CN111551470A - Semi-online equipment and method for measuring acid particles in atmosphere - Google Patents
Semi-online equipment and method for measuring acid particles in atmosphere Download PDFInfo
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Abstract
The invention provides a semi-online device for measuring acid particles in the atmosphere, which comprises: a diffusion sampler and a quartz crystal microbalance; the sensor of the quartz crystal microbalance is arranged in the diffusion sampler; the surface of the sensor of the quartz crystal microbalance is covered with a metal film. Compared with the prior art, the equipment provided by the invention mainly comprises a diffusion sampler and a quartz crystal microbalance, wherein an atmospheric sample is collected by the diffusion sampler at a lower flow rate, acid particles fall on a metal film on the surface of the sensor through deposition and react with the metal film, and the quality of the acid particles can be obtained by removing unreacted particles, so that the content of the acid particles in the atmosphere can be obtained.
Description
This application claims priority from U.S. patent application filed on 10.2.2019, entitled "Semi-online Equipment and Method for measuring of Acidic ultrafine particles in The Atmosphere," by The United states patent office, application number 62/909263, The entire contents of which are incorporated herein by reference.
Technical Field
The invention belongs to the technical field of air detection, and particularly relates to semi-online equipment and a method for measuring acidic ions in the atmosphere.
Background
Since particulate matters in the atmosphere are closely related to the health of the human respiratory system and cause a series of environmental problems such as reduced visibility of air, destruction of ecological environment, global climate change and the like, atmospheric particulate pollution has attracted extensive attention of global governments and the public.
Over the past few decades, much research has focused on mass concentration studies of airborne particulate matter having particle sizes of less than 10 μm (PM10) and less than 2.5 μm (PM 2.5). Recently, more and more research has found that many smaller particles in the air, such as ultra-fine particles (UFPs) with a diameter of less than 100nm, have a more serious adverse effect on human health than PM2.5 and PM 10. Because they usually contain trace elements or toxins and because these particles have a high diffusion coefficient, they can penetrate deep into the pulmonary alveoli of humans, even into the blood system. Meanwhile, the particle size of the particles is potentially harmful to human health. In addition, it was found by measuring the amount concentration of particulate matter in the atmosphere that more than 90% of the particles in the air including indoor and outdoor were ultrafine particles. Therefore, people living in the air rich in these UFPs will increase the risk of suffering from diseases of heart, brain, and lung functions.
Although increasing epidemiological data indicate a correlation between the environmental ultrafine particles and the deterioration of health conditions (such as mortality and morbidity), it is not said that all components in the ultrafine particles are harmful to the human body. There is evidence that the number concentration of acid-containing ultrafine particles (AUFPs) is closely related to total mortality, morbidity, and hospitalization for respiratory diseases. In addition, acidic particulate contamination can have environmental effects including reduced air visibility, environmental damage, and climate change. Therefore, differentiating the number of AUFPs from the total number of UFPs, quantifying the number spectrum distribution of AUFPs in the air becomes very important, and can provide useful data for studying air quality, epidemiology and policy making.
Initially, the measurement of acidic particles was performed by collecting the particles on a metal coated substrate and scanning and counting under an electron microscope, however, this preliminary method does not allow accurate measurement of the number, concentration and size distribution of acidic particles, especially nanoparticles; later, the use of mobile acidic particles with diffusion sampler and scanning under Atomic Force Microscope (AFM) were developed, but the disadvantages of low time resolution, labor intensity and expensive equipment still exist.
Disclosure of Invention
In view of the above, the technical problem to be solved by the present invention is to provide a semi-online apparatus and method for measuring acidic ions in the atmosphere with high time resolution.
The invention provides a semi-online device for measuring acid particles in the atmosphere, which comprises:
a diffusion sampler and a quartz crystal microbalance; the sensor of the quartz crystal microbalance is arranged in the diffusion sampler; the surface of the sensor of the quartz crystal microbalance is covered with a metal film.
Preferably, the diffusion sampler comprises a gas inlet, a gas channel and a gas outlet which are communicated in sequence; a groove is arranged at the bottom of the gas channel, which is vertical to the gas flowing direction; the sensor of the quartz crystal microbalance is arranged in the groove.
Preferably, the number of the grooves is 2-5; and a sensor is arranged in each groove.
