  Frozen transient imbibition states in arrays of straight cylindrical pores
400 nm in diameter were imaged by phase-contrast X-ray computed tomography with
single-pore resolution. A semi-automatic algorithm yielding brightness profiles
along all pores identified within the probed sample volume is described.
Imbibition front positions are determined by descriptive statistics. A first
approach involves the evaluation of frequency densities of single-pore
imbibition lengths, a second one the evaluation of the statistical brightness
dispersion within the probed volume as a function of the distance from the pore
mouths. We plotted average imbibition front positions against systematically
varied powers of the imbibition time and determined the optimal exponent of the
imbibition time by considering the correlation coefficients of the
corresponding linear fits. Thus, slight deviations from the proportionality of
the average imbibition front position to the square root of the imbibition time
predicted by the Lucas-Washburn theory were found. A meaningful preexponential
factor in the power law relating imbibition front position and imbibition time
may only be determined after ambiguities regarding the exponent of the
imbibition time are resolved. The dispersion of peaks representing the
imbibition front in frequency densities of single-pore imbibition lengths and
in brightness dispersion profiles plotted against the pore depth is suggested
as measure of the imbibition front width. Phase-contrast X-ray computed
tomography allows the evaluation of a large number of infiltrated submicron
pores taking advantage of phase-contrast imaging; artifacts related to sample
damage by tomography requiring physical ablation of sample material are
avoided.
