RU2680661C2 - Device for measuring the spectrum of dimensions of aerosol particles and method of measuring the spectrum of dimensions of aerosol particles - Google Patents

Abstract

FIELD: metrology.SUBSTANCE: invention relates to the study of the dispersed characteristics of aerosols of different nature and can be used in meteorology, in nanoproduction, to control nano-safety at workplaces, to determine the inhalation dose when using aerosol forms of drug delivery. Claimed device for measuring the spectrum of the size of aerosol particles, which includes a diffusion battery consisting of a series of consecutive sections filled with grids consisting of, for example, from metal or polymer fibers, on which aerosol particles are deposited during the passage of an aerosol stream through a battery, a condensation enlarger of particles, an optical particle counter and a personal computer for controlling the device as a whole, accumulating and processing the obtained data. According to the invention, the number of installed grids in each section of the diffusion battery, except for the first one, is equal to the total number of grids in all previous sections located upstream, which allows calculating the average particle diameter deposited in each section of the battery as described in the mathematical formula. Method of measuring the size spectrum of aerosol particles is implemented by sequentially passing an aerosol stream through the sections of a diffusion battery filled with nets, then through a condensation enlarger of particles, measurement of aerosol concentration by an optical counter and computer data processing. According to the method, using the measured probabilities of particles passing through the battery sections, the average deposition efficiency on the individual fibers of the mesh for the fractions of particles, that is, for particles deposited in the diffusion battery sections, is determined by the formula given in the description. Next, from the magnitude of the deposition efficiency, the average particle diameter of each fraction is determined by the formulas of the fan model of Kirsch-Stechkin-Fuchs filters, the spectrum of particles of each fraction is approximated by any function of monomodal distribution, including the log-normal distribution, Gaussian distribution, then the spectrum of the original aerosol is defined as the sum of the spectra of the fractions.EFFECT: technical result is to simplify the process of measuring the spectrum of the size of aerosol particles and increase accuracy.2 cl, 3 dwg, 1 tbl

Description

The invention relates to the study of the dispersed characteristics of aerosols of various nature, and can be used in meteorology, in nanotechnology, to control nanosafety in the workplace, to determine the inhalation dose when using aerosol forms of drug delivery and in other areas of human activity.

In recent decades, in various fields of science, technology and other activities, the need for measuring the size spectra of aerosol particles has grown significantly. Such areas include ambient air quality control [1-4], aerosol forms of drug delivery [5, 6], nanotechnology [7], control of aerosol particles in the air of workrooms [8-10], etc.

Aerosol measurements can be divided into two categories. The first category involves sampling followed by laboratory analysis (optical, power, electron microscopy [11-13], impactors [11, 14, 15], etc.). The methods of the second category allow obtaining results in almost real time (light scattering, aerodynamic spectrometers, methods based on diffusion separation and measuring mobility in an electric field [16, 17]).

Among the methods of the second category, differential mobility analyzers are widely used [18]. The weaknesses of this technique are the complexity of use in field measurements, the high price and the need for electric charging of particles. Another well-known method for measuring the size spectrum of aerosol particles, free from the above disadvantages, is separation using a diffusion battery (DB). Diffusion batteries have a simple design and are well suited for use in field measurements [19], in laboratory experiments [20-22] and for monitoring the level of aerosol pollution at workplaces [23, 24]. This method uses the dependence of the deposition coefficient in sections of a diffusion battery on the particle size. Most often, diffusion batteries are made in the form of successive sections filled with a set of capillaries (parallel to the aerosol duct) or a set of flat grids (perpendicular to the flow). As the aerosol stream moves through the battery, particles are deposited on the inner surface of the capillaries or on the surface of the fibers that make up the mesh.

After the publication of works [25, 26], diffusion mesh batteries became the most popular. This type of battery is easy to manufacture and compact. Grids can be easily replaced if necessary. The number of grids in a section progressively increases with the increase of the sequential number i of the section. During battery operation, a counted concentration C _{i of} particles is measured downstream after each section. These concentrations give the probability g _{i of the} passage of particles through the sequence of sections (“breakthroughs”), where g _i is the ratio of the calculated concentration C _i to the concentration C ₀ at the entrance to the diffusion battery. The resulting breakthroughs, in turn, make it possible to calculate the particle spectrum by size. However, the particle deposition functions in the sections are smoothly dependent on size, i.e. size regions in which particles are deposited in different sections overlap with each other. Therefore, in principle, an infinite number of particle size distribution functions can satisfy the same set of breakthroughs. Nevertheless, with the correct processing of the data of experimental measurements of the diffusion battery, it is possible to calculate the function ƒ (D) of the particle distribution over the diameters D close to the real size spectrum. Note that later in this solution we will consider the diameter distribution function normalized to unity.

