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1.
《Ultrasonics sonochemistry》2014,21(4):1496-1503
Changes in the cavitation intensity of gases dissolved in water, including H2, N2, and Ar, have been established in studies of acoustic bubble growth rates under ultrasonic fields. Variations in the acoustic properties of dissolved gases in water affect the cavitation intensity at a high frequency (0.83 MHz) due to changes in the rectified diffusion and bubble coalescence rate. It has been proposed that acoustic bubble growth rates rapidly increase when water contains a gas, such as hydrogen faster single bubble growth due to rectified diffusion, and a higher rate of coalescence under Bjerknes forces. The change of acoustic bubble growth rate in rectified diffusion has an effect on the damping constant and diffusivity of gas at the acoustic bubble and liquid interface. It has been suggested that the coalescence reaction of bubbles under Bjerknes forces is a reaction determined by the compressibility and density of dissolved gas in water associated with sound velocity and density in acoustic bubbles. High acoustic bubble growth rates also contribute to enhanced cavitation effects in terms of dissolved gas in water. On the other hand, when Ar gas dissolves into water under ultrasound field, cavitation behavior was reduced remarkably due to its lower acoustic bubble growth rate. It is shown that change of cavitation intensity in various dissolved gases were verified through cleaning experiments in the single type of cleaning tool such as particle removal and pattern damage based on numerically calculated acoustic bubble growth rates.  相似文献   

2.
Scaled-up and economically viable sonochemical systems are critical for increased use of ultrasound in environmental and chemical processing applications. In this study, computational simulations and acoustic pressure maps were used to design a larger-scale sono-reactor containing a multi-stepped ultrasonic horn. Simulations in COMSOL Multiphysics showed ultrasonic waves emitted from the horn neck and tip, generating multiple regions of high acoustic pressure. The volume of these regions surrounding the horn neck were larger compared with those below the horn tip. The simulated acoustic field was verified by acoustic pressure contour maps generated from hydrophone measurements in a plexiglass box filled with water. These acoustic pressure contour maps revealed an asymmetric and discrete distribution of acoustic pressure due to acoustic cavitation, wave interaction, and water movement by ultrasonic irradiation. The acoustic pressure contour maps were consistent with simulation results in terms of the effective scale of cavitation zones (∼10 cm and <5 cm above and below horn tip, respectively). With the mapped acoustic field and identified cavitation location, a cylindrically-shaped sono-reactor with a conical bottom was designed to evaluate the treatment capacity (∼5 L) for the multi-stepped horn using COMSOL simulations. In this study, verification of simulation results with experiments demonstrates that coupling of COMSOL simulations with hydrophone measurements is a simple, effective and reliable scientific method to evaluate reactor designs of ultrasonic systems.  相似文献   

3.
Modelling of particle paths passing through an ultrasonic standing wave   总被引:3,自引:0,他引:3  
Townsend RJ  Hill M  Harris NR  White NM 《Ultrasonics》2004,42(1-9):319-324
Within an ultrasonic standing wave particles experience acoustic radiation forces causing agglomeration at the nodal planes of the wave. The technique can be used to agglomerate, suspend, or manipulate particles within a flow. To control agglomeration rate it is important to balance forces on the particles and, in the case where a fluid/particle mix flows across the applied acoustic field, it is also necessary to optimise fluid flow rate. To investigate the acoustic and fluid forces in such a system a particle model has been developed, extending an earlier model used to characterise the 1-dimensional field in a layered resonator. In order to simulate fluid drag forces, CFD software has been used to determine the velocity profile of the fluid/particle mix passing through the acoustic device. The profile is then incorporated into a MATLAB model. Based on particle force components, a numerical approach has been used to determine particle paths. Using particle coordinates, both particle concentration across the fluid channel and concentration through multiple outlets are calculated. Such an approach has been used to analyse the operation of a microfluidic flow-through separator, which uses a half wavelength standing wave across the main channel of the device. This causes particles to converge near the axial plane of the channel, delivering high and low particle concentrated flow through two outlets, respectively. By extending the model to analyse particle separation over a frequency range, it is possible to identify the resonant frequencies of the device and associated separation performance. This approach will also be used to improve the geometric design of the microengineered fluid channels, where the particle model can determine the limiting fluid flow rate for separation to occur, the value of which is then applied to a CFD model of the device geometry.  相似文献   

