1. Aerosol Physics and Particle Control

2. PM
Particle Shape:
-can be found in spherical, rectangular, fiber, or many other irregular shape
-shape is important. Affects:
-particle behavior
-transportation
-control technology
-effect on the respirotary system (fiber shaped particles particularly harmful to the lungs when they are inhaled, since it is more difficult to remove once they are settled or have clung to air ways.

3. PM
Muallimköy ortam havasından toplanan partiküllere ait SEM fotorafı

4. Particle Size The most important parameters since it affects: Behavior
Transport
Health effects
Control technology selection
Very large range from 0.01 mm to 100 mm
A dust fall following a volcano contains large particles in the range of millimeters that can settle down in a few hours and smal particles (um range) can stay airborne for months.

5. Human Respiratory System
3 major regions:
Head airways region
Tracheobronchial region (thoracic)
Pulmonary or alveolar region
O2 –CO2 transfer take place in the pulmonary region. For an adult total area of this gas exchange region is 75 m2 and total length of the pulmonary vessels is about 2,000 km.
An adult person breathes about times per minute and inhales about liters of air/min.

6. Particle Size Categories
Based on behavior in the human respiratory system 3 categories can be defined:
Inhalable particles
Thoracic particles
Respirable particles

7. Particle Size Categories
Size Range
Total
All sizes of particles in the air of concern
Inhalable (inspirable)
100 mm ≥
Thoracic
10 mm ≥
Respirable
4 mm ≥
PM10
PM2.5
2.5 mm ≥

8. Inhaled Particle Deposition in Human Respiratory System
total
Head airways
Upper bronchial
Lower bronchial
Alveolar
Deposition of Inhaled Particles in the Human Respiratory Tract and Consequences for Regional Targeting in Respiratory Drug Delivery, Joachim Heyder

9. Size Distribution Particle Diameter
The highly irregular shape together with the different densities depending on the composition of the particle complicates its size definition.
A particle’s size refers to its diameter
There are various definitions for the diameter.

10. Size Distribution Particle Diameter Equivalent volume diameter
Stokes diameter
Aerodynamic diameter

11. Particle Diameter
Equivalent volume diameter (de): diameter of a sphere that would have the same volume and density as the particle
Assume that following irregular shape has a volume of V, de will be the diameter of sphere whose volume equals to V.
20 mm

12. Particle Diameter
2. Stokes diameter (ds): diameter of the sphere that would have the same density and settling velocity as the particle.

13. Particle Diameter
3. Aerodynamic diameter (da): diameter of the sphere with a standard density (1.000 kg/m3) that would have the same settling velocity as the particle

14. Particle Diameter
de only standardizes the shape of the particle by its equivalent spherical volume
ds standardizes the settling velocity of the particle but not the density
da standardizes both the settling velocity and the particle density. Thus da is a convenient variable to use to analyze particle behavior and design of particle control equipment

15. Particle Size Distribution

16. How to display particle size distribution?
0.02
0.20

17. When shown as written in the table, we see that number of particles with diameter between um equals to particles with diameter between 0.1 and 0.3 um however, diameter range in the first one is only 0.02 um while in the second is 0.2 um (1000 times bigger than the first range)
0.02
0.20

18. ni = the value of the number size distribution function (#/μm/cm3)
The area of each rectangular gives the number of particles between Dp2 and Dp1 (Ni)
Ni = ni ΔDp
ΔDp = Dp2-Dp1 (μm)

20. Infinitely small ΔDp  dDp
Let n(Dp) denote the continous function of size distribution
n(Dp) dDp = Particle concentration with the diameters between Dp and Dp + dDp (#/cm3)
n(Dp) (/um/cm3)
Dp, um
dDp
Typical display of distribution function n(Dp)

21. Normalized Size Distributions
Normalized size distribution ( ) can be obtained by:
The fraction of particles with diameters between Dp and Dp + dDp to the total number of particles in one cm3 air
Unit of normalized number distribution: μm-1

22. Surface Area,Volume and Mass Distributions
Surface area distribution ns(Dp)
Mass distribution m(Dp)
Y: Characteristic function

23. Characteristic Functions for Particle Size Distributions (Y(Dp))*
Number of particle (Np) 1
Length (Lp) Dp
Surface area (Sp)
πDp2
Volume (Vp)
1/6πDp3
Mass (mp)
1/6πDp3ρp
*assuming particles are spherical

24. Logaritmic Size Distributions
Since particles’ sizes vary over a very large range, use of logaritmic scale for Dp is more appropriate.

25. Log Scale Size Distributions
Number of particles with diameters between logDp and logDp + dlogDp

26. Number
Surface
Volume
Seinfeld ve Pandis

27. Parameters of particle size distributions
Mean: Averaged diameter of the sampled particle stream
(number distribution)
N= Total number of particles
(mass distribution)
mT = Total mass of particles

28. 2. Median: taneciklerin %50’sinin büyük, %50’sinin küçük olduğu çap değeri
Mode:
The most frequent diameter

29. Beside mean values, it is important to know the how distribution differs from these mean values.
For all three distribution shown above, the mean diameters are the same while distribution width is different.

