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