The kinetics of ice-lens growth in porous media

We analyse the growth rate of segregated ice (ice lenses) in freezing porous media. For typical colloidal materials such as soils we show that the commonly-employed Clapeyron equation is not valid macroscopically at the interface between the ice lens and the surrounding porous medium owing to the viscous dynamics of flow in premelted films. This gives rise to an ‘interfacial resistance’ to flow towards the growing ice which causes a significant drop in predicted ice-growth (heave) rates and explains why many previous models predict ice-growth rates that are much larger than those seen in experiments. We derive an explicit formula for the ice-growth rate in a given porous medium, and show that this only depends on temperature and on the external pressures imposed on the freezing system. This growth-rate formula contains a material-specific function which can be calculated (with a knowledge of the of the geometry and material of the porous medium), but which is also readily experimentally-measurable. We apply the formula to plate-like particles, and obtain good agreement with previous experimental data. Finally we show how the interfacial resistance explains the observation that the maximum heave rate in soils occurs in medium-grained particles such as silts, while heave rates are smaller for fine- and coarse- grained particles

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

Mud peeling and horizontal crack formation in drying clays

Mud peeling is a common phenomenon whereby horizontal cracks propagate parallel to the surface of a drying clay. Differential stresses then cause the layer of clay above the crack to curl up to form a mud peel. By treating the clay as a poroelastic solid, we analyse the peeling phenomenon and show that it is caused by the gradient in tensile stress at the surface of the clay, analogously to the spalling of thermoelastic materials. For a constant water evaporation rate at the clay surface we derive equations for the depth of peeling and the time of peeling as functions of the evaporation rate. Our model predicts a simple relationship between the radius of curvature of a mud peel and the depth of peeling. The model predictions are in agreement with the available experimental data available

Ice-lens formation and connement-induced supercooling in soils and other colloidal materials

We present a new, 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 confinement-induced 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 experiments. The theory is generalizable to complex natural-soil scenarios, and should therefore be useful in the prediction of macroscopic frost heave rates