In order to extract a range of sizes, it is necessary to apply a mathematical procedure called inversion. For this it is necessary to solve the Fredholm integral equations of the first kind, which in the ideal case are expressed as

where K _i (D) is the core of the diffusion battery, i.e. a function that describes the fraction of particles passing through the first i sections for a monodisperse aerosol with a particle diameter D; a and b are the limits of the size range. However, the experimental measurement is carried out with a certain error, therefore, equation (1) is performed only within the experimental accuracy:

where ε _i are experimental errors. Equations (2) is a so-called incorrect inverse problem, which cannot be solved without involving additional information. As a rule, such inverse problems are solved numerically. There are various numerical approaches for solving equation (2), such as linear and nonlinear iterative methods [27-29], Tikhonov’s regularization method [30, 31], least squares method [32], maximum expectation method [33], matrix factor analysis [34], the method of maximum entropy [35-37], etc. The main disadvantages of numerical methods are the complexity of the algorithm and high computational costs.

Closest to the claimed invention is a device for measuring the spectrum of aerosol particles and a method for measuring the size spectrum of aerosol particles developed at the Institute of Chemical Kinetics and Combustion SB RAS [38, 39, 41]. The main elements of this device are a diffusion battery, a condensation enlarger of particles up to an optically detectable size, an optical particle counter and a communication unit with a personal computer for controlling and processing data. When using the prototype device, the restoration of the size spectrum from the experimentally measured slots of the diffusion battery is carried out using a numerical solution of the inverse problem.

The disadvantages of the spectrum reconstruction method used in the prototype device include the numerical solution of the inverse problem, i.e. systems of Fredholm integral equations of the first kind (equation (2)). The problem is that this task is incorrect, which, in particular, is manifested in the fact that one set of breakthroughs corresponds to an infinite number of solutions. In addition, small measurement errors can lead to huge errors in the solution. In order to solve these problems, it is necessary to impose restrictions on the solution, and, more importantly, apply the procedure for selecting the final solution from a large number of mathematically possible solutions. As a result, the spectrum restoration procedure becomes resource-consuming, and often unreliable solutions are obtained.

The task of the invention is to increase the accuracy of measuring the size spectra of aerosol particles and simplify the calculation method. This increase in accuracy is achieved by the implemented design of the diffusion battery, which makes it possible to carry out such a measurement method in which the size spectra of the fractions of aerosol particles deposited in individual sections, with the exception of the latter, are measured when an aerosol stream passes through them, as well as particles passing through all sections, except last one. Moreover, the total spectrum of the starting particles is the sum of the spectra of the fractions.

The technical result of the present invention is to simplify the procedure for measuring the particle size distribution function and to obtain more reliable particle size spectra compared to previously used methods.

The technical result is achieved by the proposed device for measuring the particle size spectrum, including a diffusion battery with several sections in which the mesh is installed perpendicular to the flow. According to the invention, the grids in the sections of the diffusion battery are distributed so that the number of grids in each section, except for the first, is equal to the total number of grids in all previous sections located upstream. In other words, the distribution of the grids in the sections is chosen so that the average diameter D _{i of the} fraction of particles deposited in the i-th section of the DB can be mathematically expressed using experimentally measured breakthroughs according to the formula:

h - толщина сетки, r - радиус волокна сетки, α - отношение объема, занимаемого волокнами, к полному объему сетки,

, U₀ - линейная скорость аэрозольного потока.where i is the serial number of the section, n _i and n _{i + 1} are the number of grids in the sections with numbers i and i + 1, respectively, g _i is the fraction of particles passing through the i-th section without deposition, μ _i is the deposition efficiency on single fiber in a packet containing n _i + n _{i + 1} , nets, for particles contained in the stream after the i-th section,

h is the thickness of the mesh, r is the radius of the mesh fiber, α is the ratio of the volume occupied by the fibers to the total volume of the mesh,

, U ₀ is the linear velocity of the aerosol stream.

The technical result is also achieved due to the fact that an unambiguous correspondence is established between the measured breakthroughs and the spectra of fractions, which leads to the stability of the solution, i.e. random experimental errors in measuring the diffusion battery do not lead to a significant spread in the reconstructed size spectrum, since the experimental breakthroughs of discrete breathers uniquely determine the average deposition efficiency on individual fibers of the network for particle fractions by the formula

- эффективность осаждения частиц i-й фракции на отдельном волокне i-й секции, n_i, и n_i+1 - количества сеток в секциях с номерами i и i+1, соответственно, g_i - доля частиц, прошедших через i-ю секцию, μ_i - эффективность осаждения на одиночном волокне в пакете, содержащем n_i +n_i+1 сеток, для частиц, содержащихся в потоке после i-й секции,

, h - толщина сетки, r - радиус волокна сетки, α - отношение объема, занимаемого волокнами, к полному объему сетки,

