A novel method for plastic particle sizing in suspension based on acoustic impedance spectrum

Ultrasonics 77 (2017) 224–230

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A novel method for plastic particle sizing in suspension based on acoustic impedance spectrum Xiaoming Ji, Mingxu Su ⇑, Jun Chen, Xue Wang, Xiaoshu Cai University of Shanghai for Science and Technology (USST), Institute of Particle and Two-phase Flow Measurement (IPTFM), Shanghai, China

a r t i c l e

i n f o

Article history: Received 30 September 2016 Received in revised form 26 January 2017 Accepted 28 January 2017 Available online 31 January 2017 Keywords: Acoustic impedance spectrum Numerical simulation Plastic particle size Polystyrene

a b s t r a c t The objective of this paper is to explore the relationship between the characteristics of plastic particles in suspension and acoustic impedance spectrum and to present a novel non-invasive methodology for both spherical and non-spherical particle sizing. By modifying the ultrasonic attenuation spectral model, theories relating acoustic impedance spectrum to particle characteristics have been established to implement quite a few numerical simulations for the first time, revealing that the acoustic impedance of plastic particles is sensitive to changes in particle concentration and size. Afterwards, experiments were carried out on polystyrene suspensions made by particles with different sizes. On the basis of the theoretical analysis, different transducers were employed over a frequency varied from 10 MHz to 100 MHz for different particle sizes respectively. Not only were spherical particles chosen for the experiment, but also non-spherical particles with three different size distributions considering the fact that practical particles have irregular shapes. All the samples were verified by optical microscope technique and their comparisons with the experimental results show that the plastic particles with different sizes are distinguishable by using acoustic impedance spectrum. Ó 2017 Elsevier B.V. All rights reserved.

1. Introduction Plastic materials have been used worldwide because of their properties, like greater plasticity, lower weight, higher durability and cheaper cost. However, the plastic wastes accounts for main source of municipal solid wastes and affects the ecosystem in different ways, especially on marine organism [1] nowadays. Plastic particles of different types and sizes have been detected in seawater worldwide and their adverse effects on several aquatic animals were reported [2]. The size of polystyrene beads will affect the growth of microalgae [3]. The residence time of plastic particles in seabird’s stomach is presumably varies with particle size [4]. Thus the size characterization of plastic particles has been paid extensive close attentions and investigations. Although, recent studies have demonstrated that dynamic light scattering [5], multi-wave-length light extinction [6] and image analysis [7–10] are all practical methods for measuring particle size or concentration, but the above mentioned methods illustrate a common disadvantage that they are not suitable for high concentration situations. However, by using ultrasonic waves to explore the particle characteristics in high concentration (say, volume fraction

⇑ Corresponding author. E-mail address: [email protected] (M. Su). http://dx.doi.org/10.1016/j.ultras.2017.01.024 0041-624X/Ó 2017 Elsevier B.V. All rights reserved.

>10%) will provide a promising result, because of the strong penetrability of ultrasound [11]. It is a truth universally acknowledged that ultrasound can be used to determine the size and concentration of particles in suspensions. In those applications, generally, the ultrasonic velocity and ultrasonic attenuation spectra are measured after an ultrasonic wave transmits through the suspension containing dispersed particles. As per the theories originated from some distinguished works [12,13], the information of particle properties could accordingly be obtained by analyzing the measured ultrasonic velocity and attenuation spectra [14,15]. Unfortunately, these approaches are not suitable for the analysis of the mixed suspension when the length of the measurement zone is too long (e.g. a large tank) or the suspension contains some high attenuation materials, like bubbles or glycerin, and without a proper measurement length. In these cases the transmitted ultrasonic signal is so highly attenuated that it cannot be detected or it can only yield poor signal-tonoise ratio (SNR) spectrum. Nevertheless, the mathematical expression of acoustic impedance indicates that it is possible to employ the reflection of ultrasonic wave to determine the characteristics of particles in suspension. As long as the buffer rod with appropriate impedance differential to that of suspension is selected, then a signal with higher SNR is obtained. Technically, there are bunch of fields where the reflected ultrasonic signal has

X. Ji et al. / Ultrasonics 77 (2017) 224–230

been employed to measure the properties of interest, such as measuring the characteristics of bubbles in aerated food [16], studying the dynamic shear rheology of honey [17], determining the circumferential viscosity profile in stationary journal bearing [18] and biological tissue characterization [19]. The previous works do not contain any information indicating the characterizing particle size in suspension by impedance spectrum, although it can work in the same way as ultrasonic attenuation (phase velocity) spectrum technique [14,15]. For the purpose of particle sizing, a broadband impedance spectrum should be extracted from experimental data and then be interpreted by a suitable theoretical model. The objective of this paper is to explore the possibility of the acoustic impedance spectrum being used to characterize the size of plastic particle in suspension.

