Viscosity of rock-ice mixtures and applications to the evolution of icy satellites

Theory and experiments are used to establish lower and upper bounds on the ratio of actual viscosity to pure ice viscosity for a suspension of rock particles in a water ice matrix. A rheological model for rock-ice mixtures is described, establishing bounds for the range of possible viscosity enhancements provided by a suspension of silicate spheres in an ice matrix. A parametrized thermal convection model is described and used to determine a criterion for criticality, defined as the heat flow and/or silicate volume fraction for which the satellite temperature profile intercepts the melting curve of water ice. The consequences of achieving this critical state are examined, and it is shown that under certain circumstances a 'runaway' differentiation can occur in which the silicates settle to form a core and extensive melting of water ice takes place, the latent heat being supplied by the gravitational energy of differentiation. A possible application of these results to Ganymede and Callisto is described.