4.
Polystyrene particles of 9 μm diameter were acoustically concentrated along the axis of a water-filled cylindrical waveguide containing a 3 MHz standing wave field. Modulation of the acoustic field enabled transport of the concentrated particles in the axial direction. Four modulations were investigated; 1, a fixed frequency difference introduced between two transducers; 2, ramping the transducer frequency; 3, tone burst, i.e. sound that is pulsed on and off, allowing intermittent sedimentation under gravity; and 4, switching the sound off to allow continuous sedimentation. The most efficient transport (leaving the fewest particles in suspension) of clumps to one end of the container was achieved with method 1 above. In this system the maximum speed of transport of the axial clumps was 24 mm s-1. A theory developed here for the transport of particles in a pseudo (i.e. slowly moving) standing wave field predicts an upper limit, which increases with particle size, for the speed of an entrained body. For a single 9 μm diameter particle in a field with a spatial peak pressure amplitude of 0.4 MPa this speed would be 0.5 mm s-1. The higher experimental speeds observed here emphasize the value of acoustically concentrating particles into relatively large clumps prior to initiating transport.  相似文献   

5.
Townsend RJ  Hill M  Harris NR  White NM 《Ultrasonics》2006,44(Z1):e467-e471
Within an acoustic standing wave particles experience acoustic radiation forces, a phenomenon which is exploited in particle or cell manipulation devices. When developing such devices, one-dimensional acoustic characteristics corresponding to the transducer(s) are typically of most importance and determine the primary radiation forces acting on the particles. However, radiation forces have also been observed to act in the lateral direction, perpendicular to the primary radiation force, forming striated patterns. These lateral forces are due to lateral variations in the acoustic field influenced by the geometry and materials used in the resonator. The ability to control them would present an advantage where their effect is either detrimental or beneficial to the particle manipulation process. The two-dimensional characteristics of an ultrasonic separator device have been modelled within a finite element analysis (FEA) package. The fluid chamber of the device, within which the standing wave is produced, has a width to height ratio of approximately 30:1 and it is across the height that a half-wavelength standing wave is produced to control particle movement. Two-dimensional modal analyses have calculated resonant frequencies which agree well with both the one-dimensional modelling of the device and experimentally measured frequencies. However, these two-dimensional analyses also reveal that these modes exhibit distinctive periodic variations in the acoustic pressure field across the width of the fluid chamber. Such variations lead to lateral radiation forces forming particle bands (striations) and are indicative of enclosure modes. The striation spacings predicted by the FEA simulations for several modes compare well with those measured experimentally for the ultrasonic particle separator device. It is also shown that device geometry and materials control enclosure modes and therefore the strength and characteristics of lateral radiation forces, suggesting the potential use of FEA in designing for the control of enclosure modes in similar particle manipulator devices.  相似文献   

6.
Casein solutions with different pH values were sonicated at a frequency of 35 kHz and increasing acoustic powers. As the sonication power increased, turbidity of solutions and particle diameter decreased at any given pH value, suggesting particles disruption due to the ultrasonic treatment. The magnitude of decrease in re-assembled micelles diameter was greater at a higher pH, indicating an interaction between pH and sonication power in sonodissociation. This interaction is attributed to a looser structure of micelles at higher pH values which increases the efficiency of ultrasonic disruption and not directly to the increased cavitation efficiency. We argue that increased cavitation efficiency with increasing sonication power, which enhances shear forces is the most likely reason for sonodisruption of re-assembled casein micelles.  相似文献   

7.
The velocity of micro-particles in a nonuniform electric field was examined as a function of electrical potential and particle size to illustrate the possible application of dielectrophoresis (DEP) as a new separation technique in viscous media. A new comprehensive model is presented that combines the effects of DEP and electrohydrodynamic forces on particle motion. The current model simulation takes into account the possible significant influence of electrohydrodynamic effects depending on the particle size, electrode distance, and voltage applied during DEP particle separation. The heat generated as a consequence of high electric field strength leads to density gradients in the liquid, thus inducing buoyancy forces that cause fluid convective motion.Experimental velocity measurements using two materials having extreme properties, i.e. polyethylene (PE) particles (diameter range 100–2000 μm) and water droplets (diameter range 25–275 μm), both suspended in a viscous medium (silicone oil), correspond with the proposed theoretical predictions. The comprehensive model presented was applied to insulator-based DEP in a direct current (dc) electric field, but it is expected to allow predictions of various similar systems.  相似文献   

