Coagulation - 4/8/10 Aerosol & Particulate Research...

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Unformatted text preview: 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research 11 Coagulation PbO-SiO2-PbSiO3 composite AEROSIL from Degussa, Inc. Q: How is rain droplet formed? Why is it larger in a thunderstorm? Reading: Chap 12 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research 22 Q: What are the possible external forces? Agglomeration/Aggregation (if particles do not merge) Coalescence (sintering) Q: What are the effects of coagulation on aerosol size distribution? Definition : The process whereby aerosol particles collide with one another due to a relative motion between them and adhere to from larger particles Thermal Coagulation : due to Brownian motion Kinematic Coagulation : due to external forces Q: Any difference if solid or liquid particles coagulate? Q: Do solid particles stay agglomerated? 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research 33 Collision Frequency Function (Population Balance) Rate of formation of size k particle ( 29 j i j i ij n n N , = = + k j i ij N 2 1 Rate of removal of size k particle = 1 i ik N Net rate of size k particle ( 29 ( 29 = = + = = +- =- = 1 1 , , 2 1 2 1 i i k i k k j i j i j i i ik k j i ij k n n n n N N dt dn Collision Frequency Q: What factors affect the frequency? ni : number concentration of size i particle 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research 44 Continuous Distribution Function Collision rate ~ ) ~ ( ) ( ) ~ , ( d d n n Formation in range d ( 29 d d n n -- ~ ) ~ ( ) ~ ( ~ , ~ 2 1 Loss in range d ( 29 d d n n ~ ) ( ) ~ ( , ~ Net rate of formation of particles of size ( 29 ( 29 ( 29 d d n n d d n n t nd - -- = ~ ) ( ) ~ ( , ~ ~ ) ~ ( ) ~ ( ~ , ~ 2 1 ( 29 ( 29 ~ ) ( ) ~ ( , ~ ) ~ ( ) ~ ( ~ , ~ 2 1 d n n d n n t n --- = 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research 55 Brownian Coagulation Ficks second law of diffusion (for spherical coordinate) + = = r n r r n D r r r n r D t n 2 ) / ( 2 2 2 2 Initial conditions? ) , ( n r n = Boundary conditions? ) , ( ) , 2 ( n t n t d d n pj pi = = + Solution +- +- = - + + +- = +- Dt d d r erfc r d d n d r d d r d d n t r n pj pi pj pi Dt d d r pj pi pj pi pj pi 2 2 / ) ( 2 1 ) exp( 2 1 ) , ( 2 2 / ) ( 2 Ref: Chap 10 in Atmospheric Chemistry and Physics of Air Pollution, Seinfeld, J. H., John Wiley & Sons , 1986 erf(x) + erfc(x) = 1 4/8/10 Aerosol & Particulate Research 4/8/10 Aerosol & Particulate Research...
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This note was uploaded on 09/11/2011 for the course ENV 6130 taught by Professor Wu during the Spring '08 term at University of Florida.

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Coagulation - 4/8/10 Aerosol & Particulate Research...

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