# Design of a Noise Mitigation System Using Lightweight Graded Micro-Porous Material
## 2 Establish Predictive Methods to Calculate Flow Properties of Polydisperse Particles
### Micro-Porous Hollow Bubble (\(\upmu\)-PHB) Composite Material
#### 2.2.3. Calculation of Flow Properties of \(\upmu\)PHB Composite Materials
The viscous characteristic length, which accounts for small pore sizes contributing to viscous dissipation, increases with larger microbubble sizes, a trend that  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameters** & **Small Size, d\({}_{\text{m}}\) = 95 μm** & **Medium Size, d\({}_{\text{m}}\) = 223 μm** & **Large Size, d\({}_{\text{m}}\) = 625 μm** \\ \hline Cementation exponent, m & 2.59 \(\pm\) 0.03 & 2.39 \(\pm\) 0.03 & 2.71 \(\pm\) 0.03 \\ \hline Pore complexity parameter, a & 0.0114 \(\pm\) 0.001 & 0.114 \(\pm\) 0.010 & 0.55 \(\pm\) 0.03 \\ \hline Pore shape factors, c & 7.0 \(\pm\) 1.0 & 3.48 \(\pm\) 1.79 & 1.60 \(\pm\) 0.  
appears reasonable. Likewise, the thermal characteristic length, reflecting thermal energy losses in larger pores, also increases with microbubble size, aligning with expectations. Thermal permeability, dependent on porosity and thermal characteristic length, likewise increases with microbubble size. For medium and large particle-size micro-porous materials, viscous tortuosity decreases as microbubble size increases, while thermal tortuosity remains the same for both cases. to 900 Hz. Nevertheless, it fits well between 900 to 1150 Hz, and beyond 1150 Hz a slight overestimation of about 1 dB is observed. Considering our targeted frequency range above 500 Hz (for aircraft engine acoustic liners), the predictions demonstrate reasonably good agreement with the experimental data over this threshold. Further, from Figure 11 we see that the transmission loss increased with a decrease in porosity (low permeability) and pore size or particle size. The same flow properties were used to predict both the absorption coefficient and transmission loss response of 50 mm thick specimens of all three size groups. The predictions demonstrated good agreement with the experimental results reported in the Ph.D. thesis [33]. The distinctiveness of the flow properties was validated for this particular class of materials. Additionally, for large particle-size \(\upmu\)PHB composite material, the ratio of minimum specimen dimension to mean particle diameter is 40. This finding validates the conclusion derived from the results obtained with spherical glass beads, indicating that when the ratio of minimum specimen dimension to mean particle diameter exceeds 10, the flow properties become unique (flow properties independent of specimen geometry for a specific material system). Based on this comprehensive study, we can conclude that the flow properties calculated by a multivariable-fit inverse method with G-JCAL/JCAPL equations by curve fitting the experimental absorption coefficient response of a 25 mm thick specimen can reliably predict both absorption and transmission loss for any geometry for a specific particle-size group \(\upmu\)PHB composite material. This reaffirms that the flow properties remain unique for a specific material system.