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

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Environmental Engineering Course Note 8 (Transport Processes II) Joonhong Park Yonsei CEE Department CEE3330 Y2013 WEEK3

CEE 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

Size of environmental particles CEE May 8, 2007 Joonhong Park Copy Right 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

CEE May 8, 2007 Joonhong Park Copy Right Particle Motion Drag on Particle Gravitational Settling Brownian Diffusion

CEE May 8, 2007 Joonhong Park Copy Right Particle Motion Drag on Particle Drag Force Reynolds no. of particle

CEE May 8, 2007 Joonhong Park Copy Right Drag Coefficient (Cd) vs. Particlel Reynolds Number(Re p ) Re p Cd Stoke’s law Cd=24/Re Newton’s law Cd=0.445 Intermediate regime

CEE 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

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 = micrometer at 293 oK and 1 atm f = friction coefficient

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

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

CEE 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

CEE May 8, 2007 Joonhong Park Copy Right Comparing Particle Transport by Settling and Diffusion micro-meter Traveling Distance (cm) Diffusion-air Diffusion-water x Settling-air Settling-water When a particle is lager than 1 micro-meter, settling becomes dominant

CEE 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

CEE May 8, 2007 Joonhong Park Copy Right Mass-transfer coefficient

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

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

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

CEE May 8, 2007 Joonhong Park Copy Right

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