Preferably, the diffusion sampler further comprises a filtering device; the gas inlet is communicated with the gas channel through a filtering device.
Preferably, the device further comprises a drying device; the drying device comprises a gas inlet and a gas outlet; a drying agent is arranged in the drying device; and the gas outlet of the drying device is communicated with the gas inlet of the diffusion sampler.
Preferably, the metal film is an iron film; the thickness of the metal film is 20-30 nm.
The invention also provides a method for measuring acid particles in the atmosphere, which comprises the following steps:
using the semi-online device for measuring acidic ions in the atmosphere as claimed in any one of claims 1 to 6;
introducing atmosphere containing acidic particles into the diffusion sampler, reacting the acidic particles with the metal film on the surface of the sensor to form reaction points, and recording the frequency of the sensor by the quartz crystal microbalance to obtain the mass m1；
Taking out the sensor forming the reaction point, standing in protective atmosphere, and then carrying out ultrasonic treatment in an organic solvent to remove non-acidic particles;
the ultrasonic sensor is put back into the equipment, and the mass m is obtained by a quartz crystal microbalance2；
Passing mass m1And m2The mass concentration of the acid particles in the atmosphere is obtained.
Preferably, the time of standing in the protective atmosphere is not less than 20 h.
Preferably, the organic solvent is an alcohol solvent; the power of ultrasonic treatment is 20-60 kHz; the ultrasonic treatment time is 20-40 min.
Preferably, the number concentration of the acid particles in the atmosphere is obtained by the mass concentration of the acid particles in the atmosphere according to formula 1 and formula 2:
ni＝mi/(4/3×π×ri 3× ρ) formula 1
Cn＝(∑ni/ηi) /(Q × T) formula 2
Wherein n isiThe total number of the acid particles measured in the particle size range i; rho is the density of acid particles in the atmosphere; r isiIs the average radius of the acid particles in the particle size range i; cnThe measured number concentration of the acidic particles; m isiη being the total mass of the acid particles measured in the particle size range iiIs acidic in the particle size range iThe collection efficiency of the particles in the measurement; q is the sampling flow; t is the sampling time.
The invention provides a semi-online device for measuring acid particles in the atmosphere, which comprises: a diffusion sampler and a quartz crystal microbalance; the sensor of the quartz crystal microbalance is arranged in the diffusion sampler; the surface of the sensor of the quartz crystal microbalance is covered with a metal film. Compared with the prior art, the equipment provided by the invention mainly comprises a diffusion sampler and a quartz crystal microbalance, wherein an atmospheric sample is collected by the diffusion sampler at a lower flow rate, acid particles fall on a metal film on the surface of the sensor through deposition and react with the metal film, and the quality of the acid particles can be obtained by removing unreacted particles, so that the content of the acid particles in the atmosphere can be obtained.
Drawings
FIG. 1 is a schematic cross-sectional view of a semi-online apparatus for measuring acid particles in the atmosphere according to the present invention;
FIG. 2 is a schematic longitudinal sectional view of a semi-online apparatus for measuring acid particles in the atmosphere according to the present invention;
FIG. 3 is a schematic diagram of the method A of FIG. 2;
fig. 4 is a graph showing the variation of the total ultrafine particle number concentration between 11 days 4 and 11 days 2019 and 15 days 4 and 15 months 2019 obtained by the measurement method of example 1 and a scanning mobility particle size spectrometer.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The invention provides a semi-online device for measuring acid particles in the atmosphere, which comprises: a diffusion sampler and a quartz crystal microbalance; the sensor of the quartz crystal microbalance is arranged in the diffusion sampler; the surface of the sensor of the quartz crystal microbalance is covered with a metal film.
Referring to fig. 1, fig. 2 and fig. 3, fig. 1 is a schematic cross-sectional view of a semi-online apparatus for measuring acid particles in the atmosphere according to the present invention; FIG. 2 is a schematic longitudinal sectional view of a semi-online apparatus for measuring acid particles in the atmosphere according to the present invention; FIG. 3 is an enlarged view of A in FIG. 2; wherein 1 is filter equipment, 2 is the sealing washer, 3 is the sensor, 4 is gas channel, 5 is the gas outlet, 6 is the gas inlet, 7 is drying device, 8 is the apron, 9 is the recess, 10 is quartz crystal microbalance.
