous media: a mathematical model.

We present a mathematical model of the fracturing of water-saturated rocks and other porous materials in cold climates. Ice growing inside porous rocks causes large pressures to develop that can significantly damage the rock. We study the growth of ice inside a penny-shaped cavity in a water-saturated porous rock and the consequent fracturing of the medium. Premelting of the ice against the rock, which results in thin films of unfrozen water forming between the ice and the rock, is one of the dominant processes of rock fracturing. We find that the fracture toughness of the rock, the size of pre-existing faults and the undercooling of the environment are the main parameters determining the susceptibility of a medium to fracturing. We also explore the dependence of the growth rates on the permeability and elasticity of the medium. Thin and fast-fracturing cracks are found for many types of rocks. We consider how the growth rate can be limited by the existence of pore ice, which decreases the permeability of a medium, and propose an expression for the effective 'frozen' permeability.

Experimental verification of morphological instability in freezing aqueous colloidal suspensions.

We describe an experimental test of a new theory of the unidirectional freezing of aqueous colloidal suspensions. At low freezing speeds a planar ice lens completely rejects the particles, forming a steady-state compacted boundary layer in the liquid region. At higher speeds the planar interface becomes thermodynamically unstable and breaks down geometrically to trap bulk regions of colloid within. The theoretical stability threshold is determined experimentally, thereby demonstrating that colloidal suspensions can be treated analogously to atomic or molecular alloys.

Interfacial premelting and the thermomolecular force: thermodynamic buoyancy.

The presence of a substrate can alter the equilibrium state of another material near their common boundary. Examples include wetting and interfacial premelting. In the latter case, temperature gradients induce spatial variations in the thickness of the premelted film that reflect changes in the strength of the repulsion between the substrate and the solid. We show that the net thermomolecular force on a macroscopic substrate is equivalent to a thermodynamic buoyancy force-proportional to the mass of solid that can occupy the volume enclosed by the substrate and the temperature gradient.

Possible displacement of the climate signal in ancient ice by premelting and anomalous diffusion.

The best high-resolution records of climate over the past few hundred millennia are derived from ice cores retrieved from Greenland and Antarctica. The interpretation of these records relies on the assumption that the trace constituents used as proxies for past climate have undergone only modest post-depositional migration. Many of the constituents are soluble impurities found principally in unfrozen liquid that separates the grain boundaries in ice sheets. This phase behaviour, termed premelting, is characteristic of polycrystalline material. Here we show that premelting influences compositional diffusion in a manner that causes the advection of impurity anomalies towards warmer regions while maintaining their spatial integrity. Notwithstanding chemical reactions that might fix certain species against this prevailing transport, we find that-under conditions that resemble those encountered in the Eemian interglacial ice of central Greenland (from about 125,000 to 115,000 years ago)-impurity fluctuations may be separated from ice of the same age by as much as 50 cm. This distance is comparable to the ice thickness of the contested sudden cooling events in Eemian ice from the GRIP core.