, U₀ - линейная скорость аэрозольного потока; далее из величины

однозначно определяют средний диаметр D_i частиц i-й фракции по формулам веерной модели фильтров Кирша-Стечкиной-Фукса, долю h_i частиц i-й фракции определяют по формуле h_i=g_i-g_i+1, спектр частиц i-й фракции аппроксимируют любой функцией мономодального распределения, включая логнормальное распределение, Гауссово распределение, причем D_i и h_i являются параметрами мономодального распределения, далее спектр исходного аэрозоля определяется как сумма спектров фракций.where i is the serial number of the DB section or particle fraction,

- the efficiency of deposition of particles of the i-th fraction on a separate fiber of the i-th section, n _i , and n _{i + 1} - the number of grids in sections with numbers i and i + 1, respectively, g _i - the proportion of particles passing through the i-th section, μ _i is the deposition efficiency on a single fiber in a packet containing n _i + n _{i + 1} nets for particles contained in the stream after the i-th section,

, h is the thickness of the mesh, r is the radius of the fiber of the mesh, α is the ratio of the volume occupied by the fibers to the total volume of the mesh,

, U ₀ is the linear velocity of the aerosol stream; further from

uniquely determine the average diameter D _{i of} particles of the ith fraction according to the formulas of the Kirsch-Stechkina-Fuchs fan model, the fraction h _{i of} particles of the i-fraction is determined by the formula h _i = g _i -g _{i + 1} , the spectrum of particles of the i-fraction they are approximated by any monomodal distribution function, including the lognormal distribution, the Gaussian distribution, where D _i and h _i are the parameters of the monomodal distribution, then the spectrum of the initial aerosol is determined as the sum of the spectra of the fractions.

The invention is illustrated by drawings, which depict:

in FIG. 1 - block diagram of a device for measuring the particle size spectrum: 1 - mesh diffusion battery, 2 - condensation enlarger of particles to an optically recorded size, 3 - optical particle counter, 4 - communication unit with a personal computer;

in FIG. 2 - the efficiency of deposition of aerosol particles on a single fiber depending on the diameter of the particles;

in FIG. 3 - comparison of particle diameter distribution functions measured with a diffusion battery (solid lines) with size spectra measured with transmission electron microscopy (a, b, c) and sedimentation in a gravitational field (d) (histograms).

The essence of the invention is as follows. The main elements of the device (Fig. 1) for measuring the size spectrum of aerosol particles are a mesh diffusion battery 1, a condensation particle enlarger up to an optically detectable size 2, an optical particle counter 3, and a communication unit with a personal computer 4 for controlling and processing data. The diffusion battery consists of successive sections filled with grids absorbing aerosol particles by diffusion, trapping, inertia, and other mechanisms. The grids are mounted perpendicular to the aerosol flow. Distinctive features of the device is that the number of grids in each section is equal to the total number of grids in the previous sections located upstream. In this invention, as an example, a mesh battery of nine cylindrical sections is considered, the number of grids in which increases with the section number as follows: 2, 2, 4, 8, 16, 32, 64, 128, 256. The internal diameter of the channel of the sections is 50 mm . We used kapron woven nets with a fiber diameter of 50 μm, a pitch of 172 μm, and the ratio of the volume occupied by the fibers to the total volume of the mesh α = 0.231. The space velocity of the aerosol stream through the battery was 1 l / min. The calculated aerosol concentration C _i measured after the i-th section depends on the total number N _{1, i} = n ₁ + n ₂ + ... + n _i , the nets through which the aerosol stream has passed, where n ₁ , ..., n _{i are the} number of nets in sections 1, ..., i, respectively. For an aerosol, all particles of which have the same diameter D, the fraction of particles passing through the sequence of sections 1, ..., i is [25, 26, 41-46]

, h - толщина сетки, r - радиус волокна сетки. Батарея, рассматриваемая в данном изобретении, предназначена для работы в нанометровом и субмикронном диапазонах. Для частиц в этой области размеров, осаждение на волокна в основном определяется тремя механизмами - диффузией, захватом и инерцией. Зависимость эффективности осаждения на одиночном волокне от диаметра частицы можно рассчитать в рамках теории веерных фильтров Кирша, Стечкиной и Фукса [42-45]. На фиг. 2 для монодисперсных частиц приведена эта зависимость для параметров батареи, рассмотренной в данном изобретении. Видно, что функция μ(D) имеет минимум при D≈1100 нм, что означает, что однозначное соответствие между диаметром и эффективностью осаждения имеет место при размерах частиц D<1100 нм. Другими словами, данная диффузионная батарея имеет динамический диапазон размеров 3<D<1100 нм (при размерах меньших 3 нм эффективность укрупнения частиц в конденсационном укрупнителе становится существенно меньше единицы).where μ is the efficiency of the deposition of particles on a separate fiber located perpendicular to the aerosol stream,

