Environmental Engineering Lecture Note Week 11 Transport Processes

Environmental Engineering Lecture Note Week 11 (Transport Processes) Joonhong Park Yonsei CEE Department 2016. 5. 18 CEE 3330 Y 2013 WEEK 3

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 3330 -01 May 8, 2007 Joonhong Park Copy Right

Particle Motion Drag on Particle Gravitational Settling Brownian Diffusion CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Size of environmental particles Coarse mode Fine mode Aerosol Nucleation mode Hydrosol Accumulation mode Colloidal solids Suspended solids Settleable solids Clay Soil Silt Virus Microbial Sand Bacteria Algae 10 -3 10 -2 10 -1 100 Unit (micro meter) CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right 101 102

Particle Motion Drag on Particle Drag Force Reynolds no. of particle CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Drag Coefficient (Cd) vs. Particlel Reynolds Number(Rep) 300 100 Stoke’s law Cd=24/Re Cd Intermediate regime 10 Newton’s law Cd=0. 445 1 0. 3 0. 1 0. 3 1. 0 10 100 Rep CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right 10000

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 CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

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 = 0. 066 micrometer at 293 o. K and 1 atm f = friction coefficient

Gravitational Settling (a particle is denser than fluid) Terminal settling velocity (Vt) = satisfying CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Gravitational Settling (a particle is lighter than fluid) Terminal settling velocity (Vt) = satisfying CEE 3330 -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 CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Comparing Particle Transport by Settling and Diffusion Settling-air 0. 03 Settling-water Diffusion-air Traveling Distance (cm) Diffusion-water 3 x 10 -5 0. 3 0. 7 micro-meter When a particle is lager than 1 micro-meter, settling becomes dominant CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Inter-phase Mass Transfer Y-direction Phase 2 C Boundary Layer Co Inter-phase Mass Transfer Phase 1 X-direction CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Mass-transfer coefficient CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Film Theory C Ci Flux Lf Well-mixed fluid Stagnant Fluid film Boundary CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

Penetration Theory C Ci Flux t 3 Well-mixed fluid t 2 t 1 Lf instantaneous Stagnant Fluid film Boundary CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right

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

CEE 3330 -01 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 CEE 3330 -01 May 8, 2007 Joonhong Park Copy Right