Nano-fibrous composite sound absorbers inspired by owl feather surfaces

Applied Acoustics 156 (2019) 151–157

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Nano-fibrous composite sound absorbers inspired by owl feather surfaces Guosheng Ji a,⇑, Jiang Cui a, Yi Fang a, Shanshan Yao a, Jie Zhou b,⇑, Jang-Kyo Kim a,⇑ a b

Department of Mechanical and Aerospace Engineering, Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China School of Aeronautics, Northwestern Polytechnical University, Xi’An 710072, China

a r t i c l e

i n f o

Article history: Received 17 April 2019 Received in revised form 19 June 2019 Accepted 21 June 2019

Keywords: Nanofibrous membranes Sound absorption coefficient Melamine foam

a b s t r a c t This study reports the development of a bionic sound absorber inspired by the layered microstructure found on owl feather surface. The so-called bionic sound absorber is made of a thin nano-fibrous membrane backed with a substrate melamine foam layer (NMSMF). The effects of nanofiber diameter, and the thicknesses of nano-fibrous membranes and substrate melamine foam layers on the sound absorption coefficients are systematically analyzed. The study identifies a cut-off frequency at which sound absorption coefficient suddenly increases. The effect is partially explained based on the permeable and impermeable membrane models. This finding may shed new insight into designing novel semi-permeable sound absorbers possessing a cut-off effect for engineering applications. Ó 2019 Elsevier Ltd. All rights reserved.

1. Introduction Barn owls are known for silent flights over an audible frequency range to human. Lilley [1] suggested that the velvet-like feather surface of owls was partly responsible for the silent flight. The feather surface microstructure was found similar to a morphology of a forest according to Bachmann et al., [2]. The feather surface structure in Fig. 1(a) consisted of two layers, a highly porous and fluffy canopy layer with a large number of pennulas (see Fig. 1 (b)) and a cavity layer with thick hairs (see Fig. 1(c)) [3,4]. The highly porous canopy layer may act as a buffer to extract energy from the quasi-turbulent flow and provide a bypass dissipation mechanism [5]. In addition, a multi-layer porous structure observed in a laser scanning confocal microscope indicates that intersected long barbules form a downy feather surface, and it works effectively as sound absorbers over the high-frequency range [6]. The velvet-like feather surface further leads to the mimic in bionic multi-layer sound absorbers such as micro-silt plates, micro-perforated membranes, and porous foams to improve sound absorption coefficients [7,8]. Inspired by the above dual-layer microstructure, a two-layer composite sound absorber is designed as shown in Fig. 1(d). The nanoscale poly (vinylidene fluoride-co-hexafluoropropylene) (PVDF-HFP) fibrous membrane with nanofiber diameters less than ⇑ Corresponding authors. E-mail addresses: [email protected] (G. Ji), [email protected] (J. Zhou), [email protected] (J.-K. Kim). https://doi.org/10.1016/j.apacoust.2019.06.021 0003-682X/Ó 2019 Elsevier Ltd. All rights reserved.

500 nm is considered as the upper canopy layer, which enables a high surface area to volume ratio, small pore sizes, and fluffy surfaces [9]. The melamine foam having relatively larger pore sizes and periodical microstructures is treated as the cavity layer with thick hairs. Therefore, thin PVDF-HFP nano-fibrous membranes backed with substrate melamine foam layers (NMSMF) are developed. In this paper, the fabrication and morphological analysis of PVDF-HFP nano-fibrous membranes, and their sound absorption performance are presented. The sound absorption coefficients are measured taking into account the effects of geometric parameters of nano-fibrous membranes, including membrane thickness, t, fiber diameter, a, and the thickness of the substrate melamine foam (SMF), h. Analytical models, such as the Johnson-ChampouxAllard (JCA) model for porous materials, permeable membrane (PM) and impermeable membrane (IM) models are adopted to explain the sound absorption coefficients.

2. Material preparation The PVDF-HFP nano-fibrous membranes were synthesized by a facile and scalable electrospinning method. As schematically shown in Fig. 2, the PVDF-HFP solution was ejected through a stainless-steel needle where a high voltage was applied to polarize the solution with electric charges. As a result, a strong electric field was established between the tip of the needle and the aluminium collector, allowing continuous extrusion of nanofibers. The

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Fig. 1. (a) Structure of the owl feather down including (b) the canopy layer and (c) the cavity layer [3]. (d) Two-layer composite sound absorber.

