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Motion of Aerosol

Motion of Aerosol. Reading: Chap. 3.3-3.4. Newton’s Resistance Law and Stokes’ Law Cunningham Slip Correction Factor Settling Velocity, Mechanical Mobility Particle Acceleration Aerodynamic Diameter Settling Chamber Brownian Motion & Diffusion.

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Motion of Aerosol

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  1. Motion of Aerosol Reading: Chap. 3.3-3.4 • Newton’s Resistance Law and Stokes’ Law • Cunningham Slip Correction Factor • Settling Velocity, Mechanical Mobility • Particle Acceleration • Aerodynamic Diameter • Settling Chamber • Brownian Motion & Diffusion http://aerosol.ees.ufl.edu/aerosol_trans/section01.html Aerosol & Particulate Research Lab

  2. History Tim Tebow can be a good air pollution engineer because he knows how to control the movement of particles in the air ….. History: Galileo’s (1564-1642) experiment in Pisa tower Vp Newton’s Resistance Law: The force is proportional to the gas pushed away and the relative velocity between the sphere and the gas (negligible viscous force) CD = 0.44 for Rep > 1000 Aerosol & Particulate Research Lab

  3. Stokes Law: negligible inertial force compared to viscous force (Rep < 1) Reynolds Number: inertial force/frictional force Two major parameters: V & dp Plot CD as a function of Repfor Newton’s Law Plot CD as a function of Rep for Stokes’ Law Transition Regime Aerosol & Particulate Research Lab

  4. What is the max velocity of a particle to be in the Stokes regime? 1 mm, 10 mm, 100 mm (rg = 1.2 kg/m3; m = 1.81×10-5Pa•s) Aerosol & Particulate Research Lab

  5. Categorize aerosol movement based on interaction between the particle and gas molecules Ruler of aerosol movement: Mean free path of gas (l): average distance traveled by a gas molecule between successive collisions; 0.066 mm for air at STP Cunningham Slip Correction Factor: gas velocity at the surface of small particles is not zero --> slip 1 mm 0.1 mm (derivation for dp < 1 mm @ STP) Handout Appendix A11 http://aerosol.ees.ufl.edu/aerosol_trans/section06.html Aerosol & Particulate Research Lab

  6. Settling Velocity • When the drag force is equal and opposite to the gravitational force • Particle Mechanical Mobility ~ 0 What is the impact of considering Cc on a particle’s settling velocity? Why? What is the physical meaning of B? Does a smaller or a larger particle have larger mobility? http://onprogram.blogspot.com http://worldphotocollections.blogspot.com Aerosol & Particulate Research Lab

  7. Relaxation Time: indication of the time required for a particle to adjust/relax its velocity to a new condition of force Terminal/Settling Velocity Q: What other acceleration? (Appendix A11 or Figure 5-8 on p.9 or Figure 3.8 in text) (remember B is an intrinsic property of a given aerosol) Turbulent Regime Transition Regime Aerosol & Particulate Research Lab

  8. If flow regime is unknown because VTS is unknown --> K factor Laminar K< 3.3 Turbulent K > 43.6 For a 100 µm unit-density particle, which flow regime is applicable? Fig 5-8 on P.9 Can we clean the dust in this classroom by waiting them to settle down? How long will it take? Assume the particle size is: 1 mm, 10 mm, 100 mm. The room is 3 m high. Aerosol & Particulate Research Lab

  9. Aerosol & Particulate Research Lab

  10. Particle Acceleration • Newton’s law http://aerosol.ees.ufl.edu/aerosol_trans/section04.html FD=3VTSdp FD=3V(t)dp FG=mg FG=mg FG=mg t>3 V(t)=VTS t= V(t)=? t=0 V(t)=0 Aerosol & Particulate Research Lab

  11. Non-zero Initial velocity Stopping Distance For Re0 < 1 Stopping Distance and Time to Travel 95% of the Stopping Distance for Standard Density Spheres with an Initial Velocity of 10 m/s Small aerosols adapt to the new environment (i.e. following the flow well) in a very short time, almost instantly!!! Aerosol & Particulate Research Lab

  12. Aerodynamic Diameter • The Stokes diameter, ds, is the diameter of the sphere that has the same density and settling velocity as the particle. • The aerodynamic diameter, da, is the diameter of the unit density (0=1 g/cm3) sphere that has the same settling velocity as the particle. PM10 and PM2.5 are aerodynamic diameters. Why? Is optical diameter or aerodynamic diameter more relevant? Aerosol & Particulate Research Lab

  13. Horizontal Elutriator/Settling Chamber(Plug flow model: no radial or axial mixing) If monodisperse aerosols are uniformly distributed at the entrance, what is the collection efficiency as a function of VTS (dp)? Aerosol & Particulate Research Lab

  14. Brownian Motion & Diffusion http://galileo.phys.virginia.edu/classes/109N/more_stuff/Applets/brownian/brownian.html • The primary transport mechanism for small particles (< 0.1 m); Important when transport distance is small: e.g. filter, airway in human lung • Definition: • Brownian motion: irregular wiggling motion of a particle caused by random bombardment of gas molecules against the particle • Diffusion: the net transport of the particles from a region of higher concentration to a region of lower concentration Aerosol & Particulate Research Lab

  15. Fick’s First Law of Diffusion The net flux of aerosols (the net number of particles 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) driving force Fick’s Second Law of Diffusion The rate of loss of particles is proportional to the gradient of the flux. Aerosol & Particulate Research Lab

  16. Numbers on curves are values of Dt 1 Spread of particles over time and space • Solve 1-D equation Aerosol & Particulate Research Lab

  17. Solution Mean Square Displacement of particles Result: Stokes-Einstein Equation for Diffusivity How to have a larger diffusivity? Why? Air, water, universe? Aerosol & Particulate Research Lab

  18. Quick Reflection Aerosol & Particulate Research Lab

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