Void bounds for fluid transport in sea ice

Arctic and Antarctic sea ice plays a critical role in the global ocean–climate system, as well as in polar biology. Sea ice is a porous composite of pure ice with brine, air and salt inclusions whose microstructure varies significantly with temperature. The fluid transport properties of sea ice control a broad range of geophysical and biological processes. Yet little is known, for example, about bulk flow of brine or diffusive transport of dissolved substances such as nutrients or pollutants through the porous microstructure, particularly from a theoretical standpoint. Here we give rigorous, mathematical formulations of the two key problems of fluid dynamics in sea ice: estimating the effective fluid permeability tensor k(ϕ) and its dependence on brine porosity ϕ, and estimating the trapping constant γ or mean survival time τ for a diffusion process in the pore microstructure which can react with the boundary. We bring together and review a variety of results which lay the foundation for studying fluid transport processes in sea ice from a mathematical perspective, and focus on rigorous bounds on k and γ. Void bounds evaluated by Torquato and Pham [Torquato, S., Pham, D.C., 2004. Optimal bounds on the trapping constant and permeability of porous media. Phys. Rev. Lett. 92, 255505:1–4] for classical coated cylinder geometries yield pipe bounds for the permeability k of sea ice in the vertical direction. By incorporating information about average brine inclusion sizes, the void bounds provide a useful benchmark that captures laboratory data taken on k(ϕ).