8.
In this paper the acoustic forces on particles and agglomerates caused by high-intensity ultrasound in gaseous atmosphere are derived by means of computational fluid dynamics (CFD). Sound induced forces cause an oscillating stress scenario where the primary particles of an agglomerate are alternatingly pressed together and torn apart with the frequency of the applied wave. A comparison of the calculated acoustic forces with respect to the inter particle adhesion forces from Van-der-Waals and liquid bridge interactions reveals that the separation forces may reach the same order of magnitude for 80 μm sized SiO2-particles. Hence, with finite probability acoustically agitated gases may de-agglomerate/disperse solid agglomerate structures. This effect is confirmed by dispersion experiments in an acoustic particle levitation setup.  相似文献   

9.
《Ultrasonics sonochemistry》2014,21(5):1839-1848
The enhancement of release of oak-related compounds from oak chips during wine aging with oak chips may interest the winemaking industry. In this study, the 25-kHz ultrasound waves were used to intensify the mass transfer of phenolics from oak chips into a model wine. The influences of acoustic energy density (6.3–25.8 W/L) and temperature (15–25 °C) on the release kinetics of total phenolics were investigated systematically. The results exhibited that the total phenolic yield released was not affected by acoustic energy density significantly whereas it increased with the increase of temperature during sonication. Furthermore, to describe the mechanism of mass transfer of phenolics in model wine under ultrasonic field, the release kinetics of total phenolics was simulated by both a second-order kinetic model and a diffusion model. The modeling results revealed that the equilibrium concentration of total phenolics in model wine, the initial release rate and effective diffusivity of total phenolics generally increased with acoustic energy density and temperature. In addition, temperature had a negative effect on the second-order release rate constant whereas acoustic energy density had an opposite effect.  相似文献   

10.
Objective and motivationThe method for measuring derived acoustic power of an ultrasound point source in the form of a sonotrode tip has been considered in the free acoustic field, according to the IEC 61847 standard. The main objective of this work is measuring averaged pressure magnitude spatial distribution of an sonotrode tip in the free acoustic field conditions at different electrical excitation levels and calculation of the derived acoustic power at excitation frequency (f0  25 kHz). Finding the derived acoustic power of an ultrasonic surgical device in the strong cavitation regime of working, even in the considered laboratory conditions (anechoic pool), will enable better understanding of the biological effects on the tissue produced during operation with the considered device.Experimental methodThe pressure magnitude spatial distribution is measured using B&;K 8103 hydrophone connected with a B&;K 2626 conditioning amplifier, digital storage oscilloscope LeCroy Waverunner 474, where pressure waveforms in the field points are recorded. Using MATLAB with DSP processing toolbox, averaged power spectrum density of recorded pressure signals in different field positions is calculated. The measured pressure magnitude spatial distributions are fitted with the appropriate theoretical models.Theoretical approachesIn the linear operating mode, using the acoustic reciprocity principle, the sonotrode tip is theoretically described as radially oscillating sphere (ROS) and transversely oscillating sphere (TOS) in the vicinity of pressure release boundary. The measured pressure magnitude spatial distribution is fitted with theoretical curves, describing the pressure field of the considered theoretical models. The velocity and displacement magnitudes with derived acoustic power of equivalent theoretical sources are found, and the electroacoustic efficiency factor is calculated. When the transmitter is excited at higher electrical power levels, the displacement magnitude of sonotrode tip is increased, and nonlinear behaviour in loading medium appears, with strong cavitation activity produced hydrodynamically. The presence of harmonics, subharmonics and ultraharmonics as a consequence of stable cavitation is evident in the averaged power spectral density. The cavitation noise with continuous frequency components is present as a consequence of transient cavitation. The averaged pressure magnitude at the frequency components of interest (discrete and continous) in the field points is found by calculating average power spectral density of the recorded pressure waveform signal using the welch method. The frequency band of interest where average power spectral density is calculated is in the range from 15 Hz up to 120 kHz due to measurement system restrictions. The novelty in the approach is the application of the acoustic reciprocity principle on the nonlinear system (sonotrode tip and bubble cloud) to find neccessary acoustic power of the equivalent acoustic source to produce the measured pressure magnitude in the field points at the frequency components of interest.ResultsIn the nonlinear operating mode, the ROS model for the considered sonotrode tip is chosen due to the better agreement between measurement results and theoretical considerations. At higher excitation levels, it is shown that the averaged pressure magnitude spatial distribution of discrete frequency components, produced due to stable cavitation, can be fitted in the far field with the inverse distance law. The reduced electroacoustic efficiency factor, calculated at excitation frequency component as ratio of derived acoustic power with applied electrical power, is reduced from 40% in the linear to 3% in the strong nonlinear operating mode. The derived acoustic power at other frequency components (subharmonic, harmonic and ultraharmonic) is negligible in comparison with the derived acoustic power at excitation frequency.Discussion and conclusionsThe sonotrode tip and loading medium are shown in the strong cavitation regime as the coupled nonlinear dynamical system radiating acoustic power at frequency components appearing in the spectrum. The bubble cloud in the strong nonlinear operating mode decreases the derived acoustic power significantly at the excitation frequency.  相似文献   

