## 2 Pore-Structure Characterisation and Analysis of Permeability Data  
A two-part methodology is used here: the determination of key pore-structure-related parameters via sphere packing models and X-ray computed tomography datasets as well as numerical modelling and simulation of the normal incidence sound absorption coefficients developed across the interstices of these cellular materials. Figure 1 shows that [PERSON] [28] and JCA [24] models are better predictors of the sound absorption spectra of bottleneck-shaped and tetrakaidekahedron-shaped cellular materials. Since similar materials are considered herein, the numerical application of each of these models will require the input of pore-structure related parameters that define the vibroacoustic characteristics of the materials. Simulations in [14] showed that [PERSON]'s equivalent fluid model requires inputs such as static viscous permeability (k\({}_{0}\)), high-frequency-limit of dynamic tortuosity (\(\tau\)-simple known as tortuosity), and sample porosity (\(\varepsilon\)). In addition, the numerical application of the semi-phenomenological Johnson-Champoux-Allard (JCA) model in [16; 29]requires the inclusion of viscous (\(\wedge\)) and thermal characteristic length (\(\overline{\wedge}\)) to account for the viscous thermal dissipation mechanism both at low and high frequencies. The effects imposed by monosized bottleneck-shaped structures on their acoustic behaviour were primarily determined [14; 30] by the static viscous permeability of the structure, which was determined by numerical simulation of pressure drop across air-saturated samples for superficial fluid velocities within the creeping fluid flow regime. Studies in [18; 32; 33] demonstrate that discrete element modelling and simulation (DEM) packing of spheres, as well as three-dimensional (3D) advanced imaging, can be utilised to mimic the geometrical features of bottleneck-dominated cellular metals made by replication casting (see Figure 2a-c). The study in [32] describes the creation of bimodal bottleneck structures using the same methodologies as the original study [8]. In brief, this study created packed beds of monomodal and bimodal virtual structures--varying capillary radius between 10 and 80 \(\upmu\)m and varying widely-distributed particle sizes to create structures capable of realistic manipulation; considering the available technological operating conditions and processing parameters used in the inverse casting process of manufacturing porous metals [34]. The particles were classified as large-large (L-L-(2.0-2.5 mm)), large-small (L-S-(2.0-2.5 mm + 0.5-1.0 mm)) and small-small (S-S-(0.5-1.0 mm)). While L-L and S-S structures were monomodal in nature, bimodal structures (L-S) depicted packing conditions involving the combination of small spheres into larger ones and were created for 6.25, 12.50, 25.00 and 50.00% volume addition of S-S in L-L. Then, a MatlabTM script was used to create 2D datasets of binary images from x, y, z particle conditions and capillary radius of between 10 and 80 \(\upmu\)m. Following the import of 2D datasets, a 3D imaging and characterisation software (ScanIP module of Synopsis-SimplewareTM) was used to create 3D volumes and 3D representative volume elements (RVEs). In determining the 3-D RVE structure, larger volumes were subdivided into smaller units until the model porosity reached three per cent of its bulk value. In the ScanIP module, application of the recursive Gaussian smoothing method resulted in lost features and increased pore openings, indicating the inadequacy of using this technique to filter noise within this type of material. It was then possible to preserve these geometric features by using smart mask smoothing (SMS) with ten iterations.