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# Single Particle Motion

Single Particle Motion. Reading: Chaps 3 &amp; 5. Want to be great athletes? Study aerosol science &amp; engineering because you surely need to know how to control particle movement in the air!. V.

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## Single Particle Motion

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1. Single Particle Motion Reading: Chaps 3 & 5 Want to be great athletes? Study aerosol science & engineering because you surely need to know how to control particle movement in the air!

2. V • 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 (sphere) for 103 < Rep < 2×105 Delivery van 0.04 Sports car 1.0 Airplane 0.25 ? • Reynolds Number: ratio of inertial forces to frictional forces (Chap.2.5) For a spherical particle, L = dp, Q: Choose a combination of dp and V when the Newton’s Law can be applied.

3. Stokes’ Law: negligible inertial force compared to viscous force (Rep < 1); in a laminar flow for a spherical particle • Assumptions used in solving Navier Stokes’ equation: • Incompressible flow (g = cons) • Constant motion (V = const) • Rigid sphere • Fluid velocity on the particle surface Q: How does FD change wrt V and dp in the laminar regime? Q: Under what scenario will you expect to apply Newton’s law instead of Stokes’ Law? Q: How does CD change wrt Re from 10-3 to 105?

4. Transition Regime

5. Settling Velocity • When the drag force is equal and opposite to the gravitational force • Particle Mechanical Mobility • Settling Velocity ~0 Q: What is the physical meaning of B? Q: Does a smaller or a larger particle have larger mobility?

6. 1 mm 0.1 mm Terminal Settling Velocity of unit-density spheres : mean free path (Chap 2.3) 0.066 mm for air @STP • Cunningham Slip Correction Factor: gas velocity at the surface of small particles is not zero --> slip (Re < 1) Q: So is the corrected VTS larger or smaller? Appendix A11 Q: How long do you have to wait for 0.1 mm particles to completely settle in this classroom (4 m high)?

7. Knudson Number Kn = 2/dp • A dimensionless number for the relative size of a particle in the system • Continuum regime: Kn << 1. Gas molecules striking the particle surface are strongly affected by those leaving. • Free Molecular regime: Kn >> 1. The gas molecule movement is rarely affected by the presence of the particle. Q: Kn for a 10 mm particle? In which regime?

8. Nonspherical Particles • Dynamic shape factor: the ratio of the actual resistance force of the nonspherical particle to the resistance force of a sphere having the same volume and velocity • Drag force • Settling velocity de: equivalent volume diameter Q: Does an irregular particle experience a larger or smaller force (compared to a particle with the same volume)?

9. 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. Cunningham factor should be included if dp < 1 mm Q: Can we design an instrument by applying settling velocity?

10. Horizontal Elutriator (settling chamber, spectrometer) Q: Can it be vertical? Q: Can we make the acceleration > g?

11. Vertical Elutriator http://getdomainvids.com

12. Centrifuge Separator Cheng et al., 1988

13. FD=3VTSdp FD=3V(t)dp Particle Acceleration • Newton’s law  = mB : relaxation time Q: What is the physical meaning of relaxation time? FG=mg FG=mg FG=mg t=0 V(t)=0 t= V(t)=VTS t>3 V(t)=VTS

14. Non-zero Initial velocity Displacement Stopping Distance Time for unit density particles to reach their terminal velocity • An aerosol can adjust itself very quickly to a new environment!!!

15. Inertial Impaction • Stokes number: the ratio of the stopping distance of a particle to a characteristic dimension of the obstacle • For an impactor Q: Stk << 1? Stk >> 1? http://aerosol.ees.ufl.edu/

16. Assumptions of Simplified Theory: Uniform streamlines in the jet Streamlines are arcs of a circle with the centers at A h’

17. Stk50 for 2 impactors

18. Determine dp50 Q: How to collect smaller particles using an impactor? Downstream pressure (Chap 3.4, Pdin kPa, dp in um) Q: (low pressure impactor) Advantages? Disadvantages? Q: Again, how to collect smaller particles using an impactor?

19. Cascade Impactor Aerosol flow In http://aerosol_beta.ees.ufl.edu/instrumentation/section04.html Clean air out