11.
Simulation of hydrodynamics in ultrasonic batch reactor containing immobilized enzymes as catalyst is done. A transducer with variable power and constant frequency (24 kHz) is taken as source of ultrasound (US). Simulation comprises two steps. In first step, acoustic pressure field is simulated and in second step effect of this field on particle trajectories is simulated. Simulation results are compared with experimentally determined particle trajectories using PIV Lab (particle image velocimetry). Effect of varying ultrasonic power, positioning and number of ultrasonic sources on particle trajectories is studied. It is observed that catalyst particles tend to orientate according to pattern of acoustic pressure field. An increase in ultrasonic power increases particle velocity and also brings more particles into motion. Simulation results are found to be in agreement with experimentally determined data.  相似文献   

12.
The use of ultrasonic acoustic technology to measure the concentration of fine suspended sediments has the potential to greatly increase the temporal and spatial resolution of sediment measurements while reducing the need for personnel to be present at gauging stations during storm events. The conversion of high-frequency attenuation and backscatter amplitudes to suspended silt and clay concentration has received relatively little attention in the literature. In order to improve the state of knowledge, a laboratory investigation was undertaken by the National Center for Physical Acoustics in cooperation with the USDA-ARS National Sedimentation Laboratory. In these experiments, two immersion transducers were used to measure attenuation and backscatter from 20 MHz acoustic signals propagated through suspended clay (smectite and kaolinite) and silt particles. The resulting data includes attenuation values for a wide range of concentrations (0.3–14 g/L) and particle sizes (0.03–14 μm diameter). Attenuation curves for each particle were compared to the theoretical attenuation curves developed by Urick (1948) and Sheng and Hay (1988) for scattering as presented by Landers (2010) [5,11,12]. In addition, it was found that the backscatter signal could be used to discriminate between suspensions dominated by clay or silt.  相似文献   

13.
Lead zirconate titanate (Pb(Zr0.52Ti0.48)O3) (PZT) nano-powder with a perovskite structure was fabricated using sol–gel process. The average crystallite diameter of the PZT powder is calculated to be 23.6 nm and the average agglomerate size is about 200 nm. The 0–3 cement based nano-PZT composites were obtained by pressing the mixture of white cement and the nano-PZT powders under a high pressure followed by steam curing. The properties of the nano-PZT/cement piezoelectric composites have been measured and compared to the PZT/cement composites incorporated with ground coarse PZT particles. The enhanced piezoelectricity of the nano-PZT/cement composites can be attributed to the good connectivity between the nano-PZT particles among the cement matrix.  相似文献   

14.
We present detailed measurements of field—and temperature—dependence of magnetization in nanocrystalline YIG (Y3Fe5O12) particles. The fine powders were prepared using sol–gel method. Samples with particle sizes ranging from 45 to 450 nm were obtained. We observe that the saturation magnetization decreases as the particle size is reduced due to enhancement of the surface spin effects. Below a critical diameter Ds≅190 nm, the particles become single domains and the coercive forces reaches a maximum at diameters close to the critical value. As the particle size decreases the coercivity diminishes and at Dp≃35 nm diameters the upper limit of superparamagnetic behavior is reached. A quantitative comparison of temperature and particle size dependence of coercivity shows a satisfactory agreement that is expected for an assembly of randomly oriented particles.  相似文献   

