Wrinkling instabilities of swelling hydrogels.

We investigate the formation of wrinkling instabilities at the interface between layers of hydrogel and water, which arise to relieve horizontal compressive stresses caused by either differential swelling or confinement. Modelling the gel using a linear-elastic-nonlinear-swelling approach, we determine both a criterion for marginal stability and the growth rates of normal modes. Furthermore, our formalism allows us to understand the influence of differential swelling on the stability of hydrogels brought into contact with water, and we find three distinct phases of the instability. Initially, when only a thin skin layer of gel has swollen, buckles grow rapidly and the gel deforms as an incompressible material. A balance between normal elastic stress and pore pressure selects a wavelength for these buckles that increases with the square root of time. At late times, when the gel approaches a uniformly swollen state, buckles can only grow by differential swelling on much slower timescales determined by solvent transport. At intermediate times, growth is driven by the same fluid transport process as at late times but gradients in fluid pressure in the gel as it swells destabilize the interface, driving faster growth of wrinkles. We also explain why some instabilities can be transient, "healing" as time progresses, while others must remain for all time.

Thermal regelation of single particles and particle clusters in ice.

We investigate the migration by thermal regelation of single particles and clusters of particles surrounded by ice subjected to a temperature gradient. This phenomenon is relevant to the casting of porous materials, to cryopreservation of biological tissue, and to the degradation of paleoclimatic signals held in ice sheets, for example. Using carefully controlled laboratory experiments, we measure the migration rates of single particles and clusters as they approach the freezing front. We find that clusters migrate at a constant rate, while single particles accelerate towards the freezing front. This fundamental difference is attributed to the fact that, during regelation, melt water passes through the interstices of a cluster, limited by its constant permeability, but for a single particle must flow through a thin layer of pre-melted ice whose thickness diverges as the freezing temperature is approached, reducing the viscous resistance to migration. We extend existing theories of particle and cluster migration to include the influences of different thermal conductivities and of latent heat on the local temperature field in and around the particle or cluster. We find that if the specific latent heat is large or the viscous resistance to flow is sufficiently small then the migration rate is determined solely by heat transport.

Flow-induced compaction of a deformable porous medium.

Fluid flowing through a deformable porous medium imparts viscous drag on the solid matrix, causing it to deform. This effect is investigated theoretically and experimentally in a one-dimensional configuration. The experiments consist of the downwards flow of water through a saturated pack of small, soft, hydrogel spheres, driven by a pressure head that can be increased or decreased. As the pressure head is increased, the effective permeability of the medium decreases and, in contrast to flow through a rigid medium, the flux of water is found to increase towards a finite upper bound such that it becomes insensitive to changes in the pressure head. Measurements of the internal deformation, extracted by particle tracking, show that the medium compacts differentially, with the porosity being lower at the base than at the upper free surface. A general theoretical model is derived, and the predictions of the model give good agreement with experimental measurements from a series of experiments in which the applied pressure head is sequentially increased. However, contrary to theory, all the experimental results display a distinct and repeatable hysteresis: the flux through the material for a particular applied pressure drop is appreciably lower when the pressure has been decreased to that value compared to when it has been increased to the same value.

Sea-ice thermodynamics and brine drainage.

Significant changes in the state of the Arctic ice cover are occurring. As the summertime extent of sea ice diminishes, the Arctic is increasingly characterized by first-year rather than multi-year ice. It is during the early stages of ice growth that most brine is injected into the oceans, contributing to the buoyancy flux that mediates the thermo-haline circulation. Current operational sea-ice components of climate models often treat brine rejection between sea ice and the ocean similarly to a thermodynamic segregation process, assigning a fixed salinity to the sea ice, typical of multi-year ice. However, brine rejection is a dynamical, buoyancy-driven process and the salinity of sea ice varies significantly during the first growth season. As a result, current operational models may over predict the early brine fluxes from newly formed sea ice, which may have consequences for coupled simulations of the polar oceans. Improvements both in computational power and our understanding of the processes involved have led to the emergence of a new class of sea-ice models that treat brine rejection dynamically and should enhance predictions of the buoyancy forcing of the oceans.

Periodic ice banding in freezing colloidal dispersions.

Concentrated colloidal alumina dispersions were frozen in a directional solidification apparatus that provides independent control of the freezing rate and temperature gradient. Two distinct steady-state modes of periodic ice banding were observed in the range of freezing rates examined. For each mode, the wavelength between successive bands of segregated ice decreases with increasing freezing rate. At low freezing rates (0.25-3 µm s(-1)), the ice segregates from the suspension into ice lenses, which are cracklike in appearance, and there is visible structure in the layer of rejected particles in the unfrozen region ahead of the ice lenses. In this regime, we argue that compressive cryosuction forces lead to the irreversible aggregation of the rejected particles into a close-packed cohesive layer. The temperature in the aggregated layer is depressed below the bulk freezing point by more than 2 °C before the ice lenses are encountered; moreover, this undercooled region appears as a light-colored layer. The magnitude of the undercooling and the color change in this region both suggest the presence of pore ice and the formation of a frozen fringe. The possibility of a frozen fringe is supported by a quantitative model of the freezing behavior. At intermediate freezing rates, around 4 µm s(-1), the pattern of ice segregation is disordered, coinciding with the disappearance of the dark- and light-colored layers. Finally, at high freezing rates (5-10 µm s(-1)), there is a new mode of periodic ice banding that is no longer cracklike and is absent of any visible structure in the suspension ahead of the ice bands. We discuss the implications of our experimental findings for theories of ice lensing.

Elastic response of a grounded ice sheet coupled to a floating ice shelf.

An ice sheet that spreads into an ocean is forced to bend owing to its buoyancy and detaches from the bedrock to form a floating ice shelf. The location of the transition between the grounded sheet and the floating shelf, defined as the grounding line, behaves as a free boundary. We develop a model of an elastic grounded sheet resting on a deformable elastic bed and coupled to an elastic floating shelf. We find that the grounding-line position is determined by the geometry of the bed and the bending-buoyancy length scale of the system. These two contributions depend on the reaction modulus of the bed in opposite ways. We show that the structure of the floating shelf depends on the bending-buoyancy length scale only, allowing us to calculate the bending stiffness of the elastic sheet independently of the properties of the bed. Relations between the structure of the floating shelf and the grounding-line position are also developed. Our theoretical predictions agree with laboratory experiments made using thick elastic sheets and a dense salt solution. Our findings may provide new insights into the dynamics near grounding lines, as well as methods to infer the bending stiffness of ice sheets and the grounding-line position from satellite altimetery that can be applied to elastic sheets in general.

Surface transport in premelted films with application to grain-boundary grooving.

We present a new model of surface transport in premelted films that is applicable to a wide range of materials close to their melting points. We illustrate its use by applying it to the evolution of a grain-boundary groove in a high vapor pressure material and show that Mullins's classical equation describing transport driven by gradients in surface curvature is reproduced asymptotically. The microscopic contact angle at the groove root is found to be modified over a thin boundary layer, and the apparent contact angle is determined. An explicit transport coefficient is derived that governs the evolution rate of systems controlled by surface transport through premelted films. The transport coefficient is found to depend on temperature and diverges as the bulk melting temperature is approached.