Modelling three-phase mushy layers, with applications to air bubbles and oil droplets in sea ice

Thesis

A mushy layer is a reactive porous medium that forms during the partial solidification of a multicomponent liquid. Sea ice is a naturally occurring mushy layer that forms through the freezing of seawater in the polar oceans. This multiphase mixture of solid ice crystals, liquid brine, air bubbles, and other chemical species plays a critical role in Earth’s climate and ecosystems. Two-phase mushy layers, comprising a porous solid saturated with liquid, have been well studied; however, sea ice and other mushy layers in the natural environment often contain gaseous inclusions or other immiscible liquid phases, yielding a three-phase problem. This thesis formulates appropriate conservation equations for a three-phase mushy layer that accounts for the production, migration, and trapping of a third distinct phase in the pore space of sea ice. We use an idealised model of the pore geometry to derive a novel expression for the vertical flux of a buoyant third phase dispersed as bubbles/droplets in the liquid-filled pore space. The resulting model is applied to both air bubbles and oil droplets in sea ice. Two key dimensionless parameters arise: (1) the ratio of the bubble/droplet radius to the pore throat-radius and (2) the timescale of gas exsolution relative to the timescale of solidification in the mushy layer (in the case of a solid-liquid-gas system).

We explore the three-phase mushy-layer model in a variety of settings. First, we examine the three-phase mushy layer found during the steady solidification of air-saturated saltwater in a Hele-Shaw cell. We show that neglecting the volume occupied by exsolved gas yields a reduced “tracer” model for the dissolved and free-phase gas that still describes the steady-state solution well. Then, we formulate a one-dimensional transient model for sea-ice evolution that includes parameterisations for brine convection, radiative transfer, and heat exchanges with the overlying atmosphere and snowpack, and with the underlying ocean. We validate this transient model against observations of first-year landfast sea ice at Barrow, Alaska. We use ice core measurements of bulk gas concentrations from Barrow to constrain the gas dynamics in our model and predict the seasonal evolution of the gas volume fraction and ice bulk density. This has implications for biogeochemical cycles in the Arctic and the estimation of ice thickness from remote sensing measurements. Finally, we investigate the impact of low levels of weathered oil droplets on landfast sea ice, and find that the increased absorption of solar radiation by these droplets can significantly enhance ice melt rates and delay the onset of the spring under-ice algal bloom compared with year-to-year variability. The results in this thesis have important implications for the future study of sea ice as a complex multiphase reactive material.

Authors: Fishlock, JW

• DOI: 10.5287/ora-avaq1jkey
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: droplets; sea ice; bubbles; radiative transfer; mushy layers; porous media
• Subjects: Porous materials; Sea ice; Phase transformations (Statistical physics); Arctic Ocean; Multiphase flow; Fluid dynamics; Climate