Ultrasonics 63 (2015) 135–140
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Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Acoustic separation of submicron solid particles in air Ramin J. Imani a,⇑, Etienne Robert a,b a b
KTH Mechanics, Osquars Backe 18, Stockholm 10044, Sweden Polytechnique Montréal, Dep. of Mechanical Engineering, Montréal, Quebec, Canada
a r t i c l e
i n f o
Article history: Received 24 February 2015 Received in revised form 29 June 2015 Accepted 30 June 2015 Available online 7 July 2015 Keywords: Acoustophoresis Submicron particles Gas phase
a b s t r a c t The use of ultrasound to continuously separate submicron particles suspended in air is investigated in a rectangular channel with adjustable height. An electrostatic transducer is used to generate a standing wave in the 50–80 kHz frequency range and the particles experience forces within the acoustic field causing them to concentrate at the pressure nodes. To assess the effect of several key design parameters on the separation efficiency, a simple method based on light scattering is implemented to provide information on the particle concentrations as a function of position in the channel. The images acquired are processed to yield a separation efficiency metric that is used to evaluate the effect of acoustic, flow and geometrical parameters. The results show that, in qualitative agreement with theoretical models, the maximum separation efficiency increases with the pressure amplitude of the sound wave. The separation efficiency is also linearly proportional to the standing wave frequency, when it is varied between 50–80 kHz. On the other hand, the effect of the average fluid velocity is less pronounced than expected, suggesting that in our channel separation is not limited by the interaction length between the acoustic field and the suspended particles. The effect of the parallelism of the reflector relative to the transducer is also investigated. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The separation of particles suspended in a gas is a problem relevant for a wide range of scientific and industrial applications. It is the subject of a sustained research effort aimed at developing and improving practical means for the concentration, sorting and removal of particles from gases. Currently, several mature industrial techniques are available to perform these tasks, including cyclones, electrostatic precipitators (ESP), scrubbers and filters based on porous elements. However, each have limitations such as the potential for clogging, the generation of liquid waste, reduced capabilities in harsh environments and for the handling of submicron particles [1–3]. Typically these techniques have a cut-off size, below which the particle removal efficiency significantly drops. For instance with filters relying on flowing the suspension through a porous material, the capture efficiency will obviously be low for particles smaller than the pore size. In this case, targeting smaller particles comes at the cost of an increased pressure drop. Other techniques such as ESPs can also be specifically designed to maximize submicron particle removal, with up to 90% capture efficiency [4], but this requires high energy input and results in the formation of ozone. ⇑ Corresponding author. E-mail address: [email protected] (R.J. Imani). http://dx.doi.org/10.1016/j.ultras.2015.06.021 0041-624X/Ó 2015 Elsevier B.V. All rights reserved.
During the last few decades, microfluidics applications have benefited from the development of acoustically mediated techniques for the manipulation of particles, droplets and bubbles in liquids. This approach does not require the introduction of a physical barrier or of chemical additives for the separation of particles [5]. It is also able to sort particles according to their size [6] or other physical properties such as compressibility and density [7]. Techniques developed in the liquid phase can potentially be adapted to gaseous media [8]. Acoustic separation of particles suspended in air, especially submicron particles, has received limited attention and only a few works are addressing this problem experimentally. For instance, the investigations of Budwig et al. [9] and Anderson et al. [10] are limited to the separation and fractionation of particles several microns in diameter suspended in a gaseous flow. This motivates the present experimental investigation to study the effects of acoustic, flow and geometrical parameters on the separation efficiency of submicron solid particles suspended in air. The paper is divided as follows: First, the theory behind the phenomenon under investigation is briefly explained. Then, the experimental setup and the data acquisition technique used are introduced. The effects of different parameters on the separation efficiency are then presented, including the pressure amplitude, the frequency of the standing wave, the average flow velocity and the parallelism of the channel walls. These results are followed
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by a brief discussion highlighting the implication for the design of practical acoustic separation systems. 2. Theory The acoustic forces on a particle suspended in a fluid have been studied extensively since the first observation of particle separation in a standing wave by Kundt and Lehmann [11]. King [12] was the first to derive a comprehensive theoretical formula for the acoustic radiation forces on a rigid sphere in a plane standing wave. Several other studies further developed his initial formulation to include compressible spheres [13] and the effect of viscosity [14,15]. The particles suspended in an ideal 1D acoustic standing wave experience two forces from this field: the primary radiation force (PRF), generated by the interaction of a particle with the primary field, and the secondary radiation forces (SRF), originating from the energy scattered by the other suspended particles [16]. The PRF is by far the dominating force [17], and the SRF will accordingly not be considered in this study. In a standing wave, the PRF can be divided in two components: axial and transverse relative to the direction of the wave propagation. The axial component is responsible for the displacement of particles to the nodes or anti-nodes of the standing wave. The transverse component packs the particles closer together in the direction normal to the wave propagation [18]. The equation for the axial PRF [13] shown in Eq. (1) states that the acoustic force is proportional to the particle volume V p and to the square of the pressure amplitude (pa ). The acoustic contrast factor Uðb; qÞ depends on both the particle density qp and its compressibility bp in relation to the carrier fluid properties (qf ; bf ). The wave number k is defined as 2kp, where k is wavelength, x is the distance from a pressure node.
