K3D is a fully 3-dimensional model used to study dust mantle formation. The model is essentially a thermal model, taking into account conduction, absorption of solar radiation, emission of thermal radiation, as well as heat released in crystallization of amorphous ice and absorbed in sublimation of crystalline ice. While we consider a porous structure and allow for internal sublimation, we do not compute the gas flow rate, but rather assume rapid transfer to the surface, which is acceptable for shallow depths, large porosities and steady-state conditions. We also consider dust drag, representing the dust grain size distribution by 5 discrete categories, differing in grain size. For each azimuth, depth and time, we compute the critical grain size above which grains can be dragged by gas and leave the nucleus. Those left behind form, eventually, an ice-depleted permanent dust mantle. The rate of growth of this mantle decreases considerably with repeated or bital revolutions; therefore, the results obtained here at the end of 5 orbits may be taken as representative.
The thickness of this mantle varies significantly over the nucleus surface. Depending on latitude and on thermal conductivity (but discarding as unphysical very high conductivities), the dust mantle may be as thin as 1 cm, and as thick as #10 cm. This range is significant because the former is smaller than the diurnal skin depth, while the latter exceeds it. This means that on the nucleus surface there will be areas that show diurnal variation of activity (rapid response to insolation), but also areas of more constant activity. The depth of unaltered material, marked here by the crystallization front, ranges between 1 m and several meters. The size distribution of dust grains changes along the orbit, be- ing steeper at large distances. In all cases, it is steeper than that assumed for the nucleus.