  The diffusion of water molecules through mesoporous dust of amorphous carbon
(a-C) is a key process in the evolution of prestellar, protostellar, and
protoplanetary dust, as well as in that of comets. It also plays a role in the
formation of planets. Given the absence of data on this process, we
experimentally studied the isothermal diffusion of water molecules desorbing
from water ice buried at the bottom of a mesoporous layer of aggregated a-C
nanoparticles, a material analogous to protostellar and cometary dust. We used
infrared spectroscopy to monitor diffusion in low temperature (160 to 170 K)
and pressure (6 $\times$ 10$^{-5}$ to 8 $\times$ 10$^{-4}$ Pa) conditions.
Fick's first law of diffusion allowed us to derive diffusivity values on the
order of 10$^{-2}$ cm$^2$ s$^{-1}$, which we linked to Knudsen diffusion. Water
vapor molecular fluxes ranged from 5 $\times$ 10$^{12}$ to 3 $\times$ 10$^{14}$
cm$^{-2}$ s$^{-1}$ for thicknesses of the ice-free porous layer ranging from 60
to 1900 nm. Assimilating the layers of nanoparticles to assemblies of spheres,
we attributed to this cosmic dust analog of porosity 0.80-0.90 a geometry
correction factor, similar to the tortuosity factor of tubular pore systems,
between 0.94 and 2.85. Applying the method to ices and refractory particles of
other compositions will provides us with other useful data.
