Environmental Engineering Lecture Note Week 11 (Transport Processes)

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Presentation transcript:

Environmental Engineering Lecture Note Week 11 (Transport Processes) Joonhong Park Yonsei CEE Department 2016. 5. 18 CEE3330 Y2013 WEEK3

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 CEE3330-01 May 8, 2007 Joonhong Park Copy Right

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

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) CEE3330-01 May 8, 2007 Joonhong Park Copy Right

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

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 0.1 0.3 1.0 10 100 1000 10000 Rep CEE3330-01 May 8, 2007 Joonhong Park Copy Right

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 CEE3330-01 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 oK and 1 atm f = friction coefficient

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

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

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 CEE3330-01 May 8, 2007 Joonhong Park Copy Right 0.001 1

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 CEE3330-01 May 8, 2007 Joonhong Park Copy Right

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

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

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

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 CEE3330-01 May 8, 2007 Joonhong Park Copy Right

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

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