PARTICOLATO FISICA AMBIENTALE 2 Antonio Ballarin Denti a.ballarindenti@dmf.unicatt.it

PARTICOLATOPARTICOLATO

FISICA AMBIENTALE 2

Antonio Ballarin Dentia.ballarindenti@dmf.unicatt.it

LE PARTICELLELE PARTICELLE

Volume fraction of aerosol particles in 4 quite different locationsVolume fraction of aerosol particles in 4 quite different locations

Stages in the absorption of gaseous Stages in the absorption of gaseous SOSO22 ina raindrop ina raindrop

Cattura di SO2 da parte di una goccia di Cattura di SO2 da parte di una goccia di pioggiapioggia

c (r > R, t = 0) = c∞

c (r→∞, t ) = c∞

c (R, t) = cs (t)=0

r ≤ Rr ≤ R

r = 0, t > 0r = 0, t > 0

t > 0t > 0

r ≤ Rr ≤ R

c (r, t = 0) = 0

c (R, t) = cs

c (r, t→∞ ) = cs

Cattura di SO2 da parte di una goccia di Cattura di SO2 da parte di una goccia di pioggiapioggia

Characteristic diffusion times in air and water for some drop sizesCharacteristic diffusion times in air and water for some drop sizes

τair

τdrop

2.5 × 10-2 2.5 × 10-4 2.5 × 10-6

102 10-21

R(m) 10-3(1 mm) 10-4 10-5 (10 μm)

DDgg = 10 = 10-5-5 m m2 2 ss-1-1 DDaa = 10 = 10-9-9 m m2 2 ss-1-1

Fluxes at the interface air-water drop. Fluxes at the interface air-water drop. The interface may be considered flat at x = 0The interface may be considered flat at x = 0

Cattura di SO2 da parte di una goccia di Cattura di SO2 da parte di una goccia di pioggiapioggia

Derivation of Stokes’lawDerivation of Stokes’lawFluid is flowing from bottom to top with a non-slip Fluid is flowing from bottom to top with a non-slip condition at the surface. On the left one finds the condition at the surface. On the left one finds the

general coordinate system, on the right the forces at general coordinate system, on the right the forces at the surface of the sphere. The drag is determinated by the surface of the sphere. The drag is determinated by the components of the pressure force and tangential the components of the pressure force and tangential

force in the direction of the flow.force in the direction of the flow.

LE PARTICELLELE PARTICELLEAttrito su una singola particellaAttrito su una singola particella