, h is the thickness of the mesh, r is the radius of the fiber of the mesh. The battery considered in this invention is designed to operate in the nanometer and submicron ranges. For particles in this size range, fiber deposition is mainly determined by three mechanisms — diffusion, capture, and inertia. The dependence of the deposition efficiency on a single fiber on the particle diameter can be calculated in the framework of the theory of Kirsh, Stechkina, and Fuchs fan filters [42–45]. In FIG. 2 for monodisperse particles, this relationship is shown for the parameters of the battery discussed in this invention. It can be seen that the function μ (D) has a minimum at D≈1100 nm, which means that an unambiguous correspondence between the diameter and the deposition efficiency takes place at particle sizes D <1100 nm. In other words, this diffusion battery has a dynamic range of sizes 3 <D <1100 nm (for sizes smaller than 3 nm, the particle enlargement efficiency in a condensation enlarger becomes significantly less than unity).

In order to obtain analytical expressions for calculating the size spectrum ƒ (D) of the initial aerosol particles, it can be represented as

where m is the number of DB sections, ϕ ₁ (D), ϕ ₂ (D), ..., ϕ _m-1 (D) are the spectra of the sizes of fractions of particles settled respectively in sections 1, 2, ..., m-1 when passing through aerosol flow, a ϕ _m (D) is the spectrum of the last fraction, i.e. particles emerging from section m-1. The values of h ₁ , h ₂ , ..., h _m-1 are the fractions of particles deposited in sections 1, 2, ..., m-1, respectively, and h _m is the fraction of particles leaving the section m-1. These values are associated with the slip as follows h ₁ = 1-g ₁ , h ₂ = g ₁ -g ₂ , h ₃ = g ₂ -g ₃ , ..., h _m-1 = g _m-2 -g _m-1 , h _m = g _m-1 . Thus, finding the functions ϕ _i (D), we obtain a general spectrum of sizes.

The number of grids in a section increases monotonically with increasing section number. Therefore, when an aerosol stream passes through a battery, primarily small particles are deposited in the initial sections, and larger particles settle in subsequent sections. Therefore, the average particle diameter described by the functions ϕ _i (D) monotonously increases with increasing number i. In order to find the solution ƒ (D) in the form (4), we approximate each function ϕ _i (D) by the lognormal distribution

where D _i is the geometric mean diameter and σ is the standard geometric deviation. In our case, it is convenient to consider the functions ϕ _i with the value σ = 1.35. This value of the standard geometric deviation leads to the fact that, on the one hand, the functions ϕ _i (D) are quite narrow and their superposition allows us to describe any real distribution function of any aerosol of natural or anthropogenic origin, and on the other hand, the functions ϕ _i (D) wide enough to produce a smooth final spectrum for a limited number of sections of a diffusion battery. Thus, in order to find the solution ƒ (D), it is only necessary to find the average diameters D _i for fractions of particles cut off by sections of the diffusion battery. The approximation of the initial particle size distribution function by the sum of the lognormal functions (equation (5)) is a simple and resource-free way to determine the particle size spectrum. The resulting spectrum reproduces well the structure of the initial distribution and allows you to accurately determine the average particle size. The average diameters D _i can be found from the gaps measured with a diffusion battery.

осаждения на одиночном волокне. Для частиц, выходящих из j-й секции, мы также можем ввести среднюю эффективность μ_j(N) осаждения на одиночном волокне в пакете из N сеток. Так, например, величина μ_k-1(n_k) является средней эффективностью осаждения на одиночном волокне в k-й секции, заполненной n_k сетками, для аэрозоля, вышедшего из секции k-1 (или для входного аэрозоля в случае k=1). Как видно из уравнения (3), эту величину можно выразить следующим образомThe method of determining the average diameters D _i as follows. The efficiency of deposition of μ on a single fiber is related to the particle diameter by analytical formulas in the framework of the theory of Kirsh, Stechkina, Fuchs fan filters [42–45] (see also Fig. 2), therefore, μ can be considered as a measure of particle size. It will be convenient for the fraction of particles settled in the i-th section of the DB to introduce an average efficiency

single fiber deposition. For particles emerging from the jth section, we can also introduce the average efficiency μ _j (N) of deposition on a single fiber in a packet of N grids. So, for example, μ _k-1 (n _k ) is the average deposition efficiency on a single fiber in the kth section filled with n _k nets for an aerosol leaving section k-1 (or for the input aerosol in the case k = 1 ) As can be seen from equation (3), this value can be expressed as follows

с общим числом сеток

средняя эффективность осаждения на волокне для частиц, прошедших через предыдущие

секций запишется в видеFor section sequence

with the total number of grids

average fiber deposition efficiency for particles passing through previous

sections will be written as

We now determine the average diameter D ₁ for the first fraction, i.e. for particles settled in the first section. All particles that make up the initial spectrum can be divided into two groups: the first group - particles passing through the first section, whose share is g ₁ , and the second group - particles deposited on the grids of the first section, whose share

