Europa's Ice Shell Between Conduction and Convection: A Regime Boundary Computed from Grain Size and Tidal Heat Flux

Whether Europa's ice shell transports heat by conduction alone or by solid-state convection underneath a stagnant lid decides how material and oxidants move between the surface and the ocean. This study computes both sides of that question. Conductive thicknesses for tidal heat fluxes of 30 to 100 milliwatts per square metre span 21.79 down to 6.538 kilometres. Rayleigh numbers for a warm 20-kilometre layer range from 2.74e+07 at 0.1-millimetre grain size to 2740 at 10-millimetre grains, crossing the convective threshold near millimetre grains. The shell therefore sits close to the regime boundary, and grain size, an unmeasured quantity, controls the answer. The honest conclusion is conditional: fine-grained ice convects, coarse-grained ice conducts. Computed from stated assumptions, not measured.