The semi-online equipment for measuring acid particles in the atmosphere consists of a diffusion sampler and a quartz crystal microbalance; the diffusion sampler collects particles by means of diffusion deposition.
The diffusion sampler comprises a gas inlet, a gas channel and a gas outlet which are communicated in sequence; in the present invention the gas channels are preferably flat rectangular gas channels; the gas channel is obtained by fixing an upper cover plate and a lower cover plate through a fixing device; in order to enhance the air tightness of the gas channel, a sealing ring is preferably arranged at the joint of the cover plate; a groove is arranged at the bottom of the gas channel, which is vertical to the gas flowing direction; the sensor of the quartz crystal microbalance is arranged in the groove; the number of the grooves is preferably 2-5, more preferably 3-4, the grooves are arranged at different positions along the gas flowing direction, and a sensor is arranged in each groove; the surface of the sensor is covered with a metal film; the metal film is a metal film capable of reacting with the acidic particles; the thickness of the metal film is preferably 20-30 nm, more preferably 22-28 nm, and further preferably 25 nm; the metal film is preferably an iron film; the metal film is preferably coated on the surface of the sensor by magnetron sputtering. The sensor is a key part of a quartz crystal microbalance, the sensitivity of the sensor is 0.02ng, and the sensor is used as a substrate coated with a metal thin film to collect acid particles and realize the measurement of the weight of the particles.
According to the invention, said diffusion sampler preferably further comprises filtering means; the gas inlet is communicated with the gas channel through a filtering device; the particle size of particles entering the gas can be controlled through the filtering device, so that the content of particles with different particle sizes in the gas can be measured; the transition device is preferably a differential mobility analyzer.
According to the present invention, it is preferable to further include a drying device; the drying device comprises a gas inlet and a gas outlet; the gas outlet of the drying device is communicated with the gas inlet of the diffusion sampler; a drying agent is arranged in the drying device; the desiccant is preferably silica gel; the drying device can be used for degassing moisture in the gas so as to avoid the influence of the moisture on the measurement result.
According to the invention, it is preferred to further include a pump; the pump is communicated with the diffusion sampler, and the speed of collecting gas by the diffusion sampler is controlled by the pump.
The equipment provided by the invention mainly comprises a diffusion sampler and a quartz crystal microbalance, wherein an atmospheric sample is collected by the diffusion sampler at a low flow rate, acid particles fall on a metal film on the surface of a sensor through deposition and react with the metal film, and the mass of the acid particles can be obtained by removing unreacted particles, so that the content of the acid particles in the atmosphere can be obtained.
The invention also provides a method for measuring acidic particles in the atmosphere by using the semi-online equipment, which comprises the following steps: using the semi-online equipment for measuring acid ions in the atmosphere; introducing atmosphere containing acidic particles into the diffusion sampler, reacting the acidic particles with the metal film on the surface of the sensor to form reaction points, and recording the frequency of the sensor by the quartz crystal microbalance to obtain the mass m1(ii) a Taking out the sensor forming the reaction point, standing in protective atmosphere, and then carrying out ultrasonic treatment in an organic solvent to remove non-acidic particles; will be ultrasonicThe processed sensor is put back into the apparatus and the mass m is obtained by means of a quartz crystal microbalance2(ii) a Passing mass m1And m2The mass concentration of the acid particles in the atmosphere is obtained.
The atmospheric air containing the acidic particles is passed into the diffusion sampler, preferably by being pumped into the diffusion sampler; the flow rate of the sucked atmosphere is preferably 0.05-0.2L/min; in the gas channel, the acid particles react with the metal film on the surface of the sensor to form reaction points; simultaneously, the quartz crystal microbalance records the frequency of the sensor, the frequency change of the sensor corresponds to the mass of ions deposited on the sensor, and the mass m can be obtained1The mass includes acidic particles and non-acidic particles.
Taking out the sensor forming the reaction point, preferably taking out the sensor after the frequency of the sensor recorded by a quartz crystal microbalance is stable and unchanged, and standing in a protective atmosphere to enable the acidic particles to be tightly combined with the metal film; the protective atmosphere is not particularly limited as long as it is known to those skilled in the art, and nitrogen and/or argon is preferable in the present invention; the time for the standing is preferably 20 hours or more, more preferably 24 hours or more.
