  Random walks (RW) of particles adsorbed in the internal walls of porous
deposits produced by ballistic-type growth models are studied. The particles
start at the external surface of the deposits and enter their pores, in order
to simulate an external flux of a species towards a porous solid. For short
times, the walker concentration decays as a stretched exponential of the depth
z, but a crossover to long time normal diffusion is observed in most samples.
The anomalous concentration profile remains at long times in very porous solids
if the walker steps are restricted to nearest neighbors and is accompanied with
subdiffusion features. These findings are correlated with a decay of the
explored area with z. The study of RW of tracer particles left at the internal
part of the solid rules out an interpretation by diffusion equations with
position-dependent coefficients. A model of RW in a tube of decreasing cross
section explains those results by showing long crossovers from an effective
subdiffusion regime to an asymptotic normal diffusion. The crossover position
and density are analytically calculated for a tube with area decreasing
exponentially with z and show good agreement with numerical data. The anomalous
decay of the concentration profile is interpreted as a templating effect of the
tube shape on the total number of diffusing particles at each depth, while the
volumetric concentration in the actually explored porous region may not have
significant decay. These results may explain the anomalous diffusion of metal
atoms in porous deposits observed in recent works. They also confirm the
difficulty in interpreting experimental or computational data on anomalous
transport reported in recent works, particularly if only the concentration
profiles are measured.