Fig. 2. Schematic of the electrospinning process to synthesize PVDF-HFP nano-fibrous membranes.

nanofibers naturally formed a polymer membrane consisting of interwoven webs with high porosities. The porosities, /, of PVDF-HFP nano-fibrous membranes were kept relatively constant at around 90 %. The thicknesses of the nano-fibrous membranes, t, and the diameters of electrospun nanofibers, a, were tuned to study their effects on sound absorption coefficients. To control / and t, we adjusted two key parameters of the electrospinning process, namely the duration of electrospinning and the feeding rate of the polymer solution. It is evident that the duration of electrospinning is linearly proportional to the membrane thickness, t. To control the nanofiber diameter, a, a fast feeding of polymer solution to the needle tip was applied so as to reduce the amount of accumulated charge, leading to a weak extrusion force and a large nanofiber diameter.

To prepare the polymer solution for electrospinning, PVDF-HFP pellets (Mn
130,000, supplied by Sigma-Aldrich and directly used without any additional purification) were dissolved in a mixture of dimethylformamide (DMF) and acetone at a weight ratio of 1:4 and with a concentration of 12 wt.%. The polymer solution was then electrospun using a needle under a constant voltage of 17.5 kV and at a designated feeding rate. Finally, the nanofibrous membranes were peeled off from the aluminium collector followed by evaporation of the solvent under vacuum at 80 °C. The morphology of the PVDF-HFP nano-fibrous membranes was examined on a scanning electron microscope (SEM, JSM-7100F), as shown in Fig. 3. All samples exhibited a uniformly distributed nanofibers without agglomeration, signifying the successful synthesis of PVDF-HFP nanofibers by electrospinning. Open pores with

Fig. 3. SEM images and the diameter distribution (insets) of PVDF-HFP nanofibers electrospun at feeding rates of (a) 0.45 mL/min; (b) 0.67 mL/min; (c) 1 mL/min and (d) 3 mL/min.

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several micrometers in diameter were formed as a result of the interweaving of nanofibers. Significant differences in diameters of the electrospun PVDF-HFP nanofibers prepared at different feeding rates were noted. The geometric parameters of PVDF-HFP nano-fibrous membranes, including the average diameter, a, porosity, / (which was kept constant), porosity errors,
, nano-fibrous membrane thickness, t, and surface density, q, are listed in Table 1. The sound absorption coefficients were measured by the twomicrophone transfer-function method, according to the ISO 10534-2:1998 international standard procedure [10]. The test was conducted in a B&K Impedance Tube Kit (50 Hz–6.4 kHz) Type 4206. As schematically shown in Fig. 4 (a), the sound absorption coefficient, a, is given a ¼ 1  R2 , where R is defined as the reflec-

Table 1 Parameters of PVDF-HFP nano-fibrous membranes. Sample

a (nm)

/,% (
,%)

t (lm)

q (kg/m2)

1 2 3 4

80 188 275 397

90.65 90.38 88.41 90.10

50 50 50 50

0.0083 0.0086 0.0103 0.0088

(0.7) (0.4) (1.8) (0.1)

153

tion coefficient which is the ratio of the reflected planar wave, pr , to the incident planar wave, pi . Two different samples, NMSMF and SMF, are shown in Fig. 4 (b). NMSMF was fabricated by attaching PVDF-HFP nano-fibrous membranes on the surface of SMF without using glues. The thicknesses of nano-fibrous membranes were modified by changing the number of membrane layers. 3. Parameter study in experimental measurements The mean values and standard deviations of sound absorption coefficients for NMSMFs and SMFs are given in Fig. 5. The thickness of nano-fibrous membranes was varied from 50 to 250 lm, the nanofiber diameter from 80 to 397 nm, and the thickness of SMFs h from 1 to 5 cm to study their effects on sound absorption coefficients. Effect of nano-fibrous membrane thickness, t. The sound absorption coefficient of the 1 cm-thick SMF was significantly affected by attaching the nano-fibrous membranes over the frequency range from 2000 to 6400 Hz, as shown in Fig. 5(a). The first peak of the sound absorption coefficient down-shifted with increasing t. For example, the sound absorption peak of NMSMFs shifted from about 3000 Hz for t ¼ 50 lm to about 2000 Hz for t ¼ 250 lm. Besides, the sound absorption coefficients of NMSMFs with a membrane thickness t ¼ 50 lm were much higher than

Fig. 4. (a) Schematic of the two-microphone transfer-function method. (b) NMSMF and SMF samples.