Standing, and performing ultrasonic treatment in an organic solvent to remove non-acidic particles; the organic solvent is preferably an alcohol solvent, and is more preferably ethanol; the power of ultrasonic treatment is preferably 20-60 kHz, more preferably 30-50 kHz, and further preferably 40 kHz; the time of ultrasonic treatment is preferably 20-40 min, and more preferably 30 min.
The ultrasonic sensor is put back into the equipment, and the mass m is obtained by a quartz crystal microbalance2The mass is the mass of the acid particles; passing mass m1And m2The mass concentration of the acid particles in the atmosphere is obtained, preferably by mass m1And m2The mass of the acid particles falling on the sensor in the atmosphere is obtained, and then the mass concentration of the acid particles in the atmosphere can be converted by combining the collection efficiency, the sampling time and the sampling flow of the sampler; according to the invention, the particle size and density of the acid particles can be further used to obtain the atmosphereThe number concentration of the acid particles, preferably the acid particles are assumed to be spherical, and the number concentration of the acid particles in the atmosphere is obtained by the mass concentration of the acid particles in the atmosphere according to the following formula 1 and formula 2:
ni＝mi/(4/3×π×ri 3× ρ) formula 1
Cn＝(∑ni/ηi) /(Q × T) formula 2
Wherein n isiThe total number of the acid particles measured in the particle size range i; rho is the density of acid particles in the atmosphere; r isiIs the average radius of the acid particles in the particle size range i; cnThe measured number concentration of the acidic particles; m isiη being the total mass of the acid particles measured in the particle size range iiThe collection efficiency of the acid particles in the particle size range i in the measurement is shown; q is the sampling flow; t is the sampling time.
The collection efficiency of the particles with different particle sizes in the diffusion sampler is preferably corrected and determined before atmospheric sampling, so that the collection efficiency of the particles with different particle sizes under different sampling flow conditions is obtained.
According to the method, the sensor of the quartz crystal microbalance is used as a substrate coated with a metal film to collect acidic particles, non-acidic particles are removed through ultrasonic treatment, frequency changes of the sensor before and after the non-acidic particles are removed are recorded by the quartz crystal microbalance, so that the proportion of the non-acidic particles to the total particles is obtained through the ratio of the frequency changes to the total frequency changes obtained in the sampling period, and the concentration of the acidic particles is obtained through conversion.
In order to further illustrate the present invention, the following will describe the semi-online apparatus and method for measuring acidic ions in the atmosphere in detail with reference to the following embodiments.
The reagents used in the following examples are all commercially available.
Example 1
The semi-online equipment used for measurement comprises a diffusion sampler, three sets of quartz crystal microbalances and a drying device (silica gel is arranged in the drying device), wherein a gas outlet of the drying device is communicated with a gas inlet of the diffusion sampler, and the gas inlet of the diffusion sampler is communicated with a gas channel through a filtering device (a micro powder mobility analyzer for selectively screening particles of 5-350 nm); the gas channel is a flat and prolate rectangular channel (with the height of 1.0mm, the width of 50mm and the length of 500mm), three grooves are formed in the bottom of the gas channel along the gas flowing direction, and sensors of the quartz crystal microbalance are arranged in the grooves (from the inlet direction to the outlet direction, the sensors are a sampling point A, a sampling point B and a sampling point C in sequence); the surface of the sensor is covered with an iron film of about 25 nm.
The detection is carried out according to the following method:
sucking the atmosphere containing the acidic particles into a diffusion sampler by a pump (the sampling flow is 0.1L/min, the sampling time is 44 hours), reacting the acidic particles with a metal film on the surface of the sensor to form reaction points, and simultaneously recording the frequency of the sensor by a quartz crystal microbalance;
taking out the sensor forming the reaction point, standing in nitrogen, and then carrying out ultrasonic treatment with power of 40kHz in absolute ethyl alcohol for 30min to remove non-acidic particles;
putting the sensor subjected to ultrasonic treatment back into the equipment, and obtaining the mass through a quartz crystal microbalance;
assuming the acid particles as spheres, obtaining the number concentration of the acid particles in the atmosphere according to the formula 1 and the formula 2 by the mass concentration of the acid particles in the atmosphere:
ni＝mi/(4/3×π×ri 3× ρ) formula 1
Cn＝(∑ni/ηi) /(Q × T) formula 2
Wherein n isiThe total number of the acid particles measured in the particle size range i; rho is the density of acid particles in the atmosphere; r isiIs the average radius of the acid particles in the particle size range i; cnThe measured number concentration of the acidic particles; m isiη being the total mass of the acid particles measured in the particle size range iiThe collection efficiency of the acid particles in the particle size range i in the measurement is shown; q is the sampling flow; t is the sampling time.
