1. Environmental Engineering Lecture Note Week 11 (Transport Processes)
Joonhong Park
Yonsei CEE Department
CEE3330 Y2013 WEEK3

2. Transport Processes (II)
4.B Particle Motion
Drag on Particles
Gravitational Settling
Brownian Diffusion
4.C Mass Transfer at Fluid Boundaries
Mass-Transfer Coefficient
Transport across the Air-Water Interface
CEE May 8, 2007 Joonhong Park Copy Right

3. CEE3330-01 May 8, 2007 Joonhong Park Copy Right
Particle Motion
Drag on Particle
Gravitational Settling
Brownian Diffusion
CEE May 8, 2007 Joonhong Park Copy Right

4. Size of environmental particles
Fine mode
Coarse mode
Aerosol
Nucleation mode
Accumulation mode
Colloidal solids
Suspended solids
Hydrosol
Settleable solids
Clay
Silt
Sand
Soil
Virus
Bacteria
Microbial
Algae
10-3
10-2
10-1
100
101
102
Unit (micro meter)
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5. CEE3330-01 May 8, 2007 Joonhong Park Copy Right
Particle Motion
Drag on Particle
Drag Force
Reynolds no.
of particle
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6. Drag Coefficient (Cd) vs. Particlel Reynolds Number(Rep)
300
100 10 1
0.3
Stoke’s law
Cd=24/Re
Intermediate regime Cd
Newton’s law
Cd=0.445
Rep
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7. Fluid properties influencing drag force
Stoke’s law
(Rep < 0.3)
Drag force is a function of viscosity
Newton’s law
(1000 < Rep < 350,000)
Drag force is a function of fluid density
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8. Correction for Small Particles (dp< 1µm) in air
Cc = Cunningham slip correction factor
λg = the mean free path
(the average distance that a gas molecule travels
before colliding with another molecule.)
Ex. λg = micrometer at 293 oK and 1 atm
f = friction coefficient

9. Gravitational Settling (a particle is denser than fluid)
Terminal settling velocity (Vt) =
satisfying
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10. Gravitational Settling (a particle is lighter than fluid)
Terminal settling velocity (Vt) =
satisfying
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11. CEE3330-01 May 8, 2007 Joonhong Park Copy Right
Particle Motion
Brownian Diffusion (following Fick’s 1st Law)
Diffusivity (Stoke-Einstein relation)
k: Boltzmann’s constant
T: absolute temp.
f:fricktion coefficient
CEE May 8, 2007 Joonhong Park Copy Right
0.001 1

12. Comparing Particle Transport by Settling and Diffusion
Settling-air
0.03
Settling-water
Diffusion-air
Traveling
Distance
(cm)
Diffusion-water
3 x 10-5
micro-meter
When a particle is lager than 1 micro-meter, settling becomes dominant
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13. Inter-phase Mass Transfer
Y-direction
Phase 2 C
Inter-phase Mass Transfer
Boundary Layer Co
Phase 1
X-direction
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14. Mass-transfer coefficient
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15. CEE3330-01 May 8, 2007 Joonhong Park Copy Right
Film Theory Ci C
Well-mixed
fluid
Flux Lf
Stagnant
Fluid film
Boundary
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16. CEE3330-01 May 8, 2007 Joonhong Park Copy Right
Penetration Theory Ci C
Well-mixed
fluid
Flux t3 t2 t1
instantaneous Lf
Stagnant
Fluid film
Boundary
CEE May 8, 2007 Joonhong Park Copy Right

17. Water-Air Interface (Double-Layer Theory)Pi
P Partial Pressure
Turbulently mixed
zone
Flux
Air
Stagnant film layer La
Boundary Lw
Stagnant film layer
Turbulently mixed
zone
Water C Ci

18. CEE3330-01 May 8, 2007 Joonhong Park Copy Right

19. Reading Assignment Environmental Engineering & Sciences (EES)
4.B Particle Motion
Drag on Particles
Gravitational Settling
Brownian Diffusion
4.C Mass Transfer at Fluid Boundaries
Mass-Transfer Coefficient
Transport across the Air-Water Interface
CEE May 8, 2007 Joonhong Park Copy Right