pV p p2a bf
Uðb; qÞ sinð2kxÞ 2k 5q 2qf bp Uðb; qÞ ¼ p 2qp þ qf bf F ax ¼
The signal is then shifted to positive values and amplified to 400 V peak-to-peak. The separation channel is designed with a variable height (H), adjustable from 0 to 20 mm to yield standing waves of different frequencies. In the present study, the investigated range was 50– 80 kHz, which corresponds to a channel height of 6.86–4.28 mm. The roof is manually positioned with micrometer screws at both ends while guided vertically by four supporting rods. The displacement of both extremities of the reflector is also measured optically from images captured using a digital camera, providing a resolution of 90 pixels/mm. From the measured value of the channel height, a baseline standing wave frequency is determined. The excitation frequency is then scanned around this baseline to identify the optimum resonance in the channel by visualization of the particle separation in the standing wave. The velocity of air through the channel is regulated by a flow controller (Teledyne Hastings HFC-202), connected to a clean compressed air supply. The flow is conditioned upstream of the separation region in a stabilization chamber consisting of three rows of fine grids followed by a diffuser to ensure a Poisuille-type velocity profile over the transducer. The flow is seeded using a fluidized bed with TiO2 solid particles (LaVision GmbH) with reported nominal diameter of 300 nm, density of 3900–4200 kg m3 with negligible compressibility [19]. The seeder used is based on a design by Willert and Jarius [20,21], consisting of a cylinder with a porous metal plate glued to the bottom with clean air supplied from below. Solid particles located above the porous plate are entrained by the airflow when the drag force exceeds their weight. The size distribution of submicron particles was characterized using a Scanning Mobility Particle Sizer (SMPS, TSI 3080/3010), revealing possible agglomeration in the seeder as the size distribution is broad, centered at approximately 460 nm, and extends to large sizes, as shown in Fig. 1b.
ð1Þ 3.2. Data acquisition
ð2Þ
It should be noted here that the sign of the acoustic contrast factor sets the direction of the acoustic force either towards the pressure nodes or antinodes. Generally, solid particles suspended in air or aqueous media are moved to the pressure node, while gas bubbles in aqueous media are moved towards pressure antinodes [18]. 3. Experimental setup To assess the effect of a large number of parameters on acoustic separation efficiency, a versatile separation channel, a quick diagnostic technique and a suitable evaluating metric were implemented. These are presented in the following section. 3.1. Acoustic separation channel A simple flow-through acoustic particle separator was built to study the effect of flow and acoustic parameters on the separation efficiency of solid particles suspended in air. The experimental setup is presented schematically in Fig. 1. The separation channel has a rectangular cross section, 30 mm wide, with transparent sidewalls to allow optical access to the acoustic region. An electrostatic broadband transducer (SensComp, Open face 600) is flush-mounted into the bottom wall, generating a standing wave across the channel height. The transducer can be operated in the 40–100 kHz range, generating sound pressure amplitudes up to 00 154.5 dB (re 20 lpa), measured using a type 4138 1/8 Brüel and Kjaer pressure field microphone. A function generator (TG1000, TTi Ltd.) produces a sinusoidal signal for the transducer input.
Only a few investigations in the literature have attempted to quantify the efficiency of acoustic separation in air, typically relying on directly counting the number of particles after the separation region. Budwig et al. [9] employed an off-line visualization approach using a microscope to evaluate the size distribution of the particles settling in a chamber downstream of the separation region. In a work in progress by our group [8], a Scanning Mobility Particle Sizer (SMPS) is used to quantitatively measure the particle size distribution in real time in the channel with and without a sound source. This technique can provide very precise information, but it is complex and not very fast. To investigate the effect of a wide range of parameters on the acoustic particle separation efficiency, a simple, fast and reliable method is required. For the results presented here, a technique based on light scattering (also described in [8]) is implemented. A thin laser sheet parallel to the flow direction is used to illuminate the region immediately upstream and downstream of the transducer. The light sheet is created by a diode laser and two plano-convex cylindrical lenses in Keplerian configuration and is inserted through the downstream opening, along the centerline of the channel. The entrained particles in the channel scatter light, which is captured by a camera (Nikon D7000) positioned orthogonally to the flow. The images are exposed for a sufficiently long time to provide a high signal-to-noise ratio. Consequently, individual particles are not resolved but rather their trajectories are integrated. The images acquired are then processed using Matlab to yield a metric that can be used to assess the effect of different parameters on the separation efficiency. Examples of images acquired using this technique are presented in Fig. 2 showing a nearly uniform distribution of particles in the
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(a)
(b)
Particle diameter (nm)
Fig. 1. (a) Schematic representation of the experimental setup. The gas flow is seeded with particles in the fluidized bed (1) before being sent to a stabilization chamber (2), ensuring laminar flow conditions in the separation channel (3). The position of the reflector wall (4) of the resonator is adjusted by two manually controlled micrometers (5). (b) Size distribution of the TiO2 particles, as measured in the separation channel without sound excitation in the resonator. The vertical axis represents the concentration (particles/cm3 ) normalized by the width of the size bins used by the aerosol spectrometer.
channel in the absence of acoustic excitation (Fig. 2a). Following the generation of a standing wave, particles have migrated to the central part of the channel as shown in Fig. 2b. By progressively changing the excitation frequency around the expected value calculated from the channel height the optimum resonance frequency is identified. Somewhat surprisingly, the best separation is observed when a double particle-enriched band is formed in
(a)
(b)
(c)
(d)
(e) Fig. 2. Visualization of the acoustic particle separation using the laser light scattering method, with a channel height of 6.86 mm. (a) Nearly uniform distribution without sound. (b)–(d) Images captured during the frequency tuning procedure showing a progressively sharper nodal pattern: (b) 49 kHz, (c) 49.3 kHz, (d) 49.6 kHz. (e) Optimal resonance, at 50 kHz, revealing a slightly distorted nodal pattern compared to an idealized 1D planar standing wave.