. Поэтому суммарно мы можем записать:These two groups can be considered as two independent ensembles of particles, each of which is described by its size distribution function. If we select only the first group of particles from the entire source aerosol and pass them through the first section of the battery, then the fraction of these particles passing through the first section will be g ₁ exp (-χμ ₁ (n ₁ ) n ₁ ). If we select only the second group, then the fraction of these particles passing through the first section will be

. Therefore, in total, we can write:

In our case, n ₁ = n ₂ = 2, therefore μ ₁ (n ₁ ) = μ ₁ (n ₂ ). Then, as follows from equation (6)

and we get from equations (8-10)

связана с эквивалентным диаметром частиц через уравнения теории веерных фильтров Кирша, Стечкиной, Фукса [42-45] (фиг. 2). Данный эквивалентный диаметр примерно равен искомому среднему геометрическому диаметру D₁. Таким образом, подставляя

из уравнения (11) в уравнения теории веерных фильтров и решая их численно, или графически, подставляя значения

вместо μ на фиг. 2, получаем D₁.Average fiber deposition efficiency

connected with the equivalent particle diameter through the equations of the theory of fan filters Kirsch, Stechkina, Fuchs [42-45] (Fig. 2). This equivalent diameter is approximately equal to the desired geometric mean diameter D ₁ . Thus substituting

from equation (11) to equations of the theory of fan filters and solving them numerically or graphically, substituting the values

instead of μ in FIG. 2, we obtain D ₁ .

In the general case, for 1 <i <m-1 for an aerosol passing through two adjacent sections i and i + 1, one can write an expression similar to equation (9):

As follows from equation (3),

and we get from equations (12, 13)

The value μ _i (N _{i, i + 1} ) in the right-hand side of equation (14) cannot be directly determined from the measured breakthroughs of the diffusion battery. However, given the fact that μ _i (N) is a monotonic function of N, we can find the approximate value of μ _i (N _{i, i + 1} ) using simple interpolation. In other words, for an aerosol leaving the ith section, the equivalent deposition efficiency μ _i (N _{i, i + 1} ) on a single fiber in a packet containing n _i + n _{i + 1} nets can be estimated as the arithmetic mean of the deposition efficiencies on fiber in packets of n _{i + 1} and (n _{i + 1} + n _{i + 2} ) nets. Then for 1 <i <m-2 we have:

For i = m-1, with good accuracy, we can assume that

(уравнение (14)) в рамках теории веерных фильтров средний диаметр D_i.Substituting equations (15, 16) into (14), and, further, using the unique correspondence between the deposition efficiency on the fiber and the particle diameter (Fig. 2), we obtain from the quantity

(equation (14)) in the framework of the theory of fan filters, the average diameter D _i .

определяется выражениемFor i = m, the quantity

defined by the expression

which allows to obtain D _m . Thus, knowing the average diameters D _i , we obtain the diameter distribution function ƒ (D) using equations (4) and (5).

For particles with a diameter of D <200 nm, deposition on the grids is due only to the diffusion mechanism. For diffusion in air at a temperature of 293 K and atmospheric pressure, the average diameters D _i can be calculated from the experimental breakthroughs of the diffusion battery according to the formulas:

и μ_i(N_i,i+1) рассчитывается по формулам (15, 16).Where

and μ _i (N _{i, i + 1} ) is calculated by the formulas (15, 16).

To demonstrate the accuracy of formulas (11, 14, 17), the diameter distribution function measured using a diffusion battery was compared with size spectra measured by other physical methods. The aerosol for measurements was generated using a thermocondensation generator. The essence of the thermal condensation method was to heat the initial substance (maternal phase) in a stream of filtered air. As a result, the stream was saturated with the vapor of the mother substance. Then, a saturated steam stream was fed into the cooling zone, where the steam became supersaturated. As a result, aerosolization was achieved due to homogeneous nucleation. Particle sizes were analyzed for comparison with diffusion battery measurements using a JEM-100SX transmission electron microscope (TEM) or a gravitational field sedimentation method [47, 48].

In FIG. Figure 3 compares the particle size spectra of Ag, CsCl, NaCl and dibutyl phthalate obtained using a diffusion battery (solid line) and TEM / sedimentation methods (histograms). Arithmetic average diameters obtained by various methods are shown in table 1.

As can be seen from the table, the average diameters obtained using a diffusion battery within the experimental error coincide with the values obtained by other physical methods, which confirms the validity of the developed method for determining the size spectrum by measuring the spectrum of fractions.

Information sources:

1. Interstate standard. Protection of Nature. Atmosphere. Rules of air quality control of settlements, GOST 17.2.3.01-86, Moscow, Standardinform, 2005.

