CN112949110B - Method for predicting deposition of atmospheric particulates in human lung - Google Patents

Method for predicting deposition of atmospheric particulates in human lung Download PDF

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CN112949110B
CN112949110B CN202110126458.1A CN202110126458A CN112949110B CN 112949110 B CN112949110 B CN 112949110B CN 202110126458 A CN202110126458 A CN 202110126458A CN 112949110 B CN112949110 B CN 112949110B
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CN112949110A (en
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马子健
庄依杰
任贺龙
余应新
安太成
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Guangdong University of Technology
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Abstract

The invention discloses a method for predicting atmospheric particulate deposition in a human lung, which comprises the steps of using a Weibel A symmetric model as a basic physiological structure of the lung, using a sin function to simulate an air inlet speed condition in a human breathing process, establishing an atmospheric particulate deposition judgment model considering eight variables including speed, an incident angle, viscosity, shape, water content, quality, surface property and surface property of a contact surface of atmospheric particulate, using a UDF function of software ANSYS Fluent to realize the model so as to simulate behavior of the atmospheric particulate after colliding with a tracheal wall, using a sample collection function of the ANSYS Fluent, using a statistical method to obtain the deposition amount, deposition rate and deposition position of the atmospheric particulate in the human lung model, and finally performing result verification. The method has the advantages of very low time cost and labor cost, and very accurate prediction of the deposition behavior of the atmospheric particulates in the lung of the human body.

Description

Method for predicting deposition of atmospheric particulates in human lung
Technical Field
The invention relates to the technical field of environmental health risk exposure numerical simulation, in particular to a method for predicting deposition of atmospheric particulates in human lungs.
Background
With the development of industrialization in China, atmospheric pollution is increasingly serious, people pay more and more attention to research on human body breathing exposure, and atmospheric particulates are a main pollutant in the atmosphere.
Researches show that the atmospheric particulates can cause harm to human health and can seriously cause death. The way atmospheric particulates enter the human body's internal circulation is mainly deposited in the human body's lungs through the respiratory tract. Studying the deposition of atmospheric particulates in the lungs can reveal the relationship between atmospheric particulate exposure and human health.
At present, the problems of high cost, long time, ethical involvement and the like exist in the atmospheric particulate matter exposure experiment by using a human body, and in order to conveniently carry out the experiment detection of the atmospheric particulate matter exposure related data, it is of great significance to research a method for carrying out the deposition simulation of the atmospheric particulate matter in the lung by using Computational Fluid Dynamics (CFD). The CFD can simulate the movement behavior of the atmospheric particulates in the lung in the human respiration process, and calculate the deposition position and the deposition amount of the atmospheric particulates in the lung. Many scholars have developed related studies on the deposition behavior of atmospheric particulates in the lungs of the human body today. Some researchers have used the Weibel a symmetric model as the basic physiological structure of the lung for numerical simulation of the transport and deposition of atmospheric particulates. However, in the aspect of numerical simulation, the accuracy of the result obtained by numerical simulation is not high, and the atmospheric particulates inhaled by a human body are regarded as a substance, and the influence of different factors such as the speed, the incident angle, the viscosity, the shape, the water content, the quality, the surface property of a contact surface and the like on the deposition amount of the atmospheric particulates in the lung and a main deposition part is not fully considered, wherein the surface property determines the young modulus of the measured particulates, the surface property of the contact surface determines the young modulus of a tube wall, and the both determine the adhesion coefficient. In the aspect of experiments, because the experiment cost of atmospheric particulate matter exposure experiments in human lungs is very high, and only one to dozens of particle pollutants can be tested at a time, the deposition amount of thousands of particle pollutants in the atmosphere cannot be measured, and the ethical problem exists.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for predicting the deposition of atmospheric particulates in the lung of a human body, which not only has very low time cost and labor cost, but also can very accurately predict the deposition behavior of the atmospheric particulates in the lung of the human body, which have different speed, incidence angle, viscosity, shape, water content, quality, chemical properties of the atmospheric particulates and chemical property factors of a contact surface, and provides an accurate and effective quantitative evaluation means for the evaluation of the exposure health risk of the atmospheric particulates pollution of the human body in the environment.
