ALBERT

Description: We examine steady longitudinal freezing of a two-dimensional single-component free liquid film. In the liquid, there are thermocapillary and volume-change flows as a result of temperature gradients along the film and density change upon solidification. We examine these flows, heat transfer, and interfacial shapes using an asymptotic analysis which is valid for thin films with small aspect ratios. These solutions depend sensitively on contact conditions at the tri-junctions. In particular, when the sum of the angles formed in the solid and liquid phases falls below a critical value, the existence of steady solutions is lost and the liquid film cannot be continuous, suggesting breakage of the film owing to freezing. The solutions are relevant to the freezing of foams of metals or ceramics, materials unaffected by surface active agents. © 2008 Cambridge University Press 2008.

Description: Recent directional solidification experiments with aqueous suspensions of alumina particles (Anderson & Worster, Langmuir, vol. 28 (48), 2012, pp. 16512-16523) motivate a model for freezing colloidal suspensions that builds upon a theoretical framework developed by Rempel et al. (J. Fluid Mech., vol. 498, 2004, pp. 227-244) in the context of freezing soils. Ice segregates from the suspension at slow freezing rates into discrete horizontal layers of particle-free ice, known as ice lenses. A portion of the particles is trapped between ice lenses, while the remainder are pushed ahead, forming a layer of fully compacted particles separated from the bulk suspension by a sharp compaction front. By dynamically modelling the compaction front, the growth kinetics of the ice lenses are fully coupled to the viscous flow through the evolving compacted layer. We examine the periodic states that develop at fixed freezing rates in a constant, uniform temperature gradient, and compare the results against experimental observations. Congruent with the experiments, three periodic regimes are identified. At low freezing rates, a regular periodic sequence of ice lenses is obtained; predictions for the compacted layer thickness and ice-lens characteristics as a function of freezing rate are consistent with experiments. At intermediate freezing rates, multiple modes of periodic ice lenses occur with a significantly diminished compacted layer. When the cohesion between the compacted particles is sufficiently strong, a sequence of mode-doubling bifurcations lead to chaos, which may explain the disordered ice lenses observed experimentally. Finally, beyond a critical freezing rate, the regime for sustained ice-lens growth breaks down. This breakdown is consistent with the emergence of a distinct regime of ice segregation found experimentally, which exhibits a periodic, banded structure that is qualitatively distinct from ice lenses. © Cambridge University Press 2014.

Description: Spontaneous film rupture from van der Waals instability is investigated in two dimensions. The focus is on pure liquids with clean interfaces. This case is applicable to metallic foams for which surfactants are not available. There are important implications in aqueous foams as well, but the main differences are noted. A thin liquid film between adjacent bubbles in a foam has finite length, curved boundaries (Plateau borders) and a drainage flow from capillary suction that causes it to thin. A full linear stability analysis of this thinning film shows that rupture occurs once the film has thinned to tens of nanometres, whereas for a quiescent film with a constant and uniform thickness, rupture occurs when the thickness is hundreds of nanometres. Plateau borders and flow are both found to contribute to the stabilization. The drainage flow leads to several distinct qualitative features as well. In particular, unstable disturbances are advected by the flow to the edges of the thin film. As a result, the edges of the film close to the Plateau borders appear more susceptible to rupture than the centre of the film. © 2010 Cambridge University Press.