2. Handbook of Air Pollution Analysis, Edited by Roy M. Harrison and Roger Perry, CHAPMAN and HALL, New York, 1986.

3. S. Manzoor and U. Kulshrestha, Atmospheric Aerosols: Air Quality and Climate Change Perspectives, Current World Environment, 2015, 10 (3), 738-746

4. S. Fuzzi, U. Baltensperger, K. Carslaw, S. Decesari, H. Denier van der Gon, M.C. Facchini, D. Fowler, I. Koren, B. Langford, U. Lohmann, E. Nemitz, S. Pandis, I. Riipinen, Y. Rudich, M. Schaap, J.G. Slowik, D.V. Spracklen, E. Vignati, M. Wild, M. Williams, and S. Gilardoni, Particulate matter, air quality and climate: lessons learned and future needs, Atmos. Chem. Phys., 2015, 15, 8217-8299.

5. Controlled Pulmonary Drug Delivery, H. D.C. Smyth and A.J. Hickey (Editors), Springer, New York, 2011.

6. Pulmonary Drug Delivery. Advances and Challenges, A. Nokhodchi and G.P. Martin (Editors), Wiley, London, 2015.

7. G. Biskos, V. Vons, C. U. Y. and A. Schmidt-Ott, Generation and Sizing of Particles for Aerosol-Based Nanotechnology, KONA Powder and Particle Journal, 2008, No. 28, 13-35.

8. J.C. Volkwein, A.D. Maynard, M. Harper, Workplace aerosol measurement, in book: AEROSOL MEASUREMENT. Principles, Techniques, and Applications, P. Kulkarni, P.A. Baron, K. Willeke (Editors), Willey, New Jersey, 2011, 571-590.

9. GN 2.2.5.1313-03 "Maximum permissible concentrations (MPC) of harmful substances in the air of the working zone."

10. GN 1.2.2633-10 "Hygienic standards for the content of priority nanomaterials in environmental objects."

11. S.S. Amaral, J.A. de Carvalho, M.A. M. Costa, S. Pinheiro, An Overview of Particulate Matter Measurement Instruments, Atmosphere 2015, 6, 1327-1345.

12. W.C. Hinds, Aerosol Technology: Properties, Behavior, and Measurement of Airborne Particles, John Wiley & Sons, New York, 1999.

13. J.A. Last, P. Russell, P.F. Nealey, and C.J. Murphy, The Applications of Atomic Force Microscopy to Vision Science, Investigative Ophthalmology & Visual Science, 2010, 51, 6083-6094.

14. J.P. Mitchell, and M.W. Nagel, Cascade Impactors for the Size Characterization of Aerosols from Medical Inhalers: Their Uses and Limitations, Journal of Aerosol Medicine, 2003, 16, 341-377

15. J.S. Kang, K.S. Lee, K.H. Lee, H.J. Sung & S.S. Kim, Characterization of a Microscale Cascade Impactor, Aerosol Science and Technology, 2012, 46: 966-972.

16. Aerosol Measurement. Principles, Techniques, and Applications, P. Kulkarni, P.A. Baron, K. Willeke (Editors), Willey, New Jersey, 2011.

17. P.H. McMurry, A review of atmospheric aerosol measurements, Atmospheric Environment, 2000, 34 1959-1999.

18. P. Intra and N. Tippayawong, An overview of differential mobility analyzers for size classification of nanometer-sized aerosol particles, Songklanakarin J. Sci. Technol., 2008, 30 (2), 243-256.

19. S. Dubtsov, T. Ovchinnikova, S. Valiulin, X. Chen, H.E. Manninen, P.P. Aalto, T. Petaja, Laboratory verification of Aerosol Diffusion Spectrometer and the application to ambient measurements of new particle formation, Journal of Aerosol Science, 2017, 105, 10-23.

20. A.A. Onischuk, S.V. Vosel, O.V. Borovkova, A.M. Baklanov, V.V. Karasev, and S. di Stasio, Experimental study of homogeneous nucleation from the bismuth supersaturated vapor: Evaluation of the surface tension of critical nucleus, The Journal of Chemical Physics 2012, 136, 224506 (1-18)

21. A.A. Onischuk, S.V. Valiulin, S.V. Vosel, V.V. Karasev, V.D. Zelik, A.M. Baklanov, Surface tension of sulfur nanoparticles as determined from homogeneous nucleation experiments, Journal of Aerosol Science 2016, 97 1-21.

, A.M. Baklanov, S.V. Valiulin, M.V. Khvostov, I.V. Sorokina, G.G. Dultseva, N.A. Zhukova Ibuprofen, indomethacin and diclofenac sodium nanoaerosol: Generation, inhalation delivery and biological effects in mice and rats, Journal of Aerosol Science 2016, 100 164-177.22.AA Onischuk, TG Tolstikova, SV

, AM Baklanov, SV Valiulin, MV Khvostov, IV Sorokina, GG Dultseva, NA Zhukova Ibuprofen, indomethacin and diclofenac sodium nanoaerosol: Generation, inhalation delivery and biological effects in mice and rats, Journal of Aerosol Science 2016, 100 164-177.