Fig. 5. Sound absorption coefficients of NMSMFs with (a) nanofiber diameter a ¼ 80 nm, and SMF thickness h ¼ 1 cm; (b) a ¼ 80 nm, and h ¼ 5 cm; (c) a ¼ 80 nm, and membrane thickness t ¼ 50 lm; (d) a ¼ 80 nm, and t ¼ 250 lm; (e) t ¼ 50 lm, and h ¼ 1 cm; and (f) t ¼ 50 lm, and h ¼ 5 cm.

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those for thicker membrane t ¼ 250 lm in the high-frequency range from 4000 to 6400 Hz. For instance, the sound absorption coefficient of the NMSMF with t ¼ 250 lm was about half that for t ¼ 50 lm at 6000 Hz. Effect of SMF thickness, h. When the SMF thickness, h, was increased to 5 cm, the effect of nanofibrous membranes on the improvement of sound absorption coefficients was significantly reduced, as shown in Fig. 5(b). The sound absorption coefficient in the low-frequency range from 500 to 3000 Hz increased with increasing h from 1 to 5 cm for a thin membrane of t ¼ 50 lm. For example, the sound absorption coefficient increased from about 0.15 to 0.8 when the SMF thickness h was changed from 1 to 5 cm at 500 Hz, as shown in Fig. 5(c). However, for NMSMFs with a thick membrane of t ¼ 250 lm, the sound absorption coefficients were less sensitive to SMF thickness h, see Fig. 5(d). Effect of nanofiber diameter, a. The sound absorption coefficients of SMFs were significantly improved by incorporating nano-fibrous membranes of thickness 50 lm for all nanofiber diameters a ¼ 80  397 nm studied over the frequency range from 2000 to 6400 Hz, as shown in Fig. 5(e). The similarly general trends of sound absorption coefficients of NMSMFs for different nanofiber diameters in Fig. 5(e) and (f) indicate that the nanofiber diameter was not a key factor determining the sound absorption coefficients. This is particularly true in view of their nanoscale nature. 4. Numerical simulation To explain the experimental results, the existing JCA model is adopted to study the acoustic properties of the SMFs, while three models, namely the JCA model, the PM model and the IM model are adopted to study the acoustic properties of the nano-fibrous membranes, as follows. The acoustic properties of SMFs can be described by the JCA model [11–13]. Five important acoustic parameters in the JCA model were obtained in the bottom-up method [14–16]: namely the porosity / = 0.99, the flow resistivity r = 14,700 Pasm2, the tortuosity b = 1.006, the viscous characteristic length

