New insights into temperature-dependent ice properties and their effect on ice shell convection for icy ocean worlds

Dynamics of Mixed Clathrate‐Ice Shells on Ocean Worlds

“…Methane clathrates affect the convective dynamics of an ice shell because they have higher viscosity (Durham et al., 2003; Goldsby & Kohlstedt, 2001), lower thermal conductivity (Carnahan et al., 2021; Sloan & Koh, 2007; Wolfenbarger et al., 2021), and higher density (Feistel & Wagner, 2006; Helgerud et al., 2009) than water ice (Figures 2a–2c). The physical properties of methane clathrates and ice are pressure and temperature dependent.…”

“… Physical properties of ice and methane clathrate: (a) density at 5 MPa (Feistel & Wagner, 2006; Helgerud et al., 2009), (b) thermal conductivity (Carnahan et al., 2021; Sloan & Koh, 2007), and (c) viscosity (Durham et al., 2003; Goldsby & Kohlstedt, 2001). (d) Viscosity mixing relationships and data for mineral mixtures (Ji, 2004), black dots, and ice‐salt hydrate mixtures (Durham et al., 2005), black circles.…”

“…Employing our scaling of clathrate-ice shells, we sample the uncertainty in relevant ice shell parameters for Titan, Pluto, Europa, and Ganymede (Table S1 in Supporting Information S1) and predict what fraction of ice shells will be convective before and after clathrates are entrained in the outer shell (Table 1) by comparing the calculated Rayleigh number for each sample to the critical Rayleigh number. Pure ice layers on Europa are likely conductive due to the lower expected shell thickness, whereas the thicker predicted shells on Titan are convecting (Carnahan et al, 2021;Howell, 2021). The presence of a surface clathrate layer insulates the underlying ice, resulting in a greater proportion of convective profiles for any given world (Table 1).…”

“…Instead, we adopt a first-order assumption that methane gas or clathrate emanates from the core at a constant rate throughout planetary evolution, ∼4 billion years. This assumption provides a reasonable middle ground scenario for the release rate of clathrates and provides a baseline to compare with (Feistel & Wagner, 2006;Helgerud et al, 2009), (b) thermal conductivity (Carnahan et al, 2021;Sloan & Koh, 2007), and (c) viscosity (Durham et al, 2003;Goldsby & Kohlstedt, 2001). (d) Viscosity mixing relationships and data for mineral mixtures (Ji, 2004), black dots, and ice-salt hydrate mixtures (Durham et al, 2005), black circles.…”

Cooling Crusts Create Concomitant Cryovolcanic Cracks

“…We apply an isothermal boundary condition T ( r o ) = 100 K at the surface ( r o ). The thermal conductivity k of ice is temperature‐dependent, varying by a factor of approximately 3 from 100 K to the melting temperature (e.g., Carnahan et al., 2021). We use k ( T ) = 651/ T for T in Kelvin and k in W m −1 K −1 (Petrenko & Whitworth, 1999).…”