middle of the channel and as well as additional single bands near the upper and lower walls, instead of the two bands located k=4 from the walls expected assuming that a 1D planar standing wave is established in the channel. This phenomenon can result from the superposition of several resonant modes in our 2D channel [22] or from near field effects [23] caused by the finite size of the transducer used. This reveals that, at optimum resonance the pressure field is most likely distorted compared to the idealized 1D case, with pressure minima located close to the transducer face and reflector wall. Further investigations are needed to clearly identify the physical cause of this observation, which will be covered in future work. In the following, the efficiency is assessed around the condition for optimal separation, corresponding to the slightly distorted nodal pattern of Fig. 2e. The migration of particles close to the reflector wall and transducer face can be difficult to resolve, due to reflections. Consequently, only the central part of channel is investigated, from: H/6 to 5H/6. Also to account for artefacts such as background noise and fouling of the windows, reference images were taken frequently without flow and sound in the channel and subtracted from the images analyzed. It is assumed that attenuation of scattered light from other particles is negligible as the particle concentration falls in the dilute regime [24,25]. Accordingly, the intensity of each pixel in the image is expected to be proportional to the particle number density. The purpose of the metric used here is to provide qualitative information regarding the effect of different acoustic and flow parameters on the efficiency of the separation process. This efficiency metric is based on the collected light intensity integrated over sections upstream (REF) and downstream (SEP) of the transducer, as shown schematically in Fig. 3. The parameter (I) is the image spatial light intensity, defined from pixel values in 14-bit images. Integration of I along the y direction in SEP and REF regions yields Iysep and Iyref signals which are plotted at the bottom of Fig. 3. For the results presented, the channel height was adjusted to match a complete wavelength, i.e. two pressure nodes are expected across the channels height. In Fig. 3 the centroids of the two particle-enriched bands can easily be detected in the Iy signals. To assess the quality of the separation achieved, the maximum light intensity in the (REF) and (SEP) signals could simply be subtracted. This would yield a measure of the maximum particle enrichment encountered punctually in the channel. It would however not provide information on the proportion of the total particle numbers that could be recovered by splitting the flow, i.e. a
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Fig. 3. Schematic of the separation efficiency assessment, with experimental results collected with a channel height of 6.86 mm and a excitation frequency of 50.3 kHz.
measure of the separation efficiency that could be achieved in practice. For this purpose, the Iy signal needs to be integrated in the direction of the wave propagation and included in the definition of a separation efficiency metric (g). The thickness of particle-enriched band is estimated to be approximately 1/6 of the channel height at optimum resonance and this value will be used in the calculation of g. The metric g is defined in Eq. (3) as the ratio of the difference between collected light intensity within particle-enriched bands in the SEP and REF sections to the collected light intensity in the whole area of the REF section. In other words, g represents the relative increase in the particle number density in two H/6-wide particle-enriched bands in the middle of the channel centered at positions X n . The magnitude of g is obviously a function of the width of the integrated band and increases as the width of integrated band decreases. However, this does not compromise the used of this metric for the purpose intended here. In the summation operator of Eq. (3), n is the number of H/6-wide-band across the channel height which is equal to two in the results presented in the following:
Pn R X n þH=12
g¼
i¼1
X n H=12
½Iysep Iyref dy
Iyxref
ð3Þ
the electrostatic transducer. As stated in Eq. (1), the magnitude of the axial PRF on a particle is proportional to the square of the pressure amplitude of the acoustic field. Measured in the following 00 using a 1/8 microphone flush-mounted in the reflector wall. The results of frequency scans at different driving voltages are presented in Fig. 4, showing an increase in the separation efficiency with increasing pressure amplitude, as expected from Eq. (1). In Fig. 5 the maximum separation efficiency for each driving voltage at the optimum resonant frequency is shown as function of the pressure amplitude. Unfortunately, the number of data points is insufficient to yield a meaningful correlation, but the separation efficiency trend is qualitatively consistent with the theoretical prediction for axial PRF on a suspended particles, as shown in Eq. (1). 4.2. Frequency The effect of standing wave frequency on the separation efficiency was studied by translating the roof of the channel and tuning the frequency to yield a wavelength matching the resonator height. In Fig. 6, the separation efficiency is shown for different channel heights, each time with two pressure nodes in the channel. The data was corrected to compensate for variation in the sound pressure amplitude at different frequencies, as the response of
4. Results and discussion
0.4
p = 528.30 Pa, SPL =148.44 dB a
0.35 0.3
a
p = 382.08 Pa, SPL =145.62 dB a
pa= 273.58 Pa, SPL =142.72 dB
0.25 0.2
η
The parameters covered in this investigation are the sound pressure amplitude (pa ), the frequency of the standing wave (f), the velocity of the flow and the parallelism of the channel walls. Following each change in the operating conditions, the driving frequency was scanned around the expected baseline to identify the optimum separation, revealing the width of the frequency band for which significant acoustic effects are observed.
p = 509.43 Pa, SPL =148.12 dB
0.15 0.1 0.05 0
4.1. Pressure amplitude The effect of sound pressure amplitude on the acoustic separation efficiency was investigated by varying the excitation voltage of
−0.05 48
48.5
49
49.5
50
50.5
51
Frequency (kHz) Fig. 4. Separation efficiency as function of sound pressure amplitude.
