SEM images and localization of specific unit cells to the critical paths (of the fluid flows) in real foam samples. (Top line) Micrographs and unit cells of sample 1, sample 2, and sample 5 in Ref. 8 . (Middle line) Micrographs and unit cells of foam samples M7, M9, and M11 in Ref. 9 . Arrows represent some positions of Ts1 . The difficulty to visualize Ts1 in M11 is attributed to the low magnification of the corresponding SEM. (Bottom line) Micrographs and unit cells of foam samples R1, R2, and R3 in Refs. 14 and 15 .
Sound absorption coefficients at normal incidence (SACNI) of real foam samples. (a) SACNI vs frequency from sample 1 (left), sample 2 (middle), and sample 5 (right) in Ref. 8 . The red thin lines in (a) correspond to our computations when using the unit cells shown in Fig. 1 to be compared with standing wave tube measurements (black thick lines with triangles). Also shown in black thin lines and circles are, respectively, the so-called predicted (J-A) and predicted (New) SACNI as obtained by Kino et al. in Ref. 8 . The error bars in red are dominated by the statistical errors in the ligament lengths measurements, which were determined from SD uncertainties using micrographs shown in Fig. 1 (top line). These uncertainties, in turn, determine the corresponding uncertainties in the SACNI. (b) SACNI vs frequency for foam samples M7 (left), M9 (middle), and M11 (right) in Ref. 9 . Error bars: the uncertainty region determined from all possible combinations of input parameters (doublets or triplets of input parameters, where an input parameter can take three possible values: mean, mean + SD, and mean − SD). (c) SACNI vs frequency for foam samples R1 (left), R2 (middle) and R3 (right) in Ref. 15 .
Comparison between semi-empirical (Ref. 9 ) and numerical estimates of multi-scale parameters derived from membrane-free 14 (M7 and M9, direct microstructural data) and membrane-based 15 (M11, iterative approach) three-dimensional unit-cells. (a) direct measurements and characterization techniques and (b) semi-empirical estimates.
Article metrics loading...
Full text loading...