In order to achieve the purpose, the technical scheme provided by the invention is as follows:
a method for predicting atmospheric particulate matter deposition in human lung, by using Weibel A symmetric model as basic physiological structure of lung, using sin function to simulate air intake speed condition of human respiration process, establishing atmospheric particulate deposition judgment model considering eight variables including speed, incident angle, viscosity, shape, water content, quality, surface property and surface property of contact surface, wherein the surface property determines Young modulus of particulate matter to be measured, the surface property of contact surface determines Young modulus of pipe wall, and the two determine adhesion coefficient together; and then, the model is realized by using the UDF function of the software ANSYS Fluent to realize the simulation of the behavior of the atmospheric particulates after the atmospheric particulates collide with the tracheal wall, then, the deposition amount, the deposition rate and the deposition positions of the atmospheric particulates in the human lung model are obtained by using the sample collection function of the ANSYS Fluent and a statistical method, and finally, the result verification is carried out.
Further, the method comprises the following specific steps:
s1, establishing a three-dimensional geometric model of the human lung according to a Weibel A symmetric model as a geometric structure of the lung, and outputting a three-dimensional model file of the human lung;
s2, importing the three-dimensional model drawn in the S1 into ANSYS ICEM software, dividing grids, and setting boundary attributes;
s3, importing the grid drawn in the S2 into an ANSYS Fluent, adjusting the unit length of the grid and checking the quality of the grid;
s4, selecting a solver type, starting a solving model, and starting gravity influence;
s5, setting inlet and outlet boundary conditions: the inlet is a speed inlet, and the outlet is a pressure outlet;
s6, setting an inlet to use a first UDF function, and setting an outlet to be a pressure constant;
s7, setting parameters of injection of the particle phase injector, and setting gas phase parameters;
s8, setting the boundary type of the discrete phase: the inlet and outlet are set as escapes;
s9, the parameter E is included S 、E P 、v S 、v P The second UDF function of (3) is inserted into the discrete facies model; e S And E P Respectively the Young's modulus of the atmospheric particulates and the surface of the pipe wall; v. of S And v P Respectively the poisson ratio of the atmospheric particulates and the tube wall surface;
s10, setting solver parameters;
s11, opening a sample collector, and collecting samples of the wall surface, the air outlet and the air inlet;
s12, starting to solve, and ending sample collection after calculation convergence;
s13, using ANSYS Fluent software to output a result and obtaining the deposition N of the atmospheric particulates in the human respiration process P Deposition rate σ and deposition position;
s14, checking air inflow, calculating a difference value of the flow rates of an air outlet and an air inlet by using a report function of an ANSYS flow, and reworking the model mesh if the difference value is too large; comparing the flow of the air inlet with a calculated value obtained by integrating the first UDF function, and if the difference value between the flow of the air inlet and the calculated value is too large, adjusting the grid of the air inlet;
s15, comparing the experimental result with the calculation result;
s16, if the calculation result is not consistent with the experiment result, modifying the parameter value of the first UDF function according to the physiological parameter measured by the experiment; according to the comparison between the calculation result and the experiment result, the parameter E in the second UDF function is corrected S 、E P 、v S 、v P The value of the parameter(s) of (c),and returning to the step S9; if the calculation result is consistent with the experiment result, a prediction function is obtained;
s17, performing parameter E in a second UDF function on different types of pollution S 、E P 、v S 、v P Finding the corresponding E S 、E P 、v S 、v P To find out the deposition law of different pollutants.
Further, in the step S4, the solver type is selected as Pressure-Based, and the time type is non-steady state; the open model is: readable-k-epsilon Model, single-coupled DPM Model.
Further, in step S6, the establishing manner of the first UDF function is: and establishing a speed self-defined function when the particles collide with the tube wall according to the physical collision process of the discrete phase particles and the trachea of the lung.
Further, in step S6, the first UDF function is specifically a custom function of an intake air speed and time:
Figure BDA0002924230720000041
in the above formula, V M At the maximum intake air amount, D 1 Is the diameter of the primary pipeline, T is the breathing cycle, and a is the breathing cycle adjustment coefficient.