51.5
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Experimental data Quadratic fit
0.3
0.5
U = 0.10±2.00% m/s 0.4
0.2
0.3
U = 0.15±1.66% m/s U = 0.20±1.70% m/s U = 0.25±2.36% m/s
η
η
0.25
0.15
0.2
0.1
0.1
0.05 0.25
U = 0.05±5.94% m/s
0
0.3
0.35
0.4
0.45
0.5
0.55 −0.1 47.5
Pressure amplitude (kPa)
the transducer used was frequency dependent. The axial PRF is expected to be linearly proportional to the frequency of the standing wave as predicted by Eq. (1) and, the maximum separation efficiency indeed increases approximately linearly between 50 kHz and 80 kHz. The deviation observed from the expected theoretical trend can be due to the limitation of the separation efficiency metric used, as it only qualitatively links the accumulation of particles in the middle of the channel to the acoustic force causing the translation of the particles. In these two figures, the error bars represent the observed variation in the calculated separation efficiency from different images. 4.3. Velocity In addition to the effect of acoustic parameters, we investigated the effect of flow and geometric parameters relevant in the design of practical gas-phase acoustic separation systems. The first such parameter is the gas velocity, with the results presented in Fig. 7. As expected, the separation efficiency is higher at lower averaged channel velocity due to longer particle residence time over the transducer. The velocity measurements were performed using a Laser Doppler Anemometer (LDA, Dantec Dynamics). In Fig. 7, the error bars for the separation efficiency data represent the standard deviation, which is largest for the lowest velocity case. At such low velocities, perturbations from the laboratory can travel upstream from the exit of the channel and affect flow quality over the transducer. The LDA results obtained at the highest velocity, corresponding to a channel Reynolds number (ReH ) of 112, also indicate only a moderate increase in the residual turbulence intensity. In Fig. 8, the maximum separation efficiency is plotted against
48
48.5
49
49.5
50
50.5
51
51.5
52
Frequency (kHz)
Fig. 5. Maximum separation efficiency at optimum resonance as a function of acoustic pressure amplitude.
Fig. 7. Separation efficiency as function of averaged channel velocity.
the channel average velocity. The separation efficiency is expected to be inversely proportional to average channel velocity, as a result of the reduced interaction time between the acoustic field and the suspended particles and hence the reduced number of cycles available for the particles to migrates to the pressure nodes. The result presented in Fig. 8 shows a more gradual decay with an exponent of 0.70. This hints that in our experiment the separation is not limited by the interaction length and that the effect of the measured turbulence intensity (about 2.5% at the maximum velocity) is not significant. Another possible explanation for this can be the occurrence of a concentration threshold at lower velocities around particle-enriched bands that limits further accumulation in these regions. 4.4. Parallelism of channel walls The effect of the parallelism between the reflector and to the transducer was also investigated. The result are presented in Fig. 9, where the separation efficiency is plotted against the inclination angle of the reflector wall (in minutes of arc) for two different channel heights. Our experimental results on the degradation of the separation efficiency are consistent with the work of Gröschl [26] who investigated the effect of transducer-reflector parallelism by calculating a resonance quality factor (resonance sharpness) for the separation channel. Besides his experimental investigation, he also derived a set of analytical equations to quantify the quality factor for a resonant channel at different inclination angle of the reflector. As shown in Fig. 9 our results show a trend very similar to the analytical predictions, using a normalized quality factor (QQo ), where Q o is the maximum quality factor for a perfectly aligned channel.
1.2
Linear fit H = 6.82 mm H = 5.75 mm H = 4.88 mm H = 4.33 mm
1 0.8
0.5
Experimental data
0.45
η = 0.28.f − 0.48
Power law fit
0.4
M
0.6
η
M
0.35
η
0.4
0.3
η = 0.054⋅v−0.70
0.25
0.2
0.2
0
0.15 −0.2
45
50
55
60
65
70
75
80
85
Frequency (kHz)
0.1 0.05
0.1
0.15
0.2
0.25
Velocity (m/s) Fig. 6. Separation efficiency as a function of standing wave frequency, carried out in channels with different heights and corrected for the frequency-dependent response of the transducer.
Fig. 8. Variation of the maximum separation efficiency as a function of the averaged channel velocity.
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Acknowledgments
1
H = 5.71 mm, Exp (η ) H = 6.86 mm, Analytical (Q)
0.2
0.8
η
Q/Q
o
H = 5.71mm, Analytical (Q)
0.1 0.6 0 −0.05 −20
The research presented here has received funding from the KTH Linné Flow Center and the European Union’s Seventh Framework Programme (FP7) under Grant Agreement No. 604244 (Norosensor). References
−15
−10
−5
0
5
10
15
0.4 20
Minute of arc Fig. 9. Effect of parallelism of the channel walls on the acoustic separation efficiency, showing both experimental and analytical results for two different channel heights.
The tolerance to maintain 90% of the maximum separation efficiency is about 11 lm or 0.40 for a channel height of 5.71 mm. Both experimental and analytical results show a drop in the 90% tolerance value as the channel height decrease, i.e. higher alignment accuracy is required for smaller channels.
5. Conclusion The effect of key design parameters on the acoustic separation efficiency of submicron-solid particles suspended in air has been investigated. The results show that variation of the separation efficiency can be approximated by the equation of the primary radiation force (Eq. (1)). The efficiency increases with pressure amplitude and increases approximately linearly with frequency. However the effect of gas velocity on the separation efficiency is more gradual than anticipated, with the power law decay observed having an exponent of 0.7 rather than the 1 expected from the decrease of the residence time in the resonator. This hints that the acoustic separation in our current channel, as expressed through the efficiency metric presented, is saturated and that the interaction length between the field and the particles has only a limited effect on the result. Finally, the parallelism of the reflector relative to the transducer face was investigated, showing approximately the same rate of degradation for the separation efficiency as predicted from the decrease of the quality factor of the channel. This experiment also shows that the geometrical tolerance required to maintain 90% of the maximum separation efficiency are more demanding as the channel height decreases. These results demonstrate that acoustic forces can be used for the separation of submicron particles suspended in gases. They also provide a guideline for the design of practical separators in terms of acoustic, flow and geometric parameters suitable for effective separation. The work presented here also raises a few interesting questions that will be addressed in future works. These include finding the underlying cause for the optimum separation being observed when the nodal pattern is distorted compared to that of an idealized 1D planar standing wave and quantifying an intensity threshold when turbulence starts to affect separation efficiency.
