J. S. Wettlaufer

The premelting of ice and its environmental consequences

Several mechanisms can extend the equilibrium domain of a liquid phase into the solid region of the normal phase diagram. The causes of premelting, which include surface melting, interface curvature and substrate disorder, occur in all types of substances, including H2O. In the case of H2O, premelting can have important environmental consequences, among which are the heaving of frozen ground, breakdown of rock and concrete, sintering of snow, flow of glaciers, scavenging of atmospheric trace gases by snow and ice, and the electrification of thunderclouds. The article reviews the basic mechanisms of premelting and discusses their roles in the environmental phenomena. The principal results of numerous studies are reviewed, and trends in current research are outlined.

Natural convection during solidification of an alloy from above with application to the evolution of sea ice

We describe a series of laboratory experiments in which aqueous salt solutions were cooled and solidied from above. These solutions serve as model systems of metallic castings, magma chambers and sea ice. As the solutions freeze they form a matrix of ice crystals and interstitial brine, called a mushy layer. The brine initially remains conned to the mushy layer. Convection of brine from the interior of the mushy layer begins abruptly once the depth of the layer exceeds a critical value. The principal path for brine expelled from the mushy layer is through ‘brine channels’, vertical channels of essentially zero solid fraction, which are commonly observed in sea ice and metallic castings. By varying the initial and boundary conditions in the experiments, we have been able to determine the parameters controlling the critical depth of the mushy layer. The results are consistent with the hypothesis that brine expulsion is initially determined by a critical Rayleigh number for the mushy layer. The convection of salty fluid out of the mushy layer allows additional solidication within it, which increases the solid fraction. We present the rst measurements of the temporal evolution of the solid fraction within a laboratory simulation of growing sea ice. We show how the additional growth of ice within the layer aects its rate of growth.

Nonlinear threshold behavior during the loss of Arctic sea ice.

In light of the rapid recent retreat of Arctic sea ice, a number of studies have discussed the possibility of a critical threshold (or “tipping point”) beyond which the ice–albedo feedback causes the ice cover to melt away in an irreversible process. The focus has typically been centered on the annual minimum (September) ice cover, which is often seen as particularly susceptible to destabilization by the ice–albedo feedback. Here, we examine the central physical processes associated with the transition from ice-covered to ice-free Arctic Ocean conditions. We show that although the ice–albedo feedback promotes the existence of multiple ice-cover states, the stabilizing thermodynamic effects of sea ice mitigate this when the Arctic Ocean is ice covered during a sufficiently large fraction of the year. These results suggest that critical threshold behavior is unlikely during the approach from current perennial sea-ice conditions to seasonally ice-free conditions. In a further warmed climate, however, we find that a critical threshold associated with the sudden loss of the remaining wintertime-only sea ice cover may be likely.

Universal deformation of soft substrates near a contact line and the direct measurement of solid surface stresses

Droplets deform soft substrates near their contact lines. Using confocal microscopy, we measure the deformation of silicone gel substrates due to glycerol and fluorinated-oil droplets for a range of droplet radii and substrate thicknesses. For all droplets, the substrate deformation takes a universal shape close to the contact line that depends on liquid composition, but is independent of droplet size and substrate thickness. This shape is determined by a balance of interfacial tensions at the contact line and provides a novel method for direct determination of the surface stresses of soft substrates. Moreover, we measure the change in contact angle with droplet radius and show that Youngs law fails for small droplets when their radii approach an elastocapillary length scale. For larger droplets the macroscopic contact angle is constant, consistent with Youngs law.

Premelting dynamics in a continuum model of frost heave

Frost heave is the process by which the freezing of water-saturated soil causes the deformation and upward thrust of the ground surface. We describe the fundamental interactions between phase change and fluid flow in partially frozen, saturated porous media (soils) that are responsible for frost heave. Water remains only partially frozen in a porous medium at temperatures below

Surface tension and contact with soft elastic solids

0\,^\circ

Sea ice is a mushy layer

C owing both to the depression of the freezing temperature at curved phase boundaries and to interfacial premelting caused by long-range intermolecular forces. We show that while the former contributes to the geometry of fluid pathways, it is solely the latter effect that generates the forces necessary for frost heave. We develop a simple model describing the formation and evolution of the ice lenses (layers of ice devoid of soil particles) that drive heave, based on integral force balances. We determine conditions under which either (i) a single ice lens propagates with no leading frozen fringe, or (ii) a single, propagating ice lens is separated from unfrozen soil by a partially frozen fringe, or (iii) multiple ice lenses form.

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

The Johnson-Kendall-Roberts theory is the basis of modern contact mechanics. It describes how two deformable objects adhere together, driven by adhesion energy and opposed by elasticity. Here we characterize the indentation of glass particles into soft, silicone substrates using confocal microscopy. We show that, whereas the Johnson-Kendall-Roberts theory holds for particles larger than a critical, elastocapillary lengthscale, it fails for smaller particles. Instead, adhesion of small particles mimics the adsorption of particles at a fluid interface, with a size-independent contact angle between the undeformed surface and the particle given by a generalized version of the Youngs law. A simple theory quantitatively captures this behaviour and explains how solid surface tension dominates elasticity for small-scale indentation of soft materials.

Patterning droplets with durotaxis

Sea ice is a two-phase, two-component, reactive porous medium: an example of what is known in other contexts as a mushy layer. The fundamental conservation laws underlying the mathematical description of mushy layers provide a robust foundation for the prediction of sea-ice evolution. Here we show that the general equations describing mushy layers reduce to the model of Maykut and Untersteiner (1971) under the same approximations employed therein.

the phase evolution of Young Sea Ice

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.