Further, in step S9, the specific establishment manner of the second UDF function is:
establishing an atmospheric particulate deposition model according to the stress conditions of the discrete phase particles and the tracheal wall;
for the atmospheric particulates colliding to the pipe wall, calculating the capture speed of the atmospheric particulates according to a capture model in the atmospheric particulates model; if the normal speed of the atmospheric particulates and the pipe wall is less than the capture speed, setting the state of the atmospheric particulates as capture; if the normal speed is greater than the capture speed, setting the state of the atmospheric particulate matter as reflection;
judging the captured atmospheric particulate according to a leaving model in the atmospheric particulate deposition model; if the turbulent flow friction speed is greater than the critical shearing speed, the atmospheric particles leave the wall surface;
wherein: the atmospheric particulate deposition model is based on an EI-Batsh deposition model;
the capture model in the deposition model is as follows:
Figure BDA0002924230720000042
in the above formula, D P Is the aerodynamic diameter of the atmospheric particulate matter,
Figure BDA0002924230720000043
Figure BDA0002924230720000051
the critical capture speed of the atmospheric particulates is obtained; rho P Is the mass density of the atmospheric particulates; e S And E P Respectively the Young's modulus of the atmospheric particulates and the surface of the pipe wall; v. of S And v P Respectively the poisson ratio of the atmospheric particulates and the tube wall surface;
the leaving pattern in the deposition pattern was as follows:
Figure BDA0002924230720000052
in the above formula, W A The sticking coefficient depends on the properties of the atmospheric particulates and the surface of the pipe wall; ρ is the fluid mass density; k C Is the composite Young's modulus expressed as
Figure BDA0002924230720000053
Further, in the step S13, the deposition amount N P The deposition position is obtained by using a samples function of an ANSYS fluid self-contained device, the deposition position is obtained by using a particle track function of the ANSYS fluid self-contained device, and the XY Plot function in options of the particle track is started to obtain an accurate position;
and the deposition rate σ:
Figure BDA0002924230720000054
N t is the intake of atmospheric particulates.
Compared with the prior art, the principle and the advantages of the scheme are as follows:
1) By providing a belt E S 、E P 、v S 、v P The function is combined with the discrete phase numerical simulation function and the experimental result of ANSYS Fluent software to fit E S 、E P 、v S 、v P The method can accurately predict the deposition amount and the deposition position of the atmospheric particulates in the lung in the breathing process of the human body, and provides a certain theoretical basis for the research on the exposure health of the atmospheric particulate pollution of the human body in the environment.
2) And importing the compiled UDF program into the discrete facies model, and finishing secondary development in a user-defined mode. The relation equation of the atmospheric particulates and the tracheal wall is written into a program, and the real situation that the particles are possibly reflected due to factors such as the speed, the incident angle, the surface property and the surface property of the tracheal wall after colliding with the tracheal wall under the real situation is considered. And fitting is carried out by combining with an experimental result, so that the effectiveness and the accuracy of the model are verified, convenience is brought to numerical simulation work, and the deposition behavior of atmospheric particulates in the lung in the human breathing process is more accurately predicted.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the services required for the embodiments or the technical solutions in the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to these drawings without creative efforts.
FIG. 1 is a schematic view of a particle deposition model;
FIG. 2 is a flow chart of particle deposition determination;
FIG. 3 is a schematic diagram of a three-dimensional model of a human lung;
FIG. 4 is a grid diagram of a three-dimensional model of a human lung;
FIG. 5 is a graph of atmospheric particulate deposition behavior.
Detailed Description
The invention is further described below with reference to the example of airborne aluminum metal particles and the lung model of fig. 3 and 4:
the technical scheme adopted by the invention is as follows: the invention provides a method for predicting the deposition of atmospheric particulates in the lung of a human body, which is further explained by combining the accompanying drawings and comprises the following steps:
s1, establishing a three-dimensional geometric model (figure 3) of the human lung according to a Weibel A symmetric model as a geometric structure of the lung, and outputting a three-dimensional model file of the human lung;
the Weibel A symmetric model has the following specific parameters:
TABLE 1 Weibel A symmetric model parameters
Figure BDA0002924230720000061
Figure BDA0002924230720000071
Wherein the bifurcation included angle of each bronchus is 35 degrees.
