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# Single - Single Particle Motion Reading Chaps 3 5 Want to...

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09/13/11 1 Aerosol & Particulate Research Laboratory 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!

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09/13/11 2 Aerosol & Particulate Research Laboratory 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) V d dt dm p g 2 4 π ρ = 2 2 8 V d C F p g D D ρ π = Reynolds Number : ratio of inertial forces to frictional forces (Chap.2.5) μ ρ = = L F F g f I p V Re For a spherical particle, L = d p , V Delivery van 0.04 Sports car 1.0 Airplane 0.25 Q: Choose a combination of d p and V when the Newton’s Law can be applied.
09/13/11 3 Aerosol & Particulate Research Laboratory Stokes’ Law : negligible inertial force compared to viscous F Vd D p = 3 πμ p D C Re 24 = Q: How does F D change wrt V and d p in the laminar regime? Q: Under what scenario will you expect to apply Newton’s law instead of Stokes’ Law? Q: How does C D change wrt Re from 10 -3 to 10 5 ? Assumptions used in solving Navier Stokes’ equation: Incompressible flow ( ρ g = cons) Constant motion (V = const) Rigid sphere Fluid velocity on the particle surface

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09/13/11 4 Aerosol & Particulate Research Laboratory Transition Regime + = 6 Re 1 Re 24 3 / 2 p p D C
09/13/11 5 Aerosol & Particulate Research Laboratory Settling Velocity When the drag force is equal and opposite to the gravitational force Particle Mechanical Mobility Settling Velocity F F mg Vd d g D G p p g p = = = - 3 6 3 π μ ρ ρ π ( ) 1 Re & 1 for 18 2 < = m d g d V p p p TS μ μ ρ B V F d d m D p p = = 1 3 1 πμ μ for V F B TS G = Q: What is the physical meaning of B ?

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