  A handful of binary Wolf-Rayet stars are known to harbour spectacular spiral
structures spanning a few hundred AU. These systems host some of the highest
dust production rates in the Universe and are therefore interesting candidates
to address the origin of the enigmatic dust excess observed across galactic
evolution. The substantial interaction between the winds of the Wolf-Rayet star
and its companion constitutes a unique laboratory to study the mechanisms of
dust nucleation in a hostile environment. Using the grid-based
$\texttt{RAMSES}$ code, we investigate this problem by performing a 3D
hydrodynamic simulation of the inner region of the prototypical spiral nebula
around WR104. We then process the $\texttt{RAMSES}$ results using the radiative
transfer code $\texttt{RADMC3d}$ to generate a candidate observable scene. This
allows us to estimate the geometrical parameters of the shocked region. We link
those quantities to the specific chemical pathway for dust nucleation, where
the hydrogen-rich companion's wind catalyses dust formation. The scaling laws
we derive constitute a unique tool that can be directly compared to
observations. Depending on the dust nucleation locus, the velocity field
reveals a differential wind speed. Thus, the initial dust speed could be more
balanced between the speeds of the two stellar winds ($\sim$1600 km/s). With
$\texttt{RADMC3d}$, we provide constraints on the dust nucleation radius for
different combinations of dust-to-gas ratio, hydrogen enrichment and dust grain
properties. Finally, our models reveal that dust may escape beyond the
boundaries of the spiral due to hydrodynamical instabilities in the wind
collision zone.