S2, importing the three-dimensional model drawn in the S1 into ANSYS ICEM software, wherein face grids all use Prism type grids, body grids all use Hexa-core type grids, the grids are divided by using an automatic dividing function, the total grid number is 418290, an air inlet is an inlet, an air outlet is an outlet, and an air pipe wall is wall (shown in a figure 4);
s3, importing the grid drawn in the S2 into an ANSYS Fluent, adjusting the unit length of the grid and checking the quality of the grid;
s4, selecting the solver type as Presure-Based and the time type as unsteady state; the open model is: a readable-k-epsilon Model and a single coupling DPM Model; starting to be influenced by gravity, wherein the value is-9.8 m/s in the y-axis direction;
s5, setting inlet and outlet boundary conditions: the inlet is a speed inlet, and the outlet is a pressure outlet;
s6, setting an inlet to use a first UDF function, and setting an outlet to be a pressure constant;
the first UDF function is specifically a custom function of air inlet speed and time:
Figure BDA0002924230720000072
in the above formula, V M At the maximum intake air amount, D 1 Is the diameter of the primary pipeline, T is the breathing cycle, and a is the breathing cycle adjustment coefficient;
the values are different according to the motion state of the human body. In the quiescent state, V m ＝600ml，D 1 =18mm, t =3s, a =0; the outlet is provided with: the pressure is constantly 0MPa (gauge pressure);
s7, setting parameters of injection of the particle phase injector, and setting gas phase parameters; the gas phase parameter adopts an Air parameter of ANSYS Fluent software, and the particle phase parameter adopts an Aluminum parameter of the ANSYS Fluent software;
wherein the initial velocity of the particle phase is the same as the gas phase gas inlet velocity, the particle size distribution of the particle phase is Rosin-Ramler distribution, and the total mass flow is 5 multiplied by 10 -7 kg/s, minimum particle size: 0.0001mm, maximum particle diameter: 0.1mm, average particle diameter: 0.01mm, distribution index: 3.5, number of particle sizes: 50, particle shape: spherical, not initiating particle collisions;
Rosin-Ramler distribution on is abbreviated as R-R distribution on, and the accumulated frequency expression under the mass sieve is as follows:
Figure BDA0002924230720000081
in the formula: n is distribution index; β -distribution coefficient; g is the accumulated frequency under the mass sieve;
if it is provided with
Figure BDA0002924230720000082
Then the following results are obtained:
Figure BDA0002924230720000083
in the formula:
Figure BDA0002924230720000084
optionally selecting a certain particle diameter, generally selecting mass median particle diameter d 50 (MMD) or d 63.2 (particle size corresponding to G = 63.2%).
Judging whether the particle size distribution data accords with R-R distribution or not, solving two constants, and adopting a linearization mapping method; taking the logarithm of the first formula twice obtains:
Figure BDA0002924230720000085
s8, setting the boundary type of the discrete phase: the inlet and outlet are set as escape;
s9, the parameter E is included S 、E P 、v S 、v P The second UDF function of (3) is inserted into the discrete facies model;
the specific establishment mode of the second UDF function is as follows:
1) Establishing an atmospheric particulate deposition model according to the stress conditions of the discrete phase particles and the tracheal wall;
2) For the atmospheric particulates collided with the pipe wall, calculating the capture speed of the atmospheric particulates according to a capture model in the atmospheric particulates model; if the normal speed of the atmospheric particulates and the pipe wall is less than the capture speed, setting the state of the atmospheric particulates as capture; if the normal speed is greater than the capture speed, setting the state of the atmospheric particulate matter as reflection;
3) Judging the captured atmospheric particulate matter according to a leaving model in an atmospheric particulate matter deposition model; if the turbulent flow friction speed is greater than the critical shearing speed, the atmospheric particles leave the wall surface;
wherein: the atmospheric particulate deposition model is based on an EI-Batsh deposition model;
the capture model in the deposition model is as follows:
Figure BDA0002924230720000091
in the above formula, D P Is the aerodynamic diameter of the atmospheric particulate matter,
Figure BDA0002924230720000092
Figure BDA0002924230720000093
the critical capture speed of the atmospheric particulates is obtained; ρ is a unit of a gradient P Is the mass density of the atmospheric particulates; e S And E P Respectively the Young's modulus of the atmospheric particulates and the surface of the pipe wall; v. of S And v P Respectively the poisson ratio of the atmospheric particulates and the tube wall surface;
the exit pattern in the deposition pattern is as follows:
Figure BDA0002924230720000094
in the above formula, W A The sticking coefficient depends on the properties of the atmospheric particulates and the surface of the pipe wall; ρ is the fluid mass density; k C Is the composite Young's modulus expressed as