2. Principles of acoustic impedance spectrum method 2.1. Principles of acoustic impedance For the sake of characterizing particles in suspensions by acoustic impedance spectrum, first and foremost, the relationship between characteristics of particles and acoustic impedance should be established. Under the framework of the classical ECAH [12,13] model, the following expression of complex wave number of ultrasound can be derived as:




j jc

2 ¼1þ

1 3/ X

ij3c R3

ð2n þ 1ÞAn ðR; xÞ

ð1Þ

n¼0

and,

j ¼ x=cðxÞ þ iaðxÞ:

ð2Þ

The real part of the complex wave number j is associated with the phase velocity c(x) and the imaginary part is indeed the attenuation a(x). Where x is the angular frequency (=2pf), jc the compffiffiffiffiffiffiffi press wave number, i ¼ 1, / the volume fraction of particles, R the radius of the particles and An is called as the scattering coefficient, reflecting the interaction of ultrasonic waves and suspended particles in media. Then, the definition of the acoustic impedance can be expressed by the following formula [20]:


 aðxÞk Z ¼ qcðxÞ 1  i 2p

ð3Þ

where q is the equivalent density of suspension and k is the wavelength. Combining the formulae (1)–(3) and utilizing an explicit mathematical expression of a(x) [21],

aðxÞ ¼

1 3/ X ð2n þ 1ÞRe½An ðR; xÞ 2 3 2k Rj n¼0

ð4Þ

a more complicated expression of acoustic impedance can be obtained.

P1 1  4p3/ki n¼0 ð2n þ 1ÞRe½An ðR; xÞ k2c R3 Z ¼ qx 
qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi P1 Re kc 1 þ ik3/ 3 3 n¼0 ð2n þ 1ÞAn ðR; xÞ R

ð5Þ

c

The relationships between acoustic impedance and the parameters of suspension, such as diameter of particle and the concentration of suspension, are established in formula (5). In addition, the complex number Z can be decomposed into the real part Zr and the imaginary part Zi as Z = Zr + iZi, which infers that two independent and alternative equations can be employed for particle size characterization based on acoustic impedance spectrum.

225

2.2. Numerical calculation The numerical results in Fig. 1 illustrate the influences of particle concentration and size on the acoustic impedance spectrum, which were predicted with an assumption that the suspension consisted of polystyrene particles and water with known physical parameters [22] (see Table 1). And also the particles with size ranging from 10 to 100 lm and the volume fraction from 10% to 50% were considered in the numerical calculation. As indicated in Fig. 1, the real part of the impedance keeps stable at low frequency until it reaches the first and largest oscillation where the minimum and maximum values occur subsequently and swiftly on the curve. Afterwards, it fluctuates with a reduce in amplitude, until it reaches the same constant value as before. The undulation of the impedance spectrum can be attributed to the resonance phenomenon of ultrasonic waves [23], and the corresponding characteristic frequencies are called resonance frequencies. In Fig. 1(a), it shows that the resonance frequency decreases with the increase in particle radius, but the shape of curve is almost the same. As the particle concentration increases, the amplitude on the real part of impedance becomes higher, but the resonance frequency remains unchanged (Fig. 1(b)). Therefore, by measuring the amplitude and frequency of the peak it is possible to extract the information about both the size and the concentration of the polystyrene suspension. In addition, since the measurement process of particle size and concentration can be separated into two independent processes, it becomes simpler and more straightforward to inverse the particle size distribution from experimental acoustic impedance spectra. Thus, from the numerical calculation, it is clear that the real part of acoustic impedance is sensitive to particle concentration and size, so it is possible to obtain the information of particle concentration and size by analyzing the reflected wave. Even though, theoretically, the imaginary part of the acoustic impedance is also likely to be used to measure particle sizes, in the preliminary experiments we found that the particle size sensibility of imaginary part is much lower than those of real part. Therefore, only the particle sizing by real part of impedance is discussed in this paper. 3. Materials and method 3.1. Materials As shown in Fig. 2, two kinds of polystyrene particle samples were employed in the experiments, which could be identified roughly in terms to the shape of particles as spherical and nonspherical particles. The spherical polystyrene particles with relatively narrow particle size distribution were purchased from Beijing HaiAnHongMeng Reference Material Technology Co., Ltd, while the raw materials of non-spherical polystyrene particles were sieved by a sample sieve machine (Model BS-200) before conducting experiments. Fig. 3(a) and (b) illustrate three kinds of particle size distribution of the spherical and non-spherical samples respectively, labeled sample 1, sample 2 and sample 3, which were measured by the optical image analyzer (Model Pip8.1, Omec Inc.) integrated with a microscope (Model CX21FS1) from Olympus Corporation. 3.2. Apparatus and method Fig. 4 shows the sketch of ultrasonic spectrometer used to measure the reflected wave of the samples. Operating principle of this technique is similar to that of ultrasonic spectrometer that has been described in detail elsewhere [24,25]. The measurement

