Outline Outline 4 Electrostatics 4 Electrostatics 4 Particle - PowerPoint PPT Presentation

Outline Outline 4 Electrostatics 4 Electrostatics 4 Particle Charging 4 Particle Charging 4 Charged Particle Kinetic 4 Charged Particle Kinetic ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi Most aerosol particles carry some electrical charges Most aerosol particles carry some electrical charges − 2 2 exp{ n e / dkT } Boltzmann Boltzmann = f ( n ) ∞ Equilibrium Charge Equilibrium Charge ∑ − = q = Coulomb Coulomb 2 2 exp{ n e / dkT } q ne F E E Distribution Distribution Force Force = −∞ n Electric Charge Electric Charge 2 2 2 > µ e n e 0 . 02 d = − = × − = × − f ( n ) exp{ } 19 10 e 1 . 6 10 coul e 4 . 8 10 statcoul π dkT dkT qC 2 = πµ 0 . 24 0 . 05 n Particle = = Particle p c qE 3 Ud / C u Z = − > µ f ( n ) exp{ } 0 . 02 d c πµ Mobility Mobility 3 d π d d ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi 1

γ Average Number of Charge Average Number of Charge q ' q 1 = = γ = F q ' E ε ε π 2 4 r ∞ ∞ o dkT ∑ ∫ = ≈ ≈ > µ n | n | f ( n ) | n | f ( n ) dn 0 . 02 d π 2 e − ∞ − ∞ = ≈ µ n 2 . 36 d , d ( m ) − amp sec ε = × − γ 12 Permittivity Permittivity 8 . 859 10 q Point Point γ = π ε o − = 4 / volt meter E cgs cgs Charge Charge π 2 4 r 1 q ' q Coulomb’s Coulomb’s γ = π = × ε = γ = 9 4 F ( 9 10 ) Air Air 1 MKS MKS ε 2 ε ε Law Law r o ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi π ε − eZ n t 2 ( 1 ) 2 Ed π ∞ = i i + p dkT 2 n [ ]( 1 ) cgs cgs π + ε + = + 1 / 2 2 eZ n t 1 2 4 e n ln[ 1 ( ) n de t ] ∞ i i p ∞ i 2 2 e m kT i ε − 2 ( 1 ) 2 Ed = + → ∞ p n [ 1 ] as t ∞ ε + 2 4 e cgs cgs 8 3 p n ∞ t ~ 10 ion sec/ cm i ε p = 4 . 3 for Quartz ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi 2

p d u Equation Equation = + + m F F F of Motion of Motion D G E dt τ p d u τ = − + τ − f p q u u g E dt m τ p d u = + τ τ + = − f p u o u g q u u E o dt m ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi p Coulomb Coulomb ^ Image Polarization Image Polarization p d u ^ Force Force Force Force τ + = − Γ Force Force u 1 For u o || E dt Eq τ p p ^ u Γ = u = mu u 0 0 Γ >> τ For | | 1 , = − u p p Eq ^ Dipole Dipole = − Γ U m neglecting inertia Interactions Interactions ME 437/537 G. Ahmadi ME 437/537 G. Ahmadi 3