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Ultrasonics journal homepage: www.elsevier.com/locate/ultras
Acoustic separation of submicron solid particles in air Ramin J. Imani a,⇑, Etienne Robert a,b a b
KTH Mechanics, Osquars Backe 18, Stockholm 10044, Sweden Polytechnique Montréal, Dep. of Mechanical Engineering, Montréal, Quebec, Canada
a r t i c l e
i n f o
Article history: Received 24 February 2015 Received in revised form 29 June 2015 Accepted 30 June 2015 Available online 7 July 2015 Keywords: Acoustophoresis Submicron particles Gas phase
a b s t r a c t The use of ultrasound to continuously separate submicron particles suspended in air is investigated in a rectangular channel with adjustable height. An electrostatic transducer is used to generate a standing wave in the 50–80 kHz frequency range and the particles experience forces within the acoustic field causing them to concentrate at the pressure nodes. To assess the effect of several key design parameters on the separation efficiency, a simple method based on light scattering is implemented to provide information on the particle concentrations as a function of position in the channel. The images acquired are processed to yield a separation efficiency metric that is used to evaluate the effect of acoustic, flow and geometrical parameters. The results show that, in qualitative agreement with theoretical models, the maximum separation efficiency increases with the pressure amplitude of the sound wave. The separation efficiency is also linearly proportional to the standing wave frequency, when it is varied between 50–80 kHz. On the other hand, the effect of the average fluid velocity is less pronounced than expected, suggesting that in our channel separation is not limited by the interaction length between the acoustic field and the suspended particles. The effect of the parallelism of the reflector relative to the transducer is also investigated. Ó 2015 Elsevier B.V. All rights reserved.
1. Introduction The separation of particles suspended in a gas is a problem relevant for a wide range of scientific and industrial applications. It is the subject of a sustained research effort aimed at developing and improving practical means for the concentration, sorting and removal of particles from gases. Currently, several mature industrial techniques are available to perform these tasks, including cyclones, electrostatic precipitators (ESP), scrubbers and filters based on porous elements. However, each have limitations such as the potential for clogging, the generation of liquid waste, reduced capabilities in harsh environments and for the handling of submicron particles [1–3]. Typically these techniques have a cut-off size, below which the particle removal efficiency significantly drops. For instance with filters relying on flowing the suspension through a porous material, the capture efficiency will obviously be low for particles smaller than the pore size. In this case, targeting smaller particles comes at the cost of an increased pressure drop. Other techniques such as ESPs can also be specifically designed to maximize submicron particle removal, with up to 90% capture efficiency [4], but this requires high energy input and results in the formation of ozone. ⇑ Corresponding author. E-mail address: [email protected] (R.J. Imani). http://dx.doi.org/10.1016/j.ultras.2015.06.021 0041-624X/Ó 2015 Elsevier B.V. All rights reserved.
During the last few decades, microfluidics applications have benefited from the development of acoustically mediated techniques for the manipulation of particles, droplets and bubbles in liquids. This approach does not require the introduction of a physical barrier or of chemical additives for the separation of particles [5]. It is also able to sort particles according to their size [6] or other physical properties such as compressibility and density [7]. Techniques developed in the liquid phase can potentially be adapted to gaseous media [8]. Acoustic separation of particles suspended in air, especially submicron particles, has received limited attention and only a few works are addressing this problem experimentally. For instance, the investigations of Budwig et al. [9] and Anderson et al. [10] are limited to the separation and fractionation of particles several microns in diameter suspended in a gaseous flow. This motivates the present experimental investigation to study the effects of acoustic, flow and geometrical parameters on the separation efficiency of submicron solid particles suspended in air. The paper is divided as follows: First, the theory behind the phenomenon under investigation is briefly explained. Then, the experimental setup and the data acquisition technique used are introduced. The effects of different parameters on the separation efficiency are then presented, including the pressure amplitude, the frequency of the standing wave, the average flow velocity and the parallelism of the channel walls. These results are followed
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by a brief discussion highlighting the implication for the design of practical acoustic separation systems. 2. Theory The acoustic forces on a particle suspended in a fluid have been studied extensively since the first observation of particle separation in a standing wave by Kundt and Lehmann [11]. King [12] was the first to derive a comprehensive theoretical formula for the acoustic radiation forces on a rigid sphere in a plane standing wave. Several other studies further developed his initial formulation to include compressible spheres [13] and the effect of viscosity [14,15]. The particles suspended in an ideal 1D acoustic standing wave experience two forces from this field: the primary radiation force (PRF), generated by the interaction of a particle with the primary field, and the secondary radiation forces (SRF), originating from the energy scattered by the other suspended particles [16]. The PRF is by far the dominating force [17], and the SRF will accordingly not be considered in this study. In a standing wave, the PRF can be divided in two components: axial and transverse relative to the direction of the wave propagation. The axial component is responsible for the displacement of particles to the nodes or anti-nodes of the standing wave. The transverse component packs the particles closer together in the direction normal to the wave propagation [18]. The equation for the axial PRF [13] shown in Eq. (1) states that the acoustic force is proportional to the particle volume V p and to the square of the pressure amplitude (pa ). The acoustic contrast factor Uðb; qÞ depends on both the particle density qp and its compressibility bp in relation to the carrier fluid properties (qf ; bf ). The wave number k is defined as 2kp, where k is wavelength, x is the distance from a pressure node.