Figure BDA0002924230720000095
S10, setting solver parameters; setting a solving mode of SIMPLEC, the iteration number of 1000 and the iteration time interval of 0.001s;
s11, opening a sample collector, and collecting samples of the wall surface, the air outlet and the air inlet;
s12, starting to solve, and finishing sample collection after calculation is converged;
s13, using ANSYS Fluent software to output results to obtain the breath of the atmospheric particulates in the human bodyDeposition amount N in suction process P Deposition rate σ and deposition position;
wherein the deposition amount N P The deposition position is obtained by using a samples function of an ANSYS flux self-contained device, the deposition position is obtained by using a particle track function of the ANSYS flux self-contained device, and an accurate position is obtained by using an XY Plot function in options of the particle track;
and the deposition rate σ:
Figure BDA0002924230720000101
N t the suction amount of the atmospheric particulate matters;
s14, checking air inflow, calculating a difference value of the flow rates of an air outlet and an air inlet by using a report function of an ANSYS flow, and reworking the model mesh if the difference value is too large; comparing the flow of the air inlet with a calculated value obtained by integrating the v (t) function, and if the difference value between the flow of the air inlet and the calculated value is too large, adjusting the grid of the air inlet;
s15, comparing the experimental result with the calculation result;
s16, if the calculation result is not consistent with the experiment result, modifying the parameter value of the first UDF function according to the physiological parameter measured by the experiment; according to the comparison between the calculation result and the experiment result, the parameter E in the second UDF function is corrected S 、E P 、v S 、v P And returning to step S9; if the calculation result is consistent with the experiment result, a prediction function is obtained;
s17, performing parameter E in a second UDF function on different types of pollution S 、E P 、v S 、v P Finding the corresponding E S 、E P 、v S 、v P To find out the deposition law of different pollutants.
The above-mentioned embodiments are only preferred embodiments of the present invention, and the scope of the present invention is not limited thereby, and all changes made in the shape and principle of the present invention should be covered within the scope of the present invention.

Claims (6)

1. A method for predicting atmospheric particulates to deposit in human lung is characterized in that a Weibel A symmetric model is used as a basic physiological structure of lung, a sin function is used for simulating an air inlet speed condition in a human breathing process, and an atmospheric particulates deposition judgment model considering eight variables including the speed, the incident angle, the viscosity, the shape, the water content, the quality, the surface property and the surface property of a contact surface is established, wherein the surface property determines the Young modulus of the measured particulates, the surface property of the contact surface determines the Young modulus of a pipe wall, and the Young modulus and the adhesion coefficient are determined by the surface property of the contact surface; then, the model is realized by using the UDF function of software ANSYS Fluent to realize the simulation of the behavior of the atmospheric particulates after the atmospheric particulates collide with the tracheal wall, then, the deposition amount, the deposition rate and the deposition position of the atmospheric particulates in the human lung model are obtained by using the sample collection function of the ANSYS Fluent and a statistical method, and finally, the result verification is carried out;
the method comprises the following specific steps:
s1, establishing a three-dimensional geometric model of the human lung according to a Weibel A symmetric model as a geometric structure of the lung, and outputting a three-dimensional model file of the human lung;
s2, importing the three-dimensional model drawn in the S1 into ANSYS ICEM software, dividing grids, and setting boundary attributes;
s3, importing the grid drawn in the S2 into an ANSYS Fluent, adjusting the unit length of the grid and checking the quality of the grid;
s4, selecting a solver type, starting a solving model, and starting gravity influence;
s5, setting inlet and outlet boundary conditions: the inlet is a speed inlet, and the outlet is a pressure outlet;
s6, setting an inlet to use a first UDF function, and setting an outlet to be a pressure constant;
s7, setting parameters of injection of the particle phase injector, and setting gas phase parameters;
s8, setting the boundary type of the discrete phase: the inlet and outlet are set as escapes;
s9, the parameter E is included S 、E P 、v S 、v P The second UDF function of (3) is inserted into the discrete phase model; e S And E P Respectively the Young's modulus of the atmospheric particulates and the surface of the pipe wall; v. of S And v P Respectively the poisson ratio of the atmospheric particulates and the tube wall surface;