30. Variance Standard Deviation=
Standard deviation: a measure of the distrubition width
Standard Deviation=

31. Normal (Gaussian) Distribution
The mean of the population
Normal Distribution Function

32. Normal (Gaussian) Distribution
Standard deviation (s) gives the characteristic width of the symetric number size distribution. 68.2% of the particles are between dp,mean –s and dp,mean + s, 84.1% of it with diameters smaller than dpmean+s , and 15.9% of it with diameters smaller than dpmean-s.

33. Are the particles in various air streams show a normal distribution?

34. They mostly show a lognormal distribution
Log-Normal Dağılım
They mostly show a lognormal distribution
Dp,g=0.4μm
σg=2.5
Asıltı parçacıkların %68.2’si Dpg/σg ile Dpgσg arasındadır.
For lognormal distributions,
Dpg =Dp,median

35. Geometrik Ortalama ve Geometrik Standart Sapma

36. Tanecik Boyut Dağılımının Log-Olasılık Kağıtta Gösterimi
taneciklerin %50’sinin küçük olduğu çap
(Dp,50)
Çap, um
Belirtilen Boyuttan Daha Küçük Olma Yüzdesi

37. Tanecik Boyut Dağılımının Log-Olasılık Kağıtta Gösterimi
Eğer dağılımdan hesaplanan noktalar bir doğru oluşturuyorsa dağılımın log-normal olduğu söylenebilir.
Tane sayısı, alanı,hacmi veya kütlesi için oluşturulabilir ve her dağılım için %50’sinin küçük olduğu çap bulunabilir.
Örnek: Dpg = 0.5 mm ise, bu taneciklerin %50sinin bu çaptan küçük olması demektir. 100 tanecik varsa toplam , 50’sinin çapı 0.5 mm’nin altındadır.
Çap, um
Belirtilen Boyuttan Daha Küçük Olma Yüzdesi

38. Örnek
Tane sayısı (n(Dp) ve yüzey alan boyut dağılımını çizin (ns(Dp). Dağılımları karşılaştırın.
Bu örneklenmiş asılı taneciklerin log-normal bir dağılım gösterdiği söylenebilir mi?

41. b) Bu dağılım log-normal mi?

42. σg=Dp,84.1/Dp,50 = 2.0
0.16
Dpg=0.08

43. Moudi Impactor for Mass Size Distribution

44. Optical Particle Counter

45. Differential Mobility Analyzer

46. Aerodynamic Aerosol Sizer (APS)

47. Motion of Particles in a Fluid
In all particle control technologies, particles are separated from the surrounding fluid by the application of one ore more forces:
-gravitational
-inertial
-centrifugal
-electrostatic
Those forces cause the accelarate the particles away from the direction of the mean fluid flow, toward the direction of the net force
The particles must then be collected and removed from the system to prevent ultimate re-entrainment into the fluid
Therefore we need to know the dynamics of particles in fluids

48. Motion of Particles in a Fluid

49. Drag Force FD = CDAppFv2r FD=Drag force, N CD=Drag coefficient
Ap=Projected area of particle, m2
pF=Density of fluid, kg/m3
vr= relative velocity, m/s
Drag coefficient must be determined experimentally since CD = f(particle shape and the flow regime characterized by Reynolds number)

50. Stokes’ Law

51. Motion of Particles in a Fluid

52. Motion of Particles in a Fluid

53. Motion of Particles in a Fluid

54. Motion of Particles in a Fluid

55. Motion of Particles in a Fluid
Note: Continous Fluid
A continuum is a region of spacee where charactheristic flow scales L are large enough that properties like density and velocity can be assumed to vary smoothly and therefore have point values.
Characteristic scale in diffusion or sedimentation for an aerosol particle is its diameter
A continuum can be assumed if d
N: number of molecules per unit volume.
In water N is about 3.3x1028/m3, in air N is 2.5x1025 /m3. It is almost safe to assume a continuum in liquids but not in gases.

56. Motion of Particles in a Fluid
Note: Continous Fluid
So does the aerosol particle sense a continuum or a series of discrete bombardements by the air molecules? This can be judged by calculating Knudsen number. d
When the Knudsen number is much less than unity (Kn<<1) a continuum can be assumed.

57. Motion of Particles in a Fluid

58. Motion of Particles in a Fluid
dp>0.1 um
C=1+2.52l/dp

59. Motion of Particles in a Fluid
If STP condition is not valid the value of l would change. STP: STP is 0 °C (32 °F or 273 Kelvin) and 1 atm ( kPa, 14.7 PSI, 760 mmHg)
Example:
At the top of a mountain, the atmospheric pressure is measured as 70 kPa, and T as -20C. What would the error of the slip correction factor be for a 0.3 um particle if the effect of P and T on l is ignored?
Solution:
Without considering the effect of T and P
C= l/dp = 1.55
When the effect of Pa nd T is taken into account:
= P0T/PT0l0 =1.34l0

60. Motion of Particles in a Fluid Re>0.1

61. Motion of Particles in a Fluid

62. Motion of Particles in a Fluid

63. Motion of Particles in a Fluid

64. Example
A grain of concrete dust particle is falling down onto the floor through room air. The particle diameter is 2 um and the particle density is 2500 kg/m3. Assuming the room air is still, determine the terminal settling velocity of the particles. The room air is at standard conditions.