K ¼ 2:6  104 m, and the thermal characteristic length K0 ¼ 5:16  104 m for SMFs [17]. The JCA model with parameters obtained in the bottom-up method has been proven in our previous experimental studies. For nanoscale fibrous materials such as the nano-fibrous membranes explored in this study, the characteristic size of the microstructure is comparable to the mean free path of gas molecular, so that the continuum models such as the Euler equation and the Navier-stokes equation are not fully applicable in the analytical study [12]. The collisionless Boltzmann equation [18,19] taking into account the transition flow and free molecular flow is applicable at the nanoscale level, but the computational costs over the audible frequency range are prohibitively high. Therefore, the continuum model is extended to the modified continuum equations by accounting for the rarefaction and sorption effects in nanopores [20]. Then a link can be established between the macroscopic acoustic properties such as characteristic impedance and wavenumber, and microstructural parameters such as porosity, flow resistivity, tortuosity and characteristic size. In the modified continuum equations, the factor in assessing the validity of the modified continuum approach is defined as the Knudsen number K n ¼ kf =l, where kf ¼ 65 nm is the molecular mean free path at the standard temperature and pressure [20], and l is the microstructure characteristic length. A good agreement has been reached previously between the analytical results obtained from the modified continuum equations and the experimental data in the transition flow regime (0.1
fibrous materials are the average fiber radii r ranging from 40 to 198.5 nm, which corresponds to the Knudsen numbers from 1.62 to 0.33 in the transition flow regime. As a result, the modified continuum equations by considering the Knudsen number can be applied. Among the modified continuum equations, linearized ones describing the harmonic oscillations in the microstructure of nano-fibrous materials include the Navier-Stokes equation, the state for the gas equation, the conservation of mass equation, and the heat conduction equation [20]. The velocity and temperature applied to the pore walls are the slip [21] and temperaturejump [22] boundary conditions. The analytical study was made of the NMSMF having a nanofiber diameter of a ¼ 80 nm, a membrane thickness of t ¼ 50 lm, and an SMF thickness of h ¼ 1 cm as an example. The five major microstructural parameters of nano-fibrous membranes in the JCA model were obtained by solving the modified continuum equations of K n using a finite element solver COMSOL, which are listed in Table 2 (see more cases in Appendix A). In the permeable membrane (PM) model [23], the sound absorption coefficients of NMSMF were obtained under zero surface tension and at the normal incidence angle. The determinate parameters in the PM model, such as the surface density q and the membrane thickness t are given in Table 1, and the specific flow resistance is R ¼ r  t ¼ 374700 Pasm1. In the impermeable membrane (IM) model, the numerical simulation was conducted based on the acoustic and membrane structure interactions using the finite element solver COMSOL. The membrane model is governed by the wave equation cast in the frequency domain. The free-edge membrane was assumed to be linear elastic. The sound absorption coefficients of the SMF and NMSMF samples with h ¼ 1 cm, a ¼ 80 nm, and t ¼ 50 lm are compared between the experimental data and predictions, as shown in Fig. 6. The measured sound absorption coefficients for SMFs agreed well with the prediction by the JCA model (black triangles & solid black lines). However, the JCA model failed to properly predict the sound absorption coefficients of NMSMFs (green dash and dotted lines). The nano-fibrous membranes with a high flow resistivity Table 2 Microstructural parameters of PVDF-HFP nano-fibrous membranes. a nm

Kn 1

/ 1

Pasm2

r

b 1

K m

K0 m

80

1.62

90.65%

7:494  109

1.047

2:113  107

3:878  107

Fig. 6. The comparison of sound absorption coefficients of SMFs and NMSMFs with h ¼ 1 cm, a ¼ 80 nm, and t ¼ 50 lm between the experiment and simulations.

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performed similarly as an acoustically hard wall [20], which significantly reduced the sound absorption coefficients according to the numerical simulation. It is interesting to note that the nano-fibrous membrane worked similarly as a semi-permeable switch, leading to a surged sound absorption coefficient. The cut-off effect was also observed in previous studies on owl feathers [7,24,6]. Once the frequencies of incident waves were higher than a critical value, namely 2300 Hz (Fig. 6), the sound absorption coefficients drastically increased (green squares). The sound absorption coefficients over the frequency ranges above and below the critical value were well predicted by the PM model (green dash lines) and the IM model (green dotted lines), respectively. For the sound waves with high frequencies, the PM model functioned as the dominant factor in absorbing the sound energy. However, the nano-fibrous membrane tended to perform as an impermeable membrane over the lowfrequency range, where the resonating effect was dominant (see more examples in Appendix A).

influence on sound absorption coefficients. A cut-off effect in terms of sound absorption coefficient was observed, which was partially explained by the PM and IM models. The proposed thin bionic sound absorber possessed great potential to improve sound absorption coefficients, especially for thin SMF samples. This requires further analytical studies about acoustic properties of nano-fibrous membranes and dual-layer composite structures. Acknowledgments Guosheng Ji and Jiang Cui contributes equally to this work. The authors appreciate the technical assistance provided by the Materials Characterization and Preparation Facilities (MCPF) at HKUST. The authors also appreciate the valuable discussion and unreserved help from Professor Kimihiro Sakagami in Kobe University. Guosheng Ji is supported by the Hong Kong PhD Fellowship Scheme. Appendix A

5. Conclusion In summary, composite sound absorbers consisting of a nanofibrous membrane backed with a substrate melamine foam layer were inspired by the canopy-cavity microstructures on owl feather surface. Their sound absorption coefficients were evaluated over a large frequency range from 500 to 6400 Hz. The effects of the thickness of nano-fibrous membrane t, the nanofiber diameter a, and the SMF thickness h on sound absorption coefficients were experimentally studied, which were compared with the predictions by several theoretical models. The difference in fiber diameter a (varying from 80 to 397 nm) on a nanoscale had a negligible