pV p p2a bf
Uðb; qÞ sinð2kxÞ 2k 5q 2qf bp Uðb; qÞ ¼ p 2qp þ qf bf F ax ¼
The signal is then shifted to positive values and amplified to 400 V peak-to-peak. The separation channel is designed with a variable height (H), adjustable from 0 to 20 mm to yield standing waves of different frequencies. In the present study, the investigated range was 50– 80 kHz, which corresponds to a channel height of 6.86–4.28 mm. The roof is manually positioned with micrometer screws at both ends while guided vertically by four supporting rods. The displacement of both extremities of the reflector is also measured optically from images captured using a digital camera, providing a resolution of 90 pixels/mm. From the measured value of the channel height, a baseline standing wave frequency is determined. The excitation frequency is then scanned around this baseline to identify the optimum resonance in the channel by visualization of the particle separation in the standing wave. The velocity of air through the channel is regulated by a flow controller (Teledyne Hastings HFC-202), connected to a clean compressed air supply. The flow is conditioned upstream of the separation region in a stabilization chamber consisting of three rows of fine grids followed by a diffuser to ensure a Poisuille-type velocity profile over the transducer. The flow is seeded using a fluidized bed with TiO2 solid particles (LaVision GmbH) with reported nominal diameter of 300 nm, density of 3900–4200 kg m3 with negligible compressibility [19]. The seeder used is based on a design by Willert and Jarius [20,21], consisting of a cylinder with a porous metal plate glued to the bottom with clean air supplied from below. Solid particles located above the porous plate are entrained by the airflow when the drag force exceeds their weight. The size distribution of submicron particles was characterized using a Scanning Mobility Particle Sizer (SMPS, TSI 3080/3010), revealing possible agglomeration in the seeder as the size distribution is broad, centered at approximately 460 nm, and extends to large sizes, as shown in Fig. 1b.
ð1Þ 3.2. Data acquisition
ð2Þ
It should be noted here that the sign of the acoustic contrast factor sets the direction of the acoustic force either towards the pressure nodes or antinodes. Generally, solid particles suspended in air or aqueous media are moved to the pressure node, while gas bubbles in aqueous media are moved towards pressure antinodes [18]. 3. Experimental setup To assess the effect of a large number of parameters on acoustic separation efficiency, a versatile separation channel, a quick diagnostic technique and a suitable evaluating metric were implemented. These are presented in the following section. 3.1. Acoustic separation channel A simple flow-through acoustic particle separator was built to study the effect of flow and acoustic parameters on the separation efficiency of solid particles suspended in air. The experimental setup is presented schematically in Fig. 1. The separation channel has a rectangular cross section, 30 mm wide, with transparent sidewalls to allow optical access to the acoustic region. An electrostatic broadband transducer (SensComp, Open face 600) is flush-mounted into the bottom wall, generating a standing wave across the channel height. The transducer can be operated in the 40–100 kHz range, generating sound pressure amplitudes up to 00 154.5 dB (re 20 lpa), measured using a type 4138 1/8 Brüel and Kjaer pressure field microphone. A function generator (TG1000, TTi Ltd.) produces a sinusoidal signal for the transducer input.
Only a few investigations in the literature have attempted to quantify the efficiency of acoustic separation in air, typically relying on directly counting the number of particles after the separation region. Budwig et al. [9] employed an off-line visualization approach using a microscope to evaluate the size distribution of the particles settling in a chamber downstream of the separation region. In a work in progress by our group [8], a Scanning Mobility Particle Sizer (SMPS) is used to quantitatively measure the particle size distribution in real time in the channel with and without a sound source. This technique can provide very precise information, but it is complex and not very fast. To investigate the effect of a wide range of parameters on the acoustic particle separation efficiency, a simple, fast and reliable method is required. For the results presented here, a technique based on light scattering (also described in [8]) is implemented. A thin laser sheet parallel to the flow direction is used to illuminate the region immediately upstream and downstream of the transducer. The light sheet is created by a diode laser and two plano-convex cylindrical lenses in Keplerian configuration and is inserted through the downstream opening, along the centerline of the channel. The entrained particles in the channel scatter light, which is captured by a camera (Nikon D7000) positioned orthogonally to the flow. The images are exposed for a sufficiently long time to provide a high signal-to-noise ratio. Consequently, individual particles are not resolved but rather their trajectories are integrated. The images acquired are then processed using Matlab to yield a metric that can be used to assess the effect of different parameters on the separation efficiency. Examples of images acquired using this technique are presented in Fig. 2 showing a nearly uniform distribution of particles in the
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(a)
(b)
Particle diameter (nm)
Fig. 1. (a) Schematic representation of the experimental setup. The gas flow is seeded with particles in the fluidized bed (1) before being sent to a stabilization chamber (2), ensuring laminar flow conditions in the separation channel (3). The position of the reflector wall (4) of the resonator is adjusted by two manually controlled micrometers (5). (b) Size distribution of the TiO2 particles, as measured in the separation channel without sound excitation in the resonator. The vertical axis represents the concentration (particles/cm3 ) normalized by the width of the size bins used by the aerosol spectrometer.
channel in the absence of acoustic excitation (Fig. 2a). Following the generation of a standing wave, particles have migrated to the central part of the channel as shown in Fig. 2b. By progressively changing the excitation frequency around the expected value calculated from the channel height the optimum resonance frequency is identified. Somewhat surprisingly, the best separation is observed when a double particle-enriched band is formed in
(a)
(b)
(c)
(d)
(e) Fig. 2. Visualization of the acoustic particle separation using the laser light scattering method, with a channel height of 6.86 mm. (a) Nearly uniform distribution without sound. (b)–(d) Images captured during the frequency tuning procedure showing a progressively sharper nodal pattern: (b) 49 kHz, (c) 49.3 kHz, (d) 49.6 kHz. (e) Optimal resonance, at 50 kHz, revealing a slightly distorted nodal pattern compared to an idealized 1D planar standing wave.