The sampler is respectively placed in a Z-seat top-building atmospheric laboratory of the university of hong Kong tally and a roadside sampling station of the university of hong Kong tally for atmospheric sampling in 2019 at 4 months and 6 months.
To test the accuracy of the system, a Scanning Mobility Particle Spectrometer (SMPS) and a validated Diffusion Sampler + atomic force microscopy method (Wang DW, Guo H and Chan CK,2014. Difusion Sampler for measurement of Acidic Ultrafine Particles in the Atmosphere, Aerosol sciences and Technology 48:12,1236 1246) were also applied to the two samplings. The scanning electric mobility particle size spectrometer is a mature commercial instrument, can detect the number concentration of different particle size superfine particles (5-350 nm) in the atmosphere in real time, and has the highest time resolution of 4 minutes. The method can only measure the concentration of the total ultrafine particles but cannot obtain the concentration of the acidic ultrafine particles. The diffusion sampler + atomic force microscopy method is a method for measuring acidic particulate matter in the atmosphere developed by the present subject matter group in 2014. The silicon slice coated with the iron film is placed in a diffusion sampler for collecting particles, and the collected sample quantifies the quantity of the total collected particles and the quantity of the acidic particles with the help of an atomic force microscope. The concentrations of the ultrafine particulate matter and acidic ultrafine particulate matter in the atmosphere were thus confirmed in consideration of the collection efficiency, the sampling time, and the number of particulate matter per unit scanning area.
For the acidic particulate matter measurer of the present invention, the sensor wafer coated with an iron film having a thickness of about 25nm is first placed in a sampler, and the resulting real-time frequency change is converted into a mass change after two consecutive samplings. Then, after the sensor wafer is placed in an inert gas environment for more than one day, the acidic particles can fully react with the iron film to generate reaction sites. The surface non-acidic particles are removed and the acidic particles remain on the wafer surface by using absolute ethanol to perform ultrasonic treatment at 40kHz for half an hour. Meanwhile, the frequency change of the sensor before and after the non-acidic particulate matters are removed can be recorded, so that the proportion of the non-acidic particulate matters in the total particulate matters is obtained through the ratio of the frequency change to the total frequency change obtained in the sampling period, and the concentration of the acidic particulate matters is obtained through conversion.
The particulate matters with different particle sizes have different collection efficiencies at different collection positions of the sampler. As an example, the collection efficiency of the particles at sample points A, 50nm,100nm and 200nm was about 3.5%, 2.8% and 2.3%, respectively. The collection efficiency of the particles at sample points B, 50nm,100nm and 200nm was about 5.8%, 4.8% and 2.2%, respectively. The present invention takes the average value thereof as the calculation result. The data obtained using the present invention are illustrated at 11/4 th to 13/4 th day, and are detailed in table 1. The particles of 5nm to 150nm were divided into 6 particle size ranges, and the total frequency change during sampling was obtained for each particle size range. The frequency variation and the mass of the particles falling on the sensor follow the formula Δ f-k · Δ m, which is mentioned in the text of the present invention. Also, in order to convert the mass of the particulate matter into the amount of the particulate matter, the present invention assumes that the density of the particulate matter is 2g/cm3。
TABLE 1 calculation example of the concentrations of acidic and total particulate matter measured at 11-13 days 4 months using the present invention
Tables 2 and 3 show the results of the two samplings. The result shows that the concentration of the ultrafine particles measured by the measurer is similar to the result measured by using a diffusion sampler and an atomic force microscope method, and the concentration of the ultrafine particles measured by the measurer is slightly higher than the result measured by using a scanning mobility particle size spectrometer. The concentration of the measured ultrafine acidic particles is slightly higher than that of the measured ultrafine acidic particles by using a diffusion sampler and an atomic force microscope method. The results obtained by the method can be regarded as accurate and reliable in consideration of the principle difference and experimental error among the methods.