65. Solution
First calculate the slip correction factor for the 2 um particle.
At STP air viscosity=1.81x10-5 (Ns/m2), air mean free path l=0.066 um and air density p=1.2 kg/m3
C = l/dp=1.08
vt = ppdp2gC/18m= m/s=0.26 mm/s

66. Nonspherical Particles and Dynamic Shape Factor
Most particle in practice are nonspherical. Particle dynamic shape factor is defined as the ratio of the actual resistance force of a nonspherical particle to the resistance force of a spherical particle that has the same equivalent volume diameter (de) and the same settling velocity as the nonspherical particle.
Shape factor = FD/3pmvtCde
Where FD is the actual drag force exerted on the nonspherical particle and C is the slp correction factor for de. The dynamic shape factor is always greater than 1 except for certain streamlined shapes .

67. Nonspherical Particles and Dynamic Shape Factor
Dynamic Shape Factor,x
Sphere
1.00
Cube
1.08
Fiber
1.06
Clustered Spheres
2 chain
1.12
3 chain
1.27
5 chain
1.35
10 chain
1.68
3 compact
1.15
Dust
Bituminous coal
Quartz
1.36
Sand
1.57
Nonspherical Particles and Dynamic Shape Factor

68. Aerodynamic Diameter
In reality it is extremely difficult to measure or calculate the equivalent volume diameters and shape factors.
Thus we need an equivalent diameter that can be physically determined and can be used to characterize the particle behavior
Aerodynamic diameter, da, is defined as the diameter of a sphere with unit density (1000 kg/m3) and the same settling velocity as the particle concern.

69. Aerodynamic Diameter
Where Cca and Cce are slip correction factors for da and de, respectively. p0=1000 kg/m3
For nonspherical particles,da then:
For spherical particles:

70. Aerodynamic Diameter The aerodynamic equivalent sphere
da=15.2 mm
rp=1000 kg/m3
An irregular particle
de =10 mm
rp = 3000 kg/m3
c =1.3
vt:= m/s
vt:= m/s

71. Aerodynamic Diameter
Particles with dp > 3 mm, the slip effect is negligible so:
for nonspherical particles, (de>3 mm)
for spherical particles, (dp>3 mm)

72. Aerodynamic Diameter
For particles with diameter smaller than 3 mm, slip effect must be considered.
For non-spherical particles and 0.1 mm<de<3 mm
Aerodynamic diameterfor particles with diameter smaller than 0.1 mm can be solved using iteration methods. In general those particles behave like gases for which diffusion transport becomes more important than aerodynamic behavior.

73. Nonsteady State Particle Motion
settling velocity

74. Nonsteady State Particle Motion

75. Nonsteady State Particle Motion

76. Nonsteady State Particle Motion

77. Nonsteady State Particle Motion

78. Nonsteady State Particle Motion
Stopping distance of a particle in a gas flow: a simple means of explaining impaction, answers how important a particle’s inertia is, relative to the viscous effects of the fluid through which it moves
Collection of particles (when a flowing fluid approaches a stationary object such as a fabric filter thread, a large water droplet, or a metal plate the fluid flow streamlines will diverge around that object) on a stationary object occur with three different mechanisms Impaction, interception, and diffusion:

79. Nonsteady State Particle Motion
Now assume a sphere in the Stokes regime is projected with an initial velocity of V0 into a motionless fluid and ignore all but drag force:
Take equaiton 3 but assume no gravitational and buoyoncy force:

80. Nonsteady State Particle Motion

81. Nonsteady State Particle Motion
Above equation is valid only for Stokes region. When Rep>1, the stopping distance is shorter than is predicted by this equation since drag force increases as the Rep increases. This increase in drag force attenuates the velocity of the particle, and hence reduces the stopping distance.
Since the Rep is proportional to the particle velocity and the drag force is proportional to the V2, it is extremely difficult to obtain stopping distance outside of Stokes region. Mercer (1973), proposed an emprical equation to calculate S within %3 accuracy.
(for 1<Rep0<1500)

82. Nonsteady State Particle Motion
If r’ is small, S (xstop) is also small. For instance if a 1 um particle with unit density is projected at 10 m/s into air, it will stop after traveling 36 um
An impaction parameter NI can be defined as the ratio of the stopping distance of a particle (based on upstream fluid velocity) to the diameter of the stationary object, or
NI=xstop/d0
If NI is large most of the particles wil impact the ojbect. If NI is very small most of the particles will follow the fluid flow around the object.

83. Nonsteady State Particle Motion

84. Example 2
Calculate the stopping distance of a particle with an aerodynamic diameter of 20 mm in still air. Assume the initial velcoity of the particles is 5 m/s. What would the error be if the particle motion were assumed to be in Stokes region?

85. Solution The initial particle Reynolds number: Since Re>1,
S = m

86. Solution If the particle were assumed to be in Stokes region, then S
The error then would be
/0.0046=33%