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Brownian Motion & Diffusion

Brownian Motion & Diffusion. Reading: Chap7. HISTORY

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Brownian Motion & Diffusion

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  1. Brownian Motion & Diffusion Reading: Chap7 HISTORY In 1827, English botanist Robert Brown noticed that pollen grains suspended in water jiggled about under the lens of the microscope, following a zigzag path. Even more remarkable was the fact that pollen grains that had been stored for a century moved in the same way. Magic? http://www.michaelorgan.org.au/robertbrown.jpg http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html Q: Observation?

  2. Definition: • Brownian motion: irregular wiggling motion of a particle caused by random bombardment of gas molecules against the particle • Diffusion: the net transport of particles from a region of higher concentration to a region of lower concentration • The primary transport mechanism for smallparticles (< 0.1 m); Important when transport distance is small: e.g. filter, airway in human lung, loss in sampling path

  3. Fick’s First Law of Diffusion • The net flux of aerosols (the net number of particle traveling through a unit area per unit time) is proportional to the concentration gradientJ: flux (#/area/time)D: diffusion coefficient (area/time)n: particle number concentration (#/cm3)

  4. Fick’s Second Law of Diffusion A’ A B B’ D’ D C C’

  5. Spread of particles over time and space 1/16 Numbers on curves are values of Dt 1/2 1

  6. Solution • Solve 1-D equation (normal distribution!) Mean Square Displacement of particles Q: Why not mean displacement? Recall Mean Surface Area Q: How does xrms depend on time?

  7. Stokes-Einstein Equation for Diffusion Coefficient HISTORY The first mathematical theory of Brownian motion was developed by Einstein in 1905. For this work he received the Nobel prize Assumptions: • the Brownian motion of an aerosol is equivalent to that of a giant gas molecule; the kinetic energy for aerosol Brownian motion is the same as the gas molecules (KE=3/2KT) • the diffusion force on a particle is equal to the friction force for particles greater than the mean free path of air Q: What are the parameters that affect an aerosol’s diffusivity?

  8. Particle Mean Free Path Mean thermal velocity (Chap. 2.2.2-2.3) Particle mean free path aerosol Gas molecule

  9. Diffusional Deposition Aerosols adhere when they hit a surface. Ex. A vertical surface in a infinitely large volume of aerosol Solution: Q: What if dp is larger?

  10. Deposition Rate General form of the concentration profile near a wall • Concentration gradient at the surface • Using Fick’s First Law • Integrating over time • Deposition velocity

  11. Q: Which mechanism (diffusion and gravitational settling) is more important to deposit particles?

  12. Penetration Tube • Dimensionless deposition parameter • Penetration Rectangular channel (h: distance between plates) tube rectangular channel

  13. Penetration versus deposition parameter for circular tubes and rectangular cross-section channels Q: How does P change if the tube diameter doubles while the volume flow rate remains the same? Why?

  14. L L W h dt • Diffusion Battery: tube bundle; parallel plate. Same equation for a single long tube or by cutting it into n parallel tubes each carrying 1/n of the total flow Penetration for an aerosol flowing through a tube (1m length) at 3 laminar flow rates

  15. Screen-type Diffusion Battery/Classifier Aerosol Measurement, Ed. Willeke, K. & Baron, P. A., 1993.

  16. Aerosol Measurement, Ed. Willeke, K. & Baron, P. A., 1993.

  17. Diffusion Denuder Aerosol Measurement, Ed. Willeke, K. & Baron, P. A., 1993.

  18. Honeycomb Denuder To pump Inlet http://www.rpco.com/products/ambprod/amb3500/

  19. Diffusion Dryer http://www.tsi.com/en-1033/segments/particle_instruments/2216/diffusion_dryer.aspx TSI Instruction Manual: Model 3306

  20. Reflection

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