1. Environmental Engineering Course Note 8 (Transport Processes II) Joonhong Park Yonsei CEE Department 2015. 5. 20 CEE3330 Y2013 WEEK3

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

3. Size of environmental particles CEE3330-01 May 8, 2007 Joonhong Park Copy Right 10 -3 10 -2 10 -1 10 0 10 1 10 2 Unit (micro meter) Aerosol Hydrosol Soil Microbial Fine mode Coarse mode Nucleation modeAccumulation mode Colloidal solidsSuspended solids Settleable solids Clay Silt Sand Virus Bacteria Algae

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

5. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Particle Motion Drag on Particle Drag Force Reynolds no. of particle

6. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Drag Coefficient (Cd) vs. Particlel Reynolds Number(Re p ) 0.1 0.3 1.0 10 100 1000 10000 300 100 10 1 0.3 Re p Cd Stoke’s law Cd=24/Re Newton’s law Cd=0.445 Intermediate regime

7. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Fluid properties influencing drag force Stoke’s law (Re p < 0.3) Newton’s law (1000 < Re p < 350,000) Drag force is a function of viscosity Drag force is a function of fluid density

8. Correction for Small Particles (d p < 1µm) in air C c = Cunningham slip correction factor λ g = the mean free path (the average distance that a gas molecule travels before colliding with another molecule.) Ex. λ g = 0.066 micrometer at 293 oK and 1 atm f = friction coefficient

9. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Gravitational Settling (a particle is denser than fluid) Terminal settling velocity (V t ) = satisfying

10. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Terminal settling velocity (V t ) = satisfying Gravitational Settling (a particle is lighter than fluid)

11. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Particle Motion Brownian Diffusion (following Fick’s 1 st Law) Diffusivity (Stoke-Einstein relation) k: Boltzmann’s constant T: absolute temp. f:fricktion coefficient 0.001 1

12. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Comparing Particle Transport by Settling and Diffusion 0.3 0.7 micro-meter Traveling Distance (cm) Diffusion-air Diffusion-water 0.03 3 x 10 -5 Settling-air Settling-water When a particle is lager than 1 micro-meter, settling becomes dominant

13. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Inter-phase Mass Transfer Phase 1 Boundary Layer Inter-phase Mass Transfer X-direction Y-direction Phase 2 CoCo C

14. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Mass-transfer coefficient

15. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Film Theory Ci C Well-mixed fluid Stagnant Fluid film Boundary Flux Lf

16. CEE3330-01 May 8, 2007 Joonhong Park Copy Right Penetration Theory Ci C Well-mixed fluid Stagnant Fluid film Boundary Flux Lf t3 t2 t1 instantaneous

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

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