middle of the channel and as well as additional single bands near the upper and lower walls, instead of the two bands located k=4 from the walls expected assuming that a 1D planar standing wave is established in the channel. This phenomenon can result from the superposition of several resonant modes in our 2D channel [22] or from near field effects [23] caused by the finite size of the transducer used. This reveals that, at optimum resonance the pressure field is most likely distorted compared to the idealized 1D case, with pressure minima located close to the transducer face and reflector wall. Further investigations are needed to clearly identify the physical cause of this observation, which will be covered in future work. In the following, the efficiency is assessed around the condition for optimal separation, corresponding to the slightly distorted nodal pattern of Fig. 2e. The migration of particles close to the reflector wall and transducer face can be difficult to resolve, due to reflections. Consequently, only the central part of channel is investigated, from: H/6 to 5H/6. Also to account for artefacts such as background noise and fouling of the windows, reference images were taken frequently without flow and sound in the channel and subtracted from the images analyzed. It is assumed that attenuation of scattered light from other particles is negligible as the particle concentration falls in the dilute regime [24,25]. Accordingly, the intensity of each pixel in the image is expected to be proportional to the particle number density. The purpose of the metric used here is to provide qualitative information regarding the effect of different acoustic and flow parameters on the efficiency of the separation process. This efficiency metric is based on the collected light intensity integrated over sections upstream (REF) and downstream (SEP) of the transducer, as shown schematically in Fig. 3. The parameter (I) is the image spatial light intensity, defined from pixel values in 14-bit images. Integration of I along the y direction in SEP and REF regions yields Iysep and Iyref signals which are plotted at the bottom of Fig. 3. For the results presented, the channel height was adjusted to match a complete wavelength, i.e. two pressure nodes are expected across the channels height. In Fig. 3 the centroids of the two particle-enriched bands can easily be detected in the Iy signals. To assess the quality of the separation achieved, the maximum light intensity in the (REF) and (SEP) signals could simply be subtracted. This would yield a measure of the maximum particle enrichment encountered punctually in the channel. It would however not provide information on the proportion of the total particle numbers that could be recovered by splitting the flow, i.e. a
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Fig. 3. Schematic of the separation efficiency assessment, with experimental results collected with a channel height of 6.86 mm and a excitation frequency of 50.3 kHz.
measure of the separation efficiency that could be achieved in practice. For this purpose, the Iy signal needs to be integrated in the direction of the wave propagation and included in the definition of a separation efficiency metric (g). The thickness of particle-enriched band is estimated to be approximately 1/6 of the channel height at optimum resonance and this value will be used in the calculation of g. The metric g is defined in Eq. (3) as the ratio of the difference between collected light intensity within particle-enriched bands in the SEP and REF sections to the collected light intensity in the whole area of the REF section. In other words, g represents the relative increase in the particle number density in two H/6-wide particle-enriched bands in the middle of the channel centered at positions X n . The magnitude of g is obviously a function of the width of the integrated band and increases as the width of integrated band decreases. However, this does not compromise the used of this metric for the purpose intended here. In the summation operator of Eq. (3), n is the number of H/6-wide-band across the channel height which is equal to two in the results presented in the following:
Pn R X n þH=12
g¼
i¼1
X n H=12
½Iysep Iyref dy
Iyxref
ð3Þ
the electrostatic transducer. As stated in Eq. (1), the magnitude of the axial PRF on a particle is proportional to the square of the pressure amplitude of the acoustic field. Measured in the following 00 using a 1/8 microphone flush-mounted in the reflector wall. The results of frequency scans at different driving voltages are presented in Fig. 4, showing an increase in the separation efficiency with increasing pressure amplitude, as expected from Eq. (1). In Fig. 5 the maximum separation efficiency for each driving voltage at the optimum resonant frequency is shown as function of the pressure amplitude. Unfortunately, the number of data points is insufficient to yield a meaningful correlation, but the separation efficiency trend is qualitatively consistent with the theoretical prediction for axial PRF on a suspended particles, as shown in Eq. (1). 4.2. Frequency The effect of standing wave frequency on the separation efficiency was studied by translating the roof of the channel and tuning the frequency to yield a wavelength matching the resonator height. In Fig. 6, the separation efficiency is shown for different channel heights, each time with two pressure nodes in the channel. The data was corrected to compensate for variation in the sound pressure amplitude at different frequencies, as the response of
4. Results and discussion
0.4
p = 528.30 Pa, SPL =148.44 dB a
0.35 0.3
a
p = 382.08 Pa, SPL =145.62 dB a
pa= 273.58 Pa, SPL =142.72 dB
0.25 0.2
η
The parameters covered in this investigation are the sound pressure amplitude (pa ), the frequency of the standing wave (f), the velocity of the flow and the parallelism of the channel walls. Following each change in the operating conditions, the driving frequency was scanned around the expected baseline to identify the optimum separation, revealing the width of the frequency band for which significant acoustic effects are observed.
p = 509.43 Pa, SPL =148.12 dB
0.15 0.1 0.05 0
4.1. Pressure amplitude The effect of sound pressure amplitude on the acoustic separation efficiency was investigated by varying the excitation voltage of
−0.05 48
48.5
49
49.5
50
50.5
51
Frequency (kHz) Fig. 4. Separation efficiency as function of sound pressure amplitude.