23. D.J.H. Vosburgh, T. Klein, M. Sheehan, T.R. Anthony and T. M. Peters, Design and Evaluation of a Personal Diffusion Battery, 2013, 47: 4, 435-443

24. B. Gorbunov, N.D. Priest, R.B. Muir, P.R. Jackson and H. Gnewuch, A Novel Size-Selective Airborne Particle Size Fractionating Instrument for Health Risk Evaluation, Ann. Occup. Hyg., 2009, 53 (3) 225-237.

25. S. Cheng and H.C. Yeh, Theory of a screen-type diffusion battery, J. Aerosol Sci. 1980, 11, 313-320.

26. Y.S. Cheng, H.C. Yeh, K.J. Brinsko, Use of Wire Screens as a Fan Model Filter, Aerosol Science and Technology, 1985, 4: 2, 165-174.

27. S. Twomey, Comparison of Constrained Linear Inversion and an Iterative Nonlinear Algorithm Applied to the Indirect Estimation of Particle Size Distributions, Journal of Computational Physics 1975, 18, 188-200.

28. F. Ferri, A. Bassini, and E. Paganini, Modified version of the Chahine algorithm to invert spectral extinction data for particle sizing, APPLIED OPTICS, 1995, 34, No. 25, 5829-5839.

29. A. Reineking and J. Porstendorfer, High-volume screen diffusion batteries and α-spectroscopy for measurement of the radon daughter activity size distributions in the environment, J. Aerosol Sci., 1986, 17, 873-879.

30 Y.S. Bashurova, V. Dreiling, T.V. Hodger, R. Jaenicke, K.P. Koutsenogii, P.K. Koutsenogii, M. Kraemer, V.I. Makarov, V.A. Obolkin, Y.L. Potjomkin and A.Y. Pusep, Measurements of Atmospheric Condensation Nuclei Size Distributions in Siberia. J. Aerosol Sci., 1992, 23, 191-199.

31 Y. Wang and Ch. Yangm, Regularizing active set method for retrieval of the atmospheric aerosol particle size distribution function, J. Opt. Soc. Am. A, 2008, 25, 348-356.

32. A. Voutilainen, V. Kolehmainen, F. Stratmann, and J.P. Kaipio, Computational Methods for the Estimation of the Aerosol Size Distributions, in Book: Mathematical Modeling. Problems, Methods, Applications, Edited by L.A. Uvarova and A.V. Latyshev, Springer Science + Business Media, Lle, 2001, New York, Page 219-230.

33. E.F. Maher, N.M. Laird, EM Algorithm Reconstruction Of Particle Size Distributions From Diffusion Battery Data, J. Aerosol Sci., 1985, Vol. 16, No. 6, pp. 557-570.

34. P. Paatero, U. Tapper, P. Aalto and M. Kulmala, Matrix Factorization Methods for Analysing Diffusion Battery Data, J. Aerosol Sci., 1991, Vol. 22, Suppl. 1. pp. S273-S276.

35. S. Eremenko and A. Ankilov, Conversion of the diffusion battery data to particle size distribution: Multiple Solutions Averaging algorithm (MSA), J. Aerosol Sci., (1995) Vol. 26. Suppl 1, 749-750.

36. Y. Gulak, E. Jayjock, F. Muzzio, A. Bauer & P. McGlynn, Inversion of Andersen Cascade Impactor Data using the Maximum Entropy Method, Aerosol Science and Technology, 2010, 44: 1.29-37.

37. E. Yee, On the interpretation of diffusion battery data, J. Aerosol Sci., 1989, 20, 797-811.

, Т.C, Podzimek, J., Preining, O., Reischl, G.P., Rudolf, R., Sem, G.J., Szymanski, W. W., Tamm, E., Vrtala, A.E., Wagner, P.E., Winklmayr, W., & Zagaynov, V. (2002). Intercomparison of number concentration measurements by various aerosol particle counters. Atmospheric Research, 62, 177-207.38. Ankilov, A., Baklanov, A., Colhoun, M., Enderle, K.-H., Gras, J., Junlanov, Yu, Kaller, D., Lindner, A., Lushnikov, A., Mavliev , R., McGovern, F., Mirme, A.,

, T.C., Podzimek, J., Preining, O., Reischl, GP, Rudolf, R., Sem, GJ, Szymanski, WW, Tamm, E., Vrtala, AE, Wagner, PE, Winklmayr, W., & Zagaynov, V. (2002). Intercomparison of number concentration measurements by various aerosol particle counters. Atmospheric Research, 62, 177-207.