s10, setting solver parameters;
s11, opening a sample collector, and collecting samples of the wall surface, the air outlet and the air inlet;
s12, starting to solve, and finishing sample collection after calculation is converged;
s13, using ANSYS Fluent software to output a result and obtaining the deposition N of the atmospheric particulates in the human respiration process P Deposition rate σ and deposition position;
s14, checking air inflow, calculating a difference value of the flow rates of an air outlet and an air inlet by using a report function of an ANSYS flow, and reworking the model mesh if the difference value is too large; comparing the flow of the air inlet with a calculated value obtained by integrating the first UDF function, and if the difference value between the flow of the air inlet and the calculated value is too large, adjusting the grid of the air inlet;
s15, comparing the experimental result with the calculation result;
s16, if the calculation result is not consistent with the experiment result, modifying the parameter value of the first UDF function according to the physiological parameter measured by the experiment; according to the comparison between the calculation result and the experiment result, the parameter E in the second UDF function is corrected S 、E P 、v S 、v P And returning to step S9; if the calculation result is consistent with the experiment result, a prediction function is obtained;
s17, performing parameter E in a second UDF function on different types of pollution S 、E P 、v S 、v P Finding the corresponding E S 、E P 、v S 、v P To find out the deposition law of different pollutants.
2. The method for predicting deposition of atmospheric particulates in human lung of claim 1, wherein in step S4, the solver type is Pressure-Based and the time type is non-steady state; the open model is: readable-k-epsilon Model, single-coupled DPM Model.
3. The method according to claim 1, wherein in step S6, the first UDF function is established by: and establishing a speed self-defined function when the particles collide with the tube wall according to the physical collision process of the discrete phase particles and the trachea of the lung.
4. The method according to claim 1, wherein in step S6, the first UDF function is a custom function of intake air velocity and time, and is specifically:
Figure FDA0003793018930000031
in the above formula, V M At the maximum intake air amount, D 1 Is the diameter of the primary pipeline, T is the breathing period, and a is the breathing period adjustment coefficient.
5. The method according to claim 1, wherein in step S9, the second UDF function is specifically established as follows:
1) Establishing an atmospheric particulate deposition model according to the stress conditions of the discrete phase particles and the tracheal wall;
2) For the atmospheric particulates collided with the pipe wall, calculating the capture speed of the atmospheric particulates according to a capture model in the atmospheric particulates model; if the normal speed of the atmospheric particulates and the pipe wall is less than the capture speed, setting the state of the atmospheric particulates as capture; if the normal speed is greater than the capture speed, setting the state of the atmospheric particulates as reflection;
3) Judging the captured atmospheric particulate according to a leaving model in the atmospheric particulate deposition model; if the turbulent flow friction speed is greater than the critical shearing speed, the atmospheric particles are separated from the wall surface;
wherein: the atmospheric particulate deposition model is based on an EI-Batsh deposition model;
the capture model in the deposition model is as follows:
Figure FDA0003793018930000032
in the above formula, D P Is the aerodynamic diameter of the atmospheric particulate matter,
Figure FDA0003793018930000033
Figure FDA0003793018930000034
Figure FDA0003793018930000035
the critical capture rate of the atmospheric particulates is obtained; rho P Is the mass density of the atmospheric particulates; e S And E P Respectively the Young's modulus of the atmospheric particulates and the surface of the pipe wall; v. of S And v P Respectively the poisson ratio of the atmospheric particulates and the tube wall surface;
the leaving pattern in the deposition pattern was as follows:
Figure FDA0003793018930000041
in the above formula, W A The sticking coefficient depends on the properties of the atmospheric particulates and the surface of the pipe wall; ρ is the fluid mass density; k C Is the composite Young's modulus expressed as
Figure FDA0003793018930000042
6. The method of claim 1, wherein the method is used to predict deposition of atmospheric particulates in the lungs of a humanCharacterized in that, in the step S13, the deposition amount N P The deposition position is obtained by using samples function of an ANSYS flow self-contained device, the deposition position is obtained by using a partiletrack function of the ANSYS flow self-contained device, and the XY Plot function in options of the partiletrack is started to obtain an accurate position;
and the deposition rate σ:
Figure FDA0003793018930000043
N t is the intake of atmospheric particulates.
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