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X. Ji et al. / Ultrasonics 77 (2017) 224–230

1.70x106

10μm

1.65x106

30μm

Concentration:10%

2.00x106

50μm

6

1.60x10

100μm

1.55x106 1.50x106 6

1.45x10

1.40x106

Diameter:30µm

10% 30% 50%

2.25x106

Zr/kg⋅m-2⋅s-1

Zr/kg⋅m-2⋅s-1

1.75x106

1.75x106 1.50x106 1.25x106 1.00x106

1.35x106

7.50x105

1.30x106 6 10

107

108

1.0x106

1.0x107

Frequency/Hz

1.0x108

Frequency/Hz

(a)

(b)

Fig. 1. (a) Numerical calculation of the real part of the acoustic impedance for polystyrene suspension in terms of the frequency with different particle sizes, but the same concentration (10 vol%). (b) Numerical calculation of the real part of the acoustic impedance for polystyrene suspension in terms of the frequency with different volume fractions, but the same particle size (30 lm).

Table 1 Physical parameters of water and polystyrene.

q/kgm3 Water Polystyrene

997.0 1055

a/Npm1

c/ms1 1483 2340

s/Wm1k1

Cp/Jkg1k1

14 2

2.53e f 1e13f2

4178.5 1193

b/K1 4

0.595 0.1151

2.57e 2.64e4

g/PaS

l/Nm2

4

9.03e –

– 1.27e9

Fig. 2. The particles’ images observed by optical microscope: (a) is for the spherical sample 3, and (b) is for non-spherical sample 2.

100

Sample1 Sample2 Sample3

75

50

25

Volume cumulative distribution/%

Volume cumulative distribution/%

100

Sample1 Sample2 Sample3 75

50

25

0

0 0

10

20

50

60

70

80

90

0

50

100

150

Diameter/µm

Diameter/µm

(a)

(b)

200

250

Fig. 3. Statistical results of particle size distribution measured by optical microscope. (a) and (b) represent the spherical and non-spherical samples respectively, where the ‘Sample 1’, ‘Sample 2’ and ‘Sample 3’ represent different particle sizes for both spherical and non-spherical samples.

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X. Ji et al. / Ultrasonics 77 (2017) 224–230

Computer

Calibration Sample

Ultrasonic Pulse Transmitter/Receiver

2

Amplitude

T/R R

A

B

0

Measurement cell -2

Transducer 207.2

Fig. 4. Sketch of the ultrasonic spectrometer used to measure the ultrasonic properties of polystyrene suspensions.

Rs ¼ Rc

M s iðhs hc Þ e Mc

ð6Þ

where the subscript S and C represent sample and calibration material, respectively. With the known physical parameters of calibration and delay-line, Rc can be calculated easily. Then the complex acoustic impedance is derived by substituting the calculated Rs into the following equation:

Z s ¼ Z dl

ð1  Rs Þ ð1 þ Rs Þ

ð7Þ

where Z dl is the impedance of delay-line, and Z s is the complex impedance of the sample which is to be determined.

207.6

207.8

Time/µs Fig. 5. The received time-domain signals (B) of calibration and sample, the sampling rate is 250 MHz.