39. Ankilov, A., Baklanov, A., Mavliev, R., & Eremenko, S. (1991). Comparison of the Novosibirsk automated diffusion battery with the Vienna electro mobility spectrometer. Journal of Aerosol Science, 22, S325-S328.

40. V.S. Bashurova, K.P. Koutsenogii, A.Y. Pusep, N.V. Shokhirev (1991) Determination of atmospheric aerosol size distribution functions from screen diffusion battery data: mathematical aspects. J. Aerosol Sci. 22, 373-388.

41. Y.S. Cheng, J.A. Keating and G.M. Kanapilly, Theory and calibration of a screen-type diffusion battery, J Aerosol Sci., 1980, 11, 549-556.

42. Kirsch, A.A., Stechkina, I.B., & Fuchs, N.A. (1975). Studies on fibrous aerosol filters-experimental determination of fibrous filters efficiency in the range of maximum particle penetration. Colloid J. USSR, 1969, 31 (2), 227-232.

43. Stechkina I.V., Kirsch A.A., Fuchs N.A., Studies on fibrous aerosol filters-IV Calculation of aerosol deposition in model filters in the range of maximum penetration, Ann. Occup. Hyg., 1969, 12, 1-8.

44. Kirsch, A.A., Stechkina, I.B. Inertial deposition of aerosol particles in model filters at low Reynolds numbers, Journal of Aerosol Science, 1977, 8, 301-307.

45. A.A. Kirsch & P.V. Chechuev, Diffusion Deposition of Aerosol in Fibrous Filters at Intermediate Peclet Numbers, Aerosol Science and Technology, 1985, 4: 1, 11-16.

46. V.A. Kirsh D.A. Pripachkin, A.K. Budyka, Inertial deposition of aerosol particles from laminar flows in fibrous filters, Colloid Journal, 2010, 72 (2), 211-215.

47. P.C. Reist, Aerosol science and technology, (McGraw-Hill Inc., USA, 1993).

48. Dust aerosols, fumes and mists, Ed. P.L. Fuchs, Chemistry, Leningrad, 1972.

Claims (6)

1. A device for measuring the size spectrum of aerosol particles, including a diffusion battery (DB), consisting of a series of successive sections filled with grids consisting, for example, of metal or polymer fibers onto which aerosol particles are deposited when the aerosol stream passes through the battery, a condensing particle enlarger , an optical particle counter and a personal computer for controlling the device as a whole, accumulating and processing the received data, characterized in that the number of installed grids in each section of the diffusion battery, with the exception of the first one, it is equal to the total number of grids in all previous sections located upstream, which allows calculating the average particle diameter D _i deposited in the i-th section of the DB, according to the mathematical formula

, where i is the sequence number of the section, n _i and n _{i + 1} are the number of grids in the sections with numbers i and i + 1, respectively, g _i is the fraction of particles passing through the i-th section without deposition, μ _i is the deposition efficiency on a single fiber in a packet containing n _i + n _{i + 1} nets for particles contained in the stream after the i-th section,

, h is the thickness of the mesh, r is the radius of the fiber of the mesh, α is the ratio of the volume occupied by the fibers to the total volume of the mesh,

, U ₀ is the linear velocity of the aerosol stream. 2. A method of measuring the size spectrum of aerosol particles by sequentially passing the aerosol stream through sections of a diffusion battery (DB) filled with grids, then through a condensing particle enlarger, measuring the aerosol concentration by an optical meter and computer processing of data, characterized in that they determine the deposition efficiency on individual fibers grids for fractions of particles, that is, for particles deposited in sections of a diffusion battery, according to the formula

where i is the serial number of the DB section or particle fraction,

is the efficiency of deposition of the i-th fraction on a separate fiber of the i-th section, n _i and n _{i + 1} are the number of grids in the sections with numbers i and i + 1, respectively, g _i is the fraction of particles passing through the i-th section, μ _i is the deposition efficiency on a single fiber in a packet containing n _i + n _{i + 1} nets for particles contained in the stream after the i-th section,

, h is the thickness of the mesh, r is the radius of the fiber of the mesh, α is the ratio of the volume occupied by the fibers to the total volume of the mesh,

, U ₀ - linear velocity of the aerosol stream, then from the value

determine the average diameter D _{i of} particles of the i-th fraction using the formulas of the fan model of Kirsch-Stechkina-Fuchs filters, the fraction h _{i of} particles of the i-th fraction is determined by the formula h _i = g _i -g _{i + 1} , the particle spectrum of the i-th fraction is approximated any function of the monomodal distribution, including the lognormal distribution, the Gaussian distribution, where D _i and h _i are the parameters of the monomodal distribution, then the spectrum of the initial aerosol is determined as the sum of the spectra of the fractions.

Images