Parameters in the JCA model. For the NMSMF having nanofiber diameters of a ¼ 188 nm, a ¼ 275 nm, and a ¼ 397 nm, the five microstructural parameters of nano-fibrous membranes in the Table A.1 Microstructure parameters of PVDF-HFP nano-fibrous membranes. a (nm)

/,% (
,%)

r (Pasm2)

b

K0 (m)

K (m) 7

8:831  107

188

90.38 (0.4)

1:411  10

1.048

4:822  10

275

88.41 (1.8)

9:197  108

1.058

5:813  107

1:049  106

397

90.10 (0.1)

3:220  108

1.050

9:885  107

1:807  106

9

Fig. A.1. The comparison of sound absorption coefficients of SMFs and NMSMFs with h ¼ 1 cm, (a) a ¼ 188 nm, (b) a ¼ 275 nm, (c) a ¼ 397 nm, and t ¼ 50 lm between the experimental and simulation.

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JCA model, including porosity /, flow resistivity r, tortuosity b, viscous characteristic length K, and thermal characteristic length K0 listed in Table A.1, were obtained by the modified bottom-up method [20]. The sound absorption coefficients of the NMSMF predicted by the JCA model (green dash and dotted lines in Fig. A.1) can be obtained in the finite element solver COMSOL. Parameters in the PM model. Membranes attached as facings of the SMF have been analytically investigated by considering the sound permeability in the PM model [23]. The determinate parameters in the PM model including the surface density q and the specific flow resistance R ¼ r  t of the nano-fibrous membranes were listed in Table A.2. The surface density q was measured by the morphology characterization. The specific flow resistance R was the product of membrane thickness t multiplying the flow resistance r of the nano-fibrous membrane. Finally, the sound absorption coefficients of the NMSMFs based on the PM model were obtained (green dash lines in Fig. A.1). Parameter study in numerical simulation. The consideration of the influence of thicknesses of nano-fibrous membranes and SMFs, and nanofiber diameters in the PM model were shown in Fig. A.2.

Table A.2 Microstructure parameters of PVDF-HFP nano-fibrous membranes in the PM model. a (nm)

q (kg/m2)

r (Pasm2)

t (lm)

R (Pasm1)

188

0.0086

1:411  109

50

70550

275

0.0103

9:197  108

50

45985

397

0.0088

3:220  108

50

16100

For the effect of nano-fibrous membrane thickness, t, in the PM model, the peak of the sound absorption coefficient down-shifted with increasing t in Fig. A.2(a). For example, the sound absorption peak of NMSMFs shifted from about 4000 Hz for t ¼ 50 lm to about 2000 Hz for t ¼ 250 lm. Besides, the sound absorption coefficients of NMSMFs with a membrane thickness t ¼ 50 lm were much higher than those for thicker membrane t ¼ 250 lm in the high-frequency range from 3000 to 6400 Hz. For the effect of SMF thickness, h, in the PM model, the sound absorption coefficient in the low-frequency range from 500 to 3000Hz increased with increasing h from 1 to 5 cm for a thin membrane of t ¼ 50 lm in Fig. A.2(b). For the effect of nanofiber diameter, a, in the PM model, the similar trends of sound absorption coefficients of NMSMFs with various nanofiber diameters in Fig. A.2(c) indicate that the nanofiber diameter was not a key factor determining the sound absorption coefficients. More examples in experimental measurements and numerical simulation. The sound absorption coefficients of more SMF and NMSMF samples in both experimental measurements and numerical simulation (including the JCA model, the PM model, and the IM model) were given in Fig. A.1. The sound absorption coefficients of the SMF obtained in the experimental tests can still be well predicted by the JCA model (black triangles & solid black lines in Fig. A.1). However, the JCA model failed to properly predict the sound absorption coefficients of NMSMFs (green dash and dotted lines in Fig. A.1). It should be noted that the accuracy of current models, such as the PM model, fluctuates in the sound absorption prediction of NMSMFs, and more accurate models are required to be developed. This requires further analytical studies about the

Fig. A.2. Sound absorption coefficients of the NMSMF with (a) a ¼ 80 nm and h ¼ 1 cm, (b) a ¼ 80 nm and t ¼ 50 lm, and (c) t ¼ 50 lm and h ¼ 1 cm in the PM model.

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