4. Experimental results and discussion 4.1. Results and discussion of spherical and non-spherical samples The real parts of the acoustic impedance spectra of spherical polystyrene suspension were measured and are shown in Fig. 6. It can be found that the oscillation features of experimental acoustic impedance spectra are similar to those predicted by the theoretical model: the bigger the particle size, the smaller the resonance frequency. However, the polydispersity of experimental samples would be expected to broaden the bandwidth between the peak and valley of impedance spectrum, simulated by assuming the particle systems were monodisperse. Thus the experimental spectra obtained don’t agree with the theoretical data in absolute value. In order to retrieve the particle size distribution (PSD) by analyzing the obtained acoustic impedance spectra, the ORT algorithm [6] was employed to solve the involved ill-conditioned equations. This independent algorithm is based on Twomey’s method and improved by optimizing the regularization factors with additional methods such as Generalized Cross Validation and L-curve criterion [26]. To make it more appropriate for the inversion of acoustic impedance spectrum, the core equation was modified by altering calculation of coefficient matrix and the form of input spectrum, but the key solving process remains the same. Hence for a polydisperse particle system, discretization of Eq. (5) performed by refer-

2.50x10 6

2.25x10

Zr/kg⋅m-2⋅s-1

system mainly comprises an ultrasonic pulse transmitter/receiver made by PANAMETRIC, INC., a computer with a data acquisition card (PCI-5114) to acquire the data and to analysis the waveform and a measurement cell that contains the samples to be investigated. As for the transducers, although scanning ultrasonic pulse transmitter/receiver with frequency ranging from 1 to 200 MHz is available commercially, while considering the current limitation of devices in the Laboratory, only three broad-band transducers at 100 MHz (Part Number: V2012 (BC), Panametrics), 30 MHz (Part Number: V356-SU, Panametrics) and 10 MHz (Part Number: V312-SU, Panametrics) could be employed during the following experiments. The selection of the center frequency was taken on the basis of the previous numerical results, which yielded the corresponding relation between resonance frequency and particle size. During a test run, the compression wave A is first emitted to the measurement cell from the ultrasonic transducer, and after it travels along the delay-line, it reflects on the delay-line/sample interface. And then, the reflected wave B travels back through the delay-line and is received by the same transducer (Fig. 4). By analyzing the spectrum analysis of the acquired signals, the magnitude (M) and the phase (h) information are extracted as a function of frequency. This procedure needs to be carried out for a calibration material with known acoustic properties, i.e. water or air, as well, and the obtained signal is treated as background signal. Not only can the reflectance (R) be calculated by combining these two signals, but also the acoustic losses which are basically resulted from the coupling of the transducer to the buffer material and the divergence of the ultrasound field can be eliminated safely. A typical time-domain signals (B) of sample and calibration material are showed in Fig. 5. The amplitude and phase differences can be found obviously between these two signals because of the influence of particles’ resonance for the special frequencies. The reflectance of delay-line/sample interface can be calculated at each frequency by the following formula:

207.4

Sample 1 Sample 2 Sample 3

6

2.00x10 6

1.75x10 6

1.50x10 6

1.25x10 6 2.0x10 7

6.0x10 7

8.0x10 7

1.0x10 8

Frequency/Hz Fig. 6. The real part of experimental impedance of spherical samples.

X. Ji et al. / Ultrasonics 77 (2017) 224–230

ring to the way of attenuation spectra inversion [17] and the equation according to the linear equations AF = G becomes

qx 

Z

1  4p3/ki k2 R3

DR

P1

n¼0 ð2n

þ 1ÞRe½An ðRj ; xi Þ

ffi!  dR rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 3/ P1 Re kc 1 þ ik3 R3 n¼0 ð2n þ 1ÞAn ðRj ; xi Þ c

j

c j

|fflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl{zfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflfflffl} 

Ai;j

X

VðDRi Þ |fflfflfflfflfflfflffl{zfflfflfflfflfflfflffl} Fi

¼ Zðxi Þ |fflffl{zfflffl}

ð8Þ

Gi

where A represents the coefficient matrix (or model matrix), F is the discrete frequency distribution of particle size to be determined and G is the vector consisting of experimental real part of acoustic impe-

Volume cumulative distribution/%

100 Impedance Image

Sample 1 75

Sample 3 Sample 2

50

25

0 0

20

60

80

Diameter/µm Fig. 7. Comparison of inversed results with image analysis of spherical samples.

