Stephen S. L. Peppin

Morphological instability in freezing colloidal suspensions

We present a linear stability analysis of a planar ice interface during unidirectional solidification of a hard-sphere colloidal suspension. We find that the interface can become unstable due to constitutional supercooling, yielding a new mechanism for pattern formation in colloidal systems. The interfacial stability is shown to depend strongly on the size and concentration of the particles. Increasing the particle radius tends to stabilize the interface, while increasing the concentration has a destabilizing effect. Additional effects that may influence the stability and morphology of such a system are described.

Ice-lens formation and geometrical supercooling in soils and other colloidal materials.

We present a physically intuitive model of ice-lens formation and growth during the freezing of soils and other dense, particulate suspensions. Motivated by experimental evidence, we consider the growth of an ice-filled crack in a freezing soil. At low temperatures, ice in the crack exerts large pressures on the crack walls that will eventually cause the crack to split open. We show that the crack will then propagate across the soil to form a new lens. The process is controlled by two factors: the cohesion of the soil and the geometrical supercooling of the water in the soil, a new concept introduced to measure the energy available to form a new ice lens. When the supercooling exceeds a critical amount (proportional to the cohesive strength of the soil) a new ice lens forms. This condition for ice-lens formation and growth does not appeal to any ad hoc, empirical assumptions, and explains how periodic ice lenses can form with or without the presence of a frozen fringe. The proposed mechanism is in good agreement with experiments, in particular explaining ice-lens pattern formation and surges in heave rate associated with the growth of new lenses. Importantly for systems with no frozen fringe, ice-lens formation and frost heave can be predicted given only the unfrozen properties of the soil. We use our theory to estimate ice-lens growth temperatures obtaining quantitative agreement with the limited experimental data that are currently available. Finally we suggest experiments that might be performed in order to verify this theory in more detail. The theory is generalizable to complex natural-soil scenarios and should therefore be useful in the prediction of macroscopic frost-heave rates.

Crust formation in drying colloidal suspensions

During the drying of colloidal suspensions, the desiccation process causes the suspension near the air interface to consolidate into a connected porous matrix or crust. Fluid transport in the porous medium is governed by Darcy’s law and the equations of poroelasticity, while the equations of colloid physics govern processes in the suspension. We derive new equations describing this process, including unique boundary conditions coupling the two regions, yielding a moving-boundary model of the concentration and stress profiles during drying. A solution is found for the steady-state growth of a one-dimensional crust during constant evaporation rate from the surface. The solution is used to demonstrate the importance of the system boundary conditions on stress profiles and diffusivity in a drying crust.

Morphological instability of a non-equilibrium ice–colloid interface

We assess the morphological stability of a non-equilibrium ice–colloidal suspension interface, and apply the theory to bentonite clay. An experimentally convenient scaling is employed that takes advantage of the vanishing segregation coefficient at low freezing velocities, and when anisotropic kinetic effects are included, the interface is shown to be unstable to travelling waves. The potential for travelling-wave modes reveals a possible mechanism for the polygonal and spiral ice lenses observed in frozen clays. A weakly nonlinear analysis yields a long-wave evolution equation for the interface shape containing a new parameter related to the highly nonlinear liquidus curve in colloidal systems. We discuss the implications of these results for the frost susceptibility of soils and the fabrication of microtailored porous materials.

Dynamics of colloidal particles in ice

We use x-ray photon correlation spectroscopy (XPCS) to probe the dynamics of colloidal particles in polycrystalline ice. During freezing, the dendritic ice morphology and rejection of particles from the ice created regions of high particle density, where some of the colloids were forced into contact and formed disordered aggregates. The particles in these high density regions underwent ballistic motion, with a characteristic velocity that increased with temperature. This ballistic motion is coupled with both stretched and compressed exponential decays of the intensity autocorrelation function. We suggest that this behavior could result from ice grain boundary migration.

Particle-scale structure in frozen colloidal suspensions from small angle X-ray scattering

During directional solidification of the solvent in a colloidal suspension, the colloidal particles segregate from the growing solid, forming high-particle-density regions with structure on a hierarchy of length scales ranging from that of the particle-scale packing to the large-scale spacing between these regions. Previous work has concentrated mostly on the medium- to large-length scale structure, as it is the most accessible and thought to be more technologically relevant. However, the packing of the colloids at the particle scale is an important component not only in theoretical descriptions of the segregation process, but also to the utility of freeze-cast materials for new applications. Here we present the results of experiments in which we investigated this structure across a wide range of length scales using a combination of small-angle x-ray scattering and direct optical imaging. As expected, during freezing the particles were concentrated into regions between ice dendrites forming a microscopic pattern of high- and low-particle-density regions. X-ray scattering indicates that the particles in the high-density regions were so closely packed as to be touching. However, the arrangement of the particles does not conform to that predicted by standard interparticle pair potentials, suggesting that the particle packing induced by freezing differs from that formed during equilibrium densification processes.

Frost heave in colloidal soils

We develop a mathematical model of frost heave in colloidal soils. The theory accounts for heave and consolidation while not requiring a frozen fringe assumption. Two solidification regimes occur: a compaction regime in which the soil consolidates to accommodate the ice lenses, and a heave regime during which liquid is sucked into the consolidated soil from an external reservoir, and the added volume causes the soil to heave. The ice fraction is found to vary inversely with the freezing velocity V, while the rate of heave is independent of V, consistent with field and laboratory observations.

Onsager Reciprocity in Premelting Solids

The diffusive motion of foreign particles dispersed in a premelting solid is analyzed within the framework of irreversible thermodynamics. We determine the mass diffusion coefficient, thermal diffusion coefficient and Soret coefficient of the particles in the dilute limit, and find good agreement with experimental data. In contrast to liquid suspensions, the unique nature of premelting solids allows us to derive an expression for the Dufour coefficient and independently verify the Onsager reciprocal relation coupling diffusion to the flow of heat.