A journey across scales: Two-phase models for Europa’s icy mantle

Kurzfassung

Europa, one of Jupiter's moons, is a prime target in the search for habitability within the solar system (e.g., [1]). While the greatest potential for life lies in the interaction between a hypothesized liquid ocean and the rocky mantle—similar to Earth's deep-sea hydrothermal vents—the outer ice shell also plays a critical role. This shell could either aid in the detection of life or serve as a potential habitat itself. In both scenarios, the transport of brine liquids is key: at the sub-kilometer-scale ice-ocean interface (localized brine intake) and across the planetary-scale ice shell (global brine transport). Despite the vast differences in spatial and temporal scales, these processes require models that account for the interplay between two phases (solid and liquid), the presence of solutes (salts), and phase changes. Within the terrestrial and extraterrestrial cryosphere research community, two-phase flow models have been independently developed. They describe processes such as mushy layer dynamics (e.g., [3]) and, more recently, global ice shell behavior involving pure water ice (e.g., [4]). Established models are often derived from a common system of conservation laws, but a variety of different simplifying assumptions makes it challenging to compare and connect them consistently. In this work, we present a unified framework for deriving process models applicable to different scales, from mushy layers to global ice shells. We begin by outlining the homogenized conservation laws for mass, momentum, energy, and solute (salt), operating under the assumption of equilibrium solidification. Subsequently, we perform a scaling analysis to develop two-phase flow models tailored to both planetary-scale ice shells and sub-kilometer-scale mushy layers, which represent the ice-ocean interface. These derived models will be systematically compared to existing published models, with a particular focus on addressing the equilibrium thermochemistry problem in the context of the significant pressure variations encountered across planetary ice shells.