# Acoustical Properties of Fiberglass Blankets Impregnated with Silica Aerogel
## 5 Conclusions  
This work is a systematic study of the acoustical properties of fibrous blankets that are impregnated with an aerogel powder. The level of impregnation (filling ratio) has been progressively changed from 0 to 100% with respect to the material weight. The complex acoustic reflection coefficient of these materials was measured in the frequency range of 300-3000 Hz using a standard impedance tube setup [25]. These data were used to invert the three parameters of the theoretical model [28] via the best fit method [30]. It was found that the adopted model can predict the reflection coefficient spectrum relatively accurately with the RMS error being below 4%. The absorption coefficient of these relatively thin (8-9 mm thick) fibrous blankets with 50-75% filling ratios is relatively high (30-50%), particularly above 1000 Hz. This level of absorption has a practical value in applications related to engineering noise control. The results of the parameter inversion obtained with the adopted model suggest that the impregnation of fibrous blanket with an aerogel powder results in a progressive reduction in the effective pore size. For the filling ratios in the range of 0-50% there is also a small but progressive reduction in the inverted porosity, which is within 3% of that measured directly. The absorption coefficient increases progressively with the increased filling ratio, reaching its maximum when the filling ratio is between 50% and 75%. This decrease in the effective pore size results in an increased acoustic attenuation and better coupling, which are important to maximize the acoustic absorption for such a thin porous layer. Increasing the filling ratio beyond 75% results in a significant drop in the absorption. This drop is associated with a considerable drop in the porosity value (\(\phi=0.505\)) and substantial increase in the pore size (\(\overline{s}=83\) um) inverted for the filling ratio of 100%. The discrepancy between the model and data for this filling ratio increases. As the proportion of aerogel powder in the material approaches 100%, the open porosity does not drop significantly, i.e., the proportion of the open interconnected pores remains relatively constant. However, the sorption and thermal diffusion effects in the inner pores in the aerogel grains become much more important [31]. These pores have nanometer scales [6], which is much smaller than the values of \(\overline{s}\) inverted with the model [28] (see Table 1). The effects that occur in nanometer pores cannot be captured by the adopted model [28], which only accounts for the classical visco-thermal and inertia effects in pores that are much larger than the mean free path (68 nm in air at ambient pressure and temperature). This work suggests that in order to predict the acoustic behavior of fibrous blankets with high aerogel filling ratios there is a clear need to refine the model [28] to include the sorption and pressure diffusion effects. The adopted model does require unrealistic values of the median pore size and porosity to achieve a good fit. This model can be refined by including in it the work by [PERSON] and [PERSON] [31]. In this way the dynamic compressibilities of the air filling the inter-fiber pores and in the nanoscale pores in the aerogel grains can be combined to account for all of the physical effects that contribute to the observed acoustical behavior. Conceptualization, H.B. and K.V.H. ; methodology, H.B. ; software, K.V.H. ; validation, formal analysis, H.B. ; investigation, H.B. ; resources, H.B. ; data curation, H.B. ; writing--original draft preparation, H.B. ; writing--review and editing, K.V.H. ; visualization, H.B. ; supervision, K.V.H. ; project administration, K.V.H. ; funding acquisition, K.V.H. All authors have read and agreed to the published version of the manuscript. **Funding:** This research was partly funded by the EPSRC-sponsored Centre for Doctoral Training in Polymers, Soft Matter and Colloids, grant number EP/L016281/1, and industry sponsors--Armacell.