  The two-step percolation behavior in aggregating systems was studied both
experimentally and by means of Monte Carlo (MC) simulations. In experimental
studies, the electrical conductivity, $\sigma$, of colloidal suspension of
multiwalled carbon nanotubes (CNTs) in decane was measured. The suspension was
submitted to mechanical de-liquoring in a planar filtration-compression
conductometric cell. During de-liquoring, the distance between the measuring
electrodes continuously decreased and the CNT volume fraction $\varphi$
continuously increased (from $10^{-3}$ up to $\approx 0.3$% v/v). The two
percolation thresholds at $\varphi_{1}\lesssim 10^{-3}$ and $\varphi_{2}\approx
10^{-2}$ can reflect the interpenetration of loose CNT aggregates and
percolation across the compact conducting aggregates, respectively. The MC
computational model accounted for the core-shell structure of conducting
particles or their aggregates, the tendency of a particle for aggregation, the
formation of solvation shells, and the elongated geometry of the conductometric
cell. The MC studies revealed two smoothed percolation transitions in
$\sigma(\varphi)$ dependencies that correspond to the percolation through the
shells and cores, respectively. The data demonstrated a noticeable impact of
particle aggregation on anisotropy in electrical conductivity $\sigma(\varphi)$
measured along different directions in the conductometric cell.