TABLE 2 number concentration and Mass concentration of acidic particles and total particles in the atmosphere in the existing method in the range of 5.5 nm to 150nm
Table 3 example 1 the number and mass concentrations of acidic particles and total particles in the atmosphere ranged from 5.5 nm to 150nm
Furthermore, to further embody the accuracy of the present invention and to embody the present invention with higher time resolution than the previous method (diffuse sampler + atomic force microscopy), the real-time results of 4 months, 11 days to 4 months, 15 days in 2019 (results at 4 hour intervals) were extracted and compared with the results of a scanning electromigration particle spectrometer (SMPS) (results at 2 hour intervals) (fig. 4). The time change of the total superfine particulate matter number concentration measured by the two methods is similar, and the accuracy of the method is further proved. Compared with the prior method (a diffusion sampler and an atomic force microscope method), the time resolution of the method is greatly improved (the sampling days required for obtaining single data by the forward method are 2-3 days, while the highest time resolution of the method is 2 hours (only two hours), but the 4-hour interval is better for ensuring the data accuracy.
Claims (10)
1. A semi-online apparatus for measuring acid particles in the atmosphere, comprising:
a diffusion sampler and a quartz crystal microbalance; the sensor of the quartz crystal microbalance is arranged in the diffusion sampler; the surface of the sensor of the quartz crystal microbalance is covered with a metal film.
2. The semi-online apparatus of claim 1, wherein the diffusion sampler comprises a gas inlet, a gas channel, and a gas outlet in sequential communication; a groove is arranged at the bottom of the gas channel, which is vertical to the gas flowing direction; the sensor of the quartz crystal microbalance is arranged in the groove.
3. The semi-online device of claim 2, wherein the number of grooves is 2-5; and a sensor is arranged in each groove.
4. The semi-online device of claim 2, wherein the diffusion sampler further comprises a filtering means; the gas inlet is communicated with the gas channel through a filtering device.
5. A semi-online apparatus according to claim 2, further comprising a drying device; the drying device comprises a gas inlet and a gas outlet; a drying agent is arranged in the drying device; and the gas outlet of the drying device is communicated with the gas inlet of the diffusion sampler.
6. The semi-online apparatus of claim 1, wherein the metal thin film is an iron film; the thickness of the metal film is 20-30 nm.
7. A method of measuring acid particles in the atmosphere, comprising:
using the semi-online device for measuring acidic ions in the atmosphere as claimed in any one of claims 1 to 6;
introducing atmosphere containing acidic particles into the diffusion sampler, reacting the acidic particles with the metal film on the surface of the sensor to form reaction points, and recording the frequency of the sensor by the quartz crystal microbalance to obtain the mass m1；
Taking out the sensor forming the reaction point, standing in protective atmosphere, and then carrying out ultrasonic treatment in an organic solvent to remove non-acidic particles;
the ultrasonic sensor is put back into the equipment, and the mass m is obtained by a quartz crystal microbalance2；
Passing mass m1And m2The mass concentration of the acid particles in the atmosphere is obtained.
8. The method according to claim 7, characterized in that the time of standing in the protective atmosphere is 20h or more.
9. The method according to claim 7, wherein the organic solvent is an alcohol solvent; the power of ultrasonic treatment is 20-60 kHz; the ultrasonic treatment time is 20-40 min.
10. The method of claim 7, wherein the number concentration of the acid particles in the atmosphere is obtained by the mass concentration of the acid particles in the atmosphere according to formula 1 and formula 2:
ni＝mi/(4/3×π×ri 3× ρ) formula 1
Cn＝(∑ni/ηi) /(Q × T) formula 2
Wherein n isiThe total number of the acid particles measured in the particle size range i; rho is the density of acid particles in the atmosphere; r isiIs the average radius of the acid particles in the particle size range i; cnThe measured number concentration of the acidic particles; m isiη being the total mass of the acid particles measured in the particle size range iiThe collection efficiency of the acid particles in the particle size range i in the measurement is shown; q is the sampling flow; t is the sampling time.
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