Table 2 Comparison of sample volume median diameter measured by acoustic spectrum and image approach. Volume median diameter/lm

Approach

Ultrasonic impedance Image analysis Relative deviation

Zr/kg⋅m-2⋅s-1

2.0x10

Sample 1

Sample 2

Sample 3

7.57 7.69 1.56%

23.84 21.58 10.47%

70.2 66.64 5.34%

6

sample 1 sample 2 sample 3

1.8x10 6

1.6x10 6

2.0x10 6

4.0x10 6

6.0x10 6

Frequency/Hz

(a)

8.0x10 6

1.0x10 7

dance at different frequencies, while the subscript i and j represent the number of discrete classification of radius for particles and frequency for acoustic impedance, respectively. After an inversion process, the resultant of samples’ PSDs was yielded and compared with those from image analysis. Fig. 7 illustrates that the PSD of sample 1 obtained from impedance spectrum is extremely close to that obtained from image analysis, while for the other two samples, acoustic impedance method yields fairly larger PSDs compared with image method. In addition, the volume median diameters (Dv50) of the samples are shown in Table 2, and the comparison with the image analysis reveals a maximum relative deviation exceeding 10% for sample 2. Overall, the acoustic impedance method has manifested a capability of reliably distinguishing these three particle systems by size. In a similar way, the acoustic impedance spectra and the inversed PSDs of non-spherical samples are illustrated in Fig. 8. Because of the sieving machine’s specification, the size distribution widths of the non-spherical samples are not as narrow as those of spherical samples as shown in Fig. 3. Observing the impedance spectra measured by a single broadband transducer (Part Number: V312-SU), since the bandwidth can sufficiently cover the resonance frequencies of samples. The resonance peaks of impedance (the key feature for inversion) can be identified obviously, even though the shapes of the curves are not as typical as those of spherical samples. The comparison with image analysis also shows that even for non-spherical particles, acoustic impedance technique is found to be an effective method to distinguish the particle systems with different mean sizes. This is evidenced by Table 3. Although the narrower particle size distribution occurs in the inversion of acoustic impedance spectra, the small relative deviations indicate that it is appropriate to determine the mean size for a polydisperse particle system in practical situations. Authors also speculate that the characterization of the distribution width using acoustic spectrum is very difficult, given current limited spectrum bandwidth and content. The aforementioned experimental results illustrate that when the volume median diameter of particle system is around or larger than 100 lm or less than 10 lm, the relative deviation is pretty small, while the particle size is about a couple of tens of micrometer, the relative deviation becomes higher and can even hit 10.47%. The reasons can be found out from the relation curve (see Fig. 9) which infers that a certain error of acoustic impedance is able to cause subtle deviation of the inversion results when the particle size is less than 10 lm; and with the increase of particle size, the same amount of impedance spectrum error causes notable

Volume accumulative distribution/%

228

100

50

0

Image Inversion

Sample 2

Sample 1

10 0

Sample3

200

Diameter/µm

(b)

Fig. 8. (a) Real part of experimental impedance of non-spherical samples. (b) Comparison with image analysis.

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X. Ji et al. / Ultrasonics 77 (2017) 224–230 Table 3 Comparison of sample volume median diameter measured by acoustic impedance spectrum and image analysis.

1.0x10

Sample 1

Sample 2

Sample 3

92.10 90.93 1.29%

142.73 146.67 2.69%

179.09 173.38 3.29%

B t4

1.8x10

B t5

1.7x106

B

* t3

1.6x106

1.4x106

2.0x106

4.0x106

7

6.0x106

8.0x106

1.0x107

1.2x107

Frequency/Hz Fig. 11. Real part of impedance of Bt1 to B*t5.

5.0x10

7

35 2.5x10

7

0

100

200

300

40 0

Particle size/µm Fig. 9. The diagram of relation between particle sizes and corresponding characteristic resonance frequencies.

deviation of inversion result. Hence, the relative deviation is greater when the particle size is around 20 lm; however, the discretization of experimental acoustic impedance spectrum is not fine enough to result in notable deviation of the inversion result of mean size, the deviation is mainly evidenced by the width of the particle size distribution.

4.2. Influence of local concentration During the experiment, we noticed that the polystyrene particles settled down in the polystyrene-water suspension continuously due to its larger density than water. Therefore, the longer the measuring time, the higher the local concentration on the delay-line/sample interface. To investigate the influence of local concentration of particles, a series of signals varying with time of spherical sample 3 were recorded with a 60 s interval. The five time-domain signals of them are shown in Fig. 10, labeled as Bt1 to Bt5. 3

B t1 B t2

2

Volume frequency distribution/%

Resonance frequency/Hz

B t3

6

1.5x106

8

Polystyrene particle 7.5x10

Zr/kg⋅m-2⋅s-1

Ultrasonic impedance Image analysis Relative deviation

B t2

1.9x106

Volume median diameter/lm

Approach

B t1

2.0x106

Bt1

30

Bt2 Bt3

25

Bt4

20

Bt5

15

B

* t3

10 5 0

60

65

70

75

80

Diameter/µm Fig. 12. Inversed result of Bt1 to B*t5.

