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

Convection and heat transfer in layered sloping warm-water\ud aquifers

What convective flow is induced if a geologically-tratified groundwater aquifer is subject to a vertical temperature gradient? How strong is the flow? What is the nett heat transfer? Is the flow stable? How does the convection affect the subsequent species distribution if a pollutant finds its way into the aquifer? This paper begins to address such questions. Quantitative models for buoyancy-driven fluid flow in long, sloping warm-water aquifers with both smoothly- and discretely-layered structures are formulated. The steady-state profiles are calculated for the temperature and for the fluid specific volume flux (Darcy velocity) parallel to the boundaries in a sloping system subjected to a perpendicular temperature gradient, at low Rayleigh numbers. The conducted and advected heat fluxes are compared and it is shown that the system acts somewhat like a heat pipe. The maximum possible ratio of naturally advected-to-conducted heat transfer is determined, together with the corresponding permeability and thermal conductivity profiles

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

Strain-dependent solid surface stress and the stiffness of soft contacts

Surface stresses have recently emerged as a key player in the mechanics of highly compliant solids. The classic theories of contact mechanics describe adhesion with a compliant substrate as a competition between surface energies driving deformation to establish contact and bulk elasticity resisting this. However, it has recently been shown that surface stresses provide an additional restoring force that can compete with and even dominate over elasticity in highly compliant materials, especially when length scales are small compared to the ratio of the surface stress to the elastic modulus, $\Upsilon/E$. Here, we investigate experimentally the contribution of surface stresses to the force of adhesion. We find that the elastic and capillary contributions to the adhesive force are of similar magnitude, and that both are required to account for measured adhesive forces between rigid silica spheres and compliant, silicone gels. Notably, the strain-dependence of the solid surface stress contributes significantly to the stiffness of soft solid contacts.Comment: 6 pages, 3 figure