15.
The electrostatic precipitator (ESP) has been extensively used for collecting aerosol particles emitted from coal combustion, but its collection efficiency of PM2.5 (Particulate matter whose aerodynamic diameter is less than 2.5 μm) is relatively low due to insufficient particle charging. The positive pulsed ESP is considered to enhance particle charging and improve collection efficiency. A laboratory-scale pulsed ESP with wire-plate electrode configuration was established to investigate the particle charging and penetration efficiency under controlled operating conditions of different applied impulse peak voltages, impulse frequencies, dust loadings and residence times. The results show that most particles larger than 0.2 μm are negatively charged, while most particles smaller than 0.2 μm are positively charged. For a given operating condition, the particle penetration efficiency curve has the highest penetration efficiency for particles with a diameter near 0.2 μm, and there is always a negative correlation between the particle penetration efficiency and the average number of charges per particle. Under the same operating conditions, the particle penetration efficiency decreases with increasing impulse peak voltage and impulse frequency, but increases as the dust loading increases. The results imply that residence time of 4 s is optimum for particle charging and collection. PM2.5 number reduction exceeding 90% was achieved in our pulsed ESP.  相似文献   

16.
Megasonic cleaning as applied in leading edge semiconductor device manufacturing strongly relies on the phenomenon of acoustic cavitation. As the occurrence of acoustic cavitation is incorporating a multitude of interdependent effects, the amount of cavitation activity in the cleaning liquid strongly depends on the sonication conditions. It is shown that cavitation activity as measured by means of ultraharmonic cavitation noise can be significantly enhanced when pulsed sonication is applied to a gas supersaturated liquid under traveling wave conditions. It is demonstrated that this enhancement coincides with a dramatic increase in particle removal and is therefore of great interest for megasonic cleaning applications. It is demonstrated that the optimal pulse parameters are determined by the dissolution time of the active bubbles, whereas the amount of cavitation activity depends on the ratio between pulse-off and pulse-on time as well as the applied acoustic power. The optimal pulse-off time is independent of the corresponding pulse-on time but increases significantly with increasing gas concentration. We show that on the other hand, supersaturation is needed to enable acoustic cavitation at aforementioned conditions, but has to be kept below values, for which active bubbles cannot dissolve anymore and are therefore lost during subsequent pulses. For the applicable range of gas contents between 100% and 130% saturation, the optimal pulse-off time reaches values between 150 and 340 ms, respectively. Full particle removal of 78 nm-diameter silica particles at a power density of 0.67 W/cm2 is obtained for the optimal pulse-off times. The optimal pulse-off time values are derived from the dissolution time of bubbles with a radius of 3.3 μm and verified experimentally. The bubble radius used in the calculations corresponds to the linear resonance size in a 928 kHz sound field, which demonstrates that the recycling of active bubbles is the main enhancement mechanism. The optimal choice of the pulsing conditions however is constrained by the trade-off between the effective sonication time and the desire to have a sufficient amount of active bubbles at lower powers, which might be necessary if very delicate structures have to be cleaned.  相似文献   

17.
Water removal is an essential step during crude oil production due to several problems such as increased transportation costs and high corrosion rate due to dissolved salts. Indirect low frequency ultrasonic energy (US), using baths, has been recently proposed as an effective alternative for crude oil demulsification. However, the reactor position during sonication and its influence on the demulsification efficiency for crude oil has not been evaluated. In this sense, the aim of this study was to develop an automated system based on an open source hardware for mapping the acoustic field distribution in an US bath operating at 35 kHz using a hydrophone. Data acquired with this system provided information to evaluate the demulsification efficiency in the different positions of the US bath and correlate it with the acoustic intensity distribution. The automated 3D-mapping system revealed a higher acoustic intensity in the regions immediately above the transducers (ca. 0.6 W cm−2), while the other regions presented a relatively lower intensity (ca. 0.1 W cm−2). Experimental data demonstrated that reactors positioned in the most intense acoustic regions provided a much higher efficiency of demulsification in comparison with the ones positioned in the less intense acoustic field regions. Demulsification efficiency up to 93% was obtained with 15 min of sonication (100% amplitude) using few amount of chemical demulsifier. Hence, this work demonstrated that the information acquired with the developed mapping system could be used for inducing a higher efficiency of demulsification only by finding the more suitable position of reactor in the US bath, which certainly will help development of appropriate reactors design when looking for such approach.  相似文献   