51.5
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Experimental data Quadratic fit
0.3
0.5
U = 0.10±2.00% m/s 0.4
0.2
0.3
U = 0.15±1.66% m/s U = 0.20±1.70% m/s U = 0.25±2.36% m/s
η
η
0.25
0.15
0.2
0.1
0.1
0.05 0.25
U = 0.05±5.94% m/s
0
0.3
0.35
0.4
0.45
0.5
0.55 −0.1 47.5
Pressure amplitude (kPa)
the transducer used was frequency dependent. The axial PRF is expected to be linearly proportional to the frequency of the standing wave as predicted by Eq. (1) and, the maximum separation efficiency indeed increases approximately linearly between 50 kHz and 80 kHz. The deviation observed from the expected theoretical trend can be due to the limitation of the separation efficiency metric used, as it only qualitatively links the accumulation of particles in the middle of the channel to the acoustic force causing the translation of the particles. In these two figures, the error bars represent the observed variation in the calculated separation efficiency from different images. 4.3. Velocity In addition to the effect of acoustic parameters, we investigated the effect of flow and geometric parameters relevant in the design of practical gas-phase acoustic separation systems. The first such parameter is the gas velocity, with the results presented in Fig. 7. As expected, the separation efficiency is higher at lower averaged channel velocity due to longer particle residence time over the transducer. The velocity measurements were performed using a Laser Doppler Anemometer (LDA, Dantec Dynamics). In Fig. 7, the error bars for the separation efficiency data represent the standard deviation, which is largest for the lowest velocity case. At such low velocities, perturbations from the laboratory can travel upstream from the exit of the channel and affect flow quality over the transducer. The LDA results obtained at the highest velocity, corresponding to a channel Reynolds number (ReH ) of 112, also indicate only a moderate increase in the residual turbulence intensity. In Fig. 8, the maximum separation efficiency is plotted against
48
48.5
49
49.5
50
50.5
51
51.5
52
Frequency (kHz)
Fig. 5. Maximum separation efficiency at optimum resonance as a function of acoustic pressure amplitude.
Fig. 7. Separation efficiency as function of averaged channel velocity.
the channel average velocity. The separation efficiency is expected to be inversely proportional to average channel velocity, as a result of the reduced interaction time between the acoustic field and the suspended particles and hence the reduced number of cycles available for the particles to migrates to the pressure nodes. The result presented in Fig. 8 shows a more gradual decay with an exponent of 0.70. This hints that in our experiment the separation is not limited by the interaction length and that the effect of the measured turbulence intensity (about 2.5% at the maximum velocity) is not significant. Another possible explanation for this can be the occurrence of a concentration threshold at lower velocities around particle-enriched bands that limits further accumulation in these regions. 4.4. Parallelism of channel walls The effect of the parallelism between the reflector and to the transducer was also investigated. The result are presented in Fig. 9, where the separation efficiency is plotted against the inclination angle of the reflector wall (in minutes of arc) for two different channel heights. Our experimental results on the degradation of the separation efficiency are consistent with the work of Gröschl [26] who investigated the effect of transducer-reflector parallelism by calculating a resonance quality factor (resonance sharpness) for the separation channel. Besides his experimental investigation, he also derived a set of analytical equations to quantify the quality factor for a resonant channel at different inclination angle of the reflector. As shown in Fig. 9 our results show a trend very similar to the analytical predictions, using a normalized quality factor (QQo ), where Q o is the maximum quality factor for a perfectly aligned channel.
1.2
Linear fit H = 6.82 mm H = 5.75 mm H = 4.88 mm H = 4.33 mm
1 0.8
0.5
Experimental data
0.45
η = 0.28.f − 0.48
Power law fit
0.4
M
0.6
η
M
0.35
η
0.4
0.3
η = 0.054⋅v−0.70
0.25
0.2
0.2
0
0.15 −0.2
45
50
55
60
65
70
75
80
85
Frequency (kHz)
0.1 0.05
0.1
0.15
0.2
0.25
Velocity (m/s) Fig. 6. Separation efficiency as a function of standing wave frequency, carried out in channels with different heights and corrected for the frequency-dependent response of the transducer.
Fig. 8. Variation of the maximum separation efficiency as a function of the averaged channel velocity.
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Acknowledgments
1
H = 5.71 mm, Exp (η ) H = 6.86 mm, Analytical (Q)
0.2
0.8
η
Q/Q
o
H = 5.71mm, Analytical (Q)
0.1 0.6 0 −0.05 −20
The research presented here has received funding from the KTH Linné Flow Center and the European Union’s Seventh Framework Programme (FP7) under Grant Agreement No. 604244 (Norosensor). References
−15
−10
−5
0
5
10
15
0.4 20
Minute of arc Fig. 9. Effect of parallelism of the channel walls on the acoustic separation efficiency, showing both experimental and analytical results for two different channel heights.
The tolerance to maintain 90% of the maximum separation efficiency is about 11 lm or 0.40 for a channel height of 5.71 mm. Both experimental and analytical results show a drop in the 90% tolerance value as the channel height decrease, i.e. higher alignment accuracy is required for smaller channels.
5. Conclusion The effect of key design parameters on the acoustic separation efficiency of submicron-solid particles suspended in air has been investigated. The results show that variation of the separation efficiency can be approximated by the equation of the primary radiation force (Eq. (1)). The efficiency increases with pressure amplitude and increases approximately linearly with frequency. However the effect of gas velocity on the separation efficiency is more gradual than anticipated, with the power law decay observed having an exponent of 0.7 rather than the 1 expected from the decrease of the residence time in the resonator. This hints that the acoustic separation in our current channel, as expressed through the efficiency metric presented, is saturated and that the interaction length between the field and the particles has only a limited effect on the result. Finally, the parallelism of the reflector relative to the transducer face was investigated, showing approximately the same rate of degradation for the separation efficiency as predicted from the decrease of the quality factor of the channel. This experiment also shows that the geometrical tolerance required to maintain 90% of the maximum separation efficiency are more demanding as the channel height decreases. These results demonstrate that acoustic forces can be used for the separation of submicron particles suspended in gases. They also provide a guideline for the design of practical separators in terms of acoustic, flow and geometric parameters suitable for effective separation. The work presented here also raises a few interesting questions that will be addressed in future works. These include finding the underlying cause for the optimum separation being observed when the nodal pattern is distorted compared to that of an idealized 1D planar standing wave and quantifying an intensity threshold when turbulence starts to affect separation efficiency.
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