Because the number of particles, attaching on the interface, increased as time went by, the amplitude and phase of signals show clear difference between these five time-domain and the background (the signal of pure water) which then result in the difference of impedance spectra. As the same as demonstrated from the theoretical results, the peak value of experimental impedance spectra increases with the enlargement of concentration (see Fig. 11) and these differences barely bring any influence on the inversion (see Fig. 12) when corresponding characteristic frequencies are fixed. However, if we artificially move the spectrum (Bt3) with a slight horizontal shift (say, 0.1 MHz) labeled as B⁄t3 which infers the change of particle size according to the theoretical predictions, this minor variation can be easily identified by the inversion algorithm, as shown in Fig. 12. That is to say, the change of concentration doesn’t pay observable impact on the calculation of particle size in that it doesn’t change the frequency feature of the acoustic impedance.

B t3

Amplitude

1

B t4

5. Conclusions

B t5 0

-1

-2 207.2

207.4

207.6

207.8

Time/µs Fig. 10. A series of time-domain signals for Sample 3 in spherical samples.

The analysis and results suggest that the acoustic impedance spectrum can be used to determine the size of the polystyrene suspension, which has been investigated theoretically and experimentally. Our experimental results indicate that the acoustic impedance of the suspension, which can be measured nondestructively and non-invasively by reflecting ultrasonic wave from the delay-line/sample interface in practical situation, is sensitive to the changes in polystyrene particle size. Meanwhile, the experiments on spherical and non-spherical samples of polystyrene particles bring relative deviations less than 11% and 5%, respec-

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X. Ji et al. / Ultrasonics 77 (2017) 224–230

tively, when compared to those obtained using image analysis. Moreover, both theoretical predications and experimental results show that the local concentration variation of suspension doesn’t obviously influence the inversion of particle size, which infers that this method is suitable for higher concentrated suspensions. However, some improvements still need to be carried out in the further research. For instance, both theoretical and experimental spectra manifest that it is possible to determine the changes of concentration, however, on account of the continuous variation of local concentration, concentration characterization didn’t realize in this paper. What’s more, the coincidence of particle size distribution between image analyzer and acoustic impedance spectrum is not quite satisfactory, thus different inversion programs need to be trialed in the next step. Thirdly, the current minimum size of measured particles is as lower as 7.69 lm, for smaller particles, although it is theoretically possible to be measured, we have not yet conducted experimental verification. Last but not least, only low density material, polystyrene particles for which resonance frequencies are notable, has been discussed in this paper. It needs further experiment to confirm whether this particle sizing technique is suitable for other materials too. Acknowledgement The authors gratefully acknowledge the support from the National Natural Science Foundation (Project No: 51176128). References [1] A.L. Andrady, Microplastics in the marine environment, Mar. Pollut. Bull. 62 (8) (2011) 1596–1605. [2] S.L. Wright, R.C. Thompson, T.S. Galloway, The physical impacts of microplastics on marine organisms: a review, Environ. Pollut. 178 (2013) 483–492. [3] S.B. Sjollema, P. Redondo-Hasselerharm, H.A. Leslie, M.H.S. Kraak, A.D. Vethaak, Do plastic particles affect microalgal photosynthesis and growth?, Aquat Toxicol. 170 (2016) 259–261. [4] P.G. Ryan, How quickly do albatrosses and petrels digest plastic particles?, Environ Pollut. 207 (2015) 438–440. [5] X.Z. Wang, L. Liu, R.F. Li, R.J. Tweedie, K. Primrose, J. Corbett, F.K. McNeilWatson, Online characterization of nanoparticle suspensions using dynamic light scattering, ultrasound spectroscopy and process tomography, Chem. Eng. Res. Des. 87 (6) (2009) 874–884. [6] M.X. Su, F. Xu, X.S. Cai, K.F. Ren, J.Q. Shen, Optimization of regularization parameter of inversion in particle sizing using light extinction method, China Part. 5 (4) (2007) 295–299.

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