18.
《Ultrasonics》2013,53(1):70-76
We propose a technique based on pulsed ultrasounds for controlling, reducing to a minimum observable value the acoustic streaming in closed ultrasonic standing wave fluidic resonators. By modifying the number of pulses and the repetition time it is possible to reduce the velocity of the acoustic streaming with respect to the velocity generated by the continuous ultrasound mode of operation. The acoustic streaming is observed at the nodal plane where a suspension of 800 nm latex particles was focused by primary radiation force. A mixture of 800 nm and 15 μm latex particles has been also used for showing that the acoustic streaming is hardly reduced while primary and secondary forces continue to operate. The parameter we call “pulse mode factor” i.e. the time of applied ultrasound divided by the duty cycle, is found to be the adequate parameter that controls the acoustic streaming. We demonstrate that pulsed ultrasound is more efficient for controlling the acoustic streaming than the variation of the amplitude of the standing waves.  相似文献   

19.
We are investigating means of handling microparticles in microfluidic systems, in particular localized acoustic trapping of microparticles in a flow-through device. Standing ultrasonic waves were generated across a microfluidic channel by ultrasonic microtransducers integrated in one of the channel walls. Particles in a fluid passing a transducer were drawn to pressure minima in the acoustic field, thereby being trapped and confined at the lateral position of the transducer. The spatial distribution of trapped particles was evaluated and compared with calculated acoustic intensity distributions. The particle trapping was found to be strongly affected by near field pressure variations due to diffraction effects associated with the finite sized transducer element. Since laterally confining radiation forces are proportional to gradients in the acoustic energy density, these near field pressure variations may be used to get strong trapping forces, thus increasing the lateral trapping efficiency of the device. In the experiments, particles were successfully trapped in linear fluid flow rates up to 1mm/s. It is anticipated that acoustic trapping using integrated transducers can be exploited in miniaturised total chemical analysis systems (microTAS), where e.g. microbeads with immobilised antibodies can be trapped in arrays and subjected to minute amounts of sample followed by a reaction, detected using fluorescence.  相似文献   

20.
Over the past decade or so the health problems associated with the inhalation of sub micron particles from industrial processes has taken prominence and has lead to the stricter emission legislation, such as the US PM 2.5 approach. Generally most forms of control equipment readily handle and collect particles greater than 1 micron diameter, however, those less than 1 micron diameter are very much more difficult to collect.In the case of electrostatic precipitation, which involves both particle charging and migration under the influence of an electric field, the larger particles, generally greater than 1 micron are charged by collision with the ions and electrons present in the inter electrode area. It will be shown that the charge on these particles is proportional to the radius squared and its migration velocity proportional to the voltage squared, both reducing with particle size. The very small particles however, are charged by a diffusion processes and migrate under the influence of Brownian motion, which increases as the particle size decreases. The result of this is that a typical particle size/efficiency curve indicates a significant penetration window in the 0.8–0.2 micron diameter range, which coincides with the change from collision to diffusion charging of the particles.Because of this penetration window, should an existing precipitator operating under optimum electrical conditions, not comply with fine particle emission requirements, the conventional performance enhancement scenario, since the charging and precipitation operating conditions have been already optimised, would be to increase the precipitator's plate area, a very expensive solution. It will be shown, however, that the replacement of the conventional mains energisation system by an SMPS approach in an existing ESP will enhance the collection efficiency of particles, particularly in the penetration window, as a result of the increase in both operating field voltages and currents.The SMPS approach was applied to a 2 field ESP dealing predominately with sub micron fume, which the Client wished to enhance the performance to enable higher recycle rates, while still complying with his emission permitting. This was initially assessed using PALCPE? (Proactive Approach to Low-Cost Precipitator Enhancement), which indicated a significant reduction in the fine particle emissions was achievable by operation under SMPS Operation. An SMPS unit was subsequently fitted to the outlet field of this precipitator and the operating data will be examined in detail. With the outlet field under a mains rectification energisation system the overall emission was ~25 mg/Nm3, which after installation of the SMPS unit reduced to less than 15 mg/Nm3.  相似文献   

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