# 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  
#### 2.2.1 \(\upmu\)-PHB Specimens for Impedance Test  
Three different size groups of hollow microbubbles (Cenospheres), commercially called Extendospheres, that are byproducts of coal-burning electric power plants supplied by SphereOne are used. In the case of hollow microbubbles, due to handling and transportation, there is a chance of some broken microbubbles; therefore, only the lightweight floaters were used. In this current study, the particle-size groups were pre-processed via sieving, using (1) small size (63 to 125 \(\upmu\)m, mean particle diameter, \(\rm{d_{m}}=95~{}\upmu\)m), (2) medium size (125 to 425 \(\upmu\)m, \(\rm{d_{m}}=223~{}\upmu\)m), and (3) large size (425 to 825 \(\upmu\)m, \(\rm{d_{m}}=625~{}\upmu\)m). The rationale for pre-processing via sieving is to eliminate extremely small-sized microbubbles that could potentially block the pores. This process also aids in managing the pore structure, ensuring the presence of nearly uniform-size microbubbles. Such control allows for engineering the acoustic responses when built as a graded pore distribution material system from large size to small size. The details of the hollow microbubbles as received from SphereOne, and the pre-processing are listed in Table 3. Also, note the particle-size distribution of the three groups of particle sizes, as received from SphereOne, and the selected three ranges shown by the dashed lines in Figure 7.  
The pre-processed narrow particle-size distribution (dashed lines in Figure 7) (see Table 3 and Figure 7) and SC1008 reside, a phenolic binder of high char yield, were used. The established binder % as a % of filler weight was 9%, 9%, and 15% for the small, medium, and large size particles, respectively. This binder amount is sufficient to create point-to-point contact between the bubbles (a good bonding strength) and not alter the pore properties by retaining the same porosities as loose hollow microbubbles (Figure 8a). The compaction pressure was 25% of the limiting pressure (small--1.1 MPa, medium--0.97 MPa, and large--0.55 MPa) to avoid crushing the microbubbles [25]. Cylindrical specimens of 100 mm diameter and 25 mm (three replicas in each case) thickness were fabricated for all three size groups of hollow microbubbles (Figure 8b). The mean values of the results are reported. Figure 8c shows the magnified images of the uPHB composite materials with different particle sizes. The processing technique is detailed in the reference [25]. \begin{table}
\begin{tabular}{c c c c c c} \hline \multirow{2}{*}{**Sl No**} & **Hollow** & **As Received from** & **Pres-Processed** & **Resole Binder** & **Porosity of** & **Mean Bulk** \\  & **Size Group** & **SphereOne** & & **Weight** & **Material** & **Density, g/cc** \\ \hline \multirow{2}{*}{\(1\)} & \multirow{2}{*}{Small} & 10–180 μm, & 63–125 μm, & \multirow{2}{*}{9} & \multirow{2}{*}{0.447} & \multirow{2}{*}{0.34} \\  & & \(\mathrm{d_{m}}\) = 70 μm & \(\mathrm{d_{m}}\) = 95 μm & & \\ \hline \multirow{2}{*}{\(2\)} & \multirow{2}{*}{Medium} & 10–500 μm, & 125–425 μm, & \multirow{2}{*}{9} & \multirow{2}{*}{0.478} & \multirow{2}{*}{0.44} \\  & & \(\mathrm{d_{m}}\) = 160 μm & \(\mathrm{d_{m}}\) = 223 μm & & \\ \hline \multirow{2}{*}{\(3\)} & \multirow{2}{*}{Large} & 150–850 μm, & 425–825 μm, & \multirow{2}{*}{15} & \multirow{2}{*}{0.602} & \multirow{2}{*}{0.35} \\  & & \(\mathrm{d_{m}}\) = 450 μm & \(\mathrm{d_{m}}\) = 625 μm & & \\ \hline \end{tabular}
\end{table} 
Table 3: Materials used to fabricate μPHB composite material. Figure 7: Particle-size distribution of the three groups of hollow microbubbles as received, and the selected range for preparing the porous materials is shown by the broken lines. In this class of uPHB composite materials, the measurement of the bonded material porosity using the porosimeter with inert gases is unsuitable because of the presence of minute holes and cracks in the microbubbles. These methods tend to overestimate the porosity.