Air / Water Gas ExchangeThe distribution of a chemical across the air-water interface between the atmospheric gas phase and the water dissolved phase

•Equilibrium transfer of organic chemical between Air and WaterKH = Pa / w Cw

Appropriate for:Exchange between air and falling raindrop (over ~10 m fall)Low MW organic gases exchanging between peat water and bubbles

(in wetlands and marshes)Confined headspace over a solutionSheltered systems with more or less constant water and atmospheric

conditionsInappropriate for :

Large LakesFlowing riversSpills in both rivers and lakesOceans ( sometimes ! )In these you must consider Mass Transport (absolute and net fluzes)

Processes of Air / Water Exchange

Depiction of the physical processes responsible for the movement of chemicals through four zones spanning an intact “air-water” interface (i.e. no bubbles or aerosols).

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Processes of Air / Water Exchange

“Little” Mixing: Stagnant, 2-film model“More” Mixing: surface renewal modelWave Breaking: intense gas transfer ( breaking bubbles)

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Stagnant Boundary Layer Model of Air / Water Exchange –Whitman Two Film Model

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Two Film Model

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Net Flux = Kol * (Cw – Ca/H*)

resistance to transport * Concentration gradient relative to equilibrium

H* is “dimesnionless” Henry’s Law Constant at ambient temperature

1/ Kol = ( 1/ Kw + 1/ (Ka H*) )

= (1 / Dw / zw) + (1/ Da/ za H*)

where Dw = diffusivity in water Da = diffusivity in air zw = water film thickness za = air film thickness

un-measurable parameters: zw, za

Two Film Model- Continued

Fw = - Dw ( Cw/a – Cw ) / zw

So, at steady state:

Fw = - Dw ( Cw/a – Cw ) / zw = -Da (Ca – Ca/w) / za = Fa

Fluxtotal= Fw = Fa

since: KH’ = Ca/w / Cw/a ( mol / Lair / mol / Lwater)

then: Dw (Cw-Cw/a) / zw = Da (KH’ Cw/a- Ca) za

Cw/a = ( ( Dw / zw) + ( Da / za) Ca ) / ( ( Dw / zw) + ( Da KH’ / za ) )

Foverall = 1 / ( zw / Dw ) + (za / Da KH’) * ( Cw- Ca / KH’) mass transfer coefficient (cm/hr) * Conc. gradient

Fnet= (+) then water ====> air b/c (Cw > Ca / KH’)Fnet = (-) then air ====> water b/c (Cw < Ca / KH’)

Two Film Model- “Velocities”

Fluxtotal= vtot * ( Cw – Ca/ KH’)

mol m-2 sec-1 = m sec-1 * mol m-3

Defining “Partial Transfer Velocities:

vw = Dw / zw & va = Da / za

1 / vtot = 1 / vw + 1 / va KH’

Resistance analogy:1 / Rtot = 1 / Rw + 1 / Ra

Transfer dominated by layers:

vw << va KH’ ==> vtot ~= vw

vw >> va KH’ ==> vtot ~= va KH’

1 / vw ~=~ 1 / va KH’ ==> Both phases important

Steady State Flux

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Two Film Model- Important Factors

za & zw : higher turbulence (wind, flow ===> decreasing thickness)

H : Temperature, Ionic Strength ( x 2-3 for every 10oC)

Surface films (surfactants) additional barrier & additional resistance.

The time needed for average molecule to cross film / boundary layer:

w ~= zw2 / Dw = zw / vw

a ~= za2 / Da = za / va

if: zw ~ 5x10-3 cmza ~ 5 x 10-2 cmDw ~10-5 cm s-1

Da ~ 0.1 cm s-1

then, diffusion times ~ seconds

a-w exchange is rapid ( & increased with greater turbulence)

Film Resistance in Whitman ModelFlux = vtot (Cw – C*)

where C* = Ca / KH

1/ vtot = 1 / vw + RT / H va

( kol ) ( kw ) ( ka )

Compounds exhibiting liquid phase resistance:

O2, CO2 kw = 2-10 cm hr -1

Compounds exhibiting gas phase resistance:H20 ka = 200 to 2000 cm hr-1

Dominant phases for resistance to transfer:Resistance = ( RT kw ) / ( KH ka ) = 0.024 * 0.005 / KH

so Resistance = 0.00012 / KH @ 25 oC

KH >~ 10-3 atm m3 mol-1 ===> resistance is 95 % in water phaseKH <~ 5 x 10-6 atm m3 mol-1 ===> resistance is primarily in air phase

Air – Water Exchange Mechanisms

4 layers of resistance to transfer in series:Vertical Transport in turbulent air and water is fast (& generally not limiting to gas exchange).

Transport is diffusion limited in stagnant films (layers) on both air and water side of the interface

Exchange is instantaneous at the air-water interface.In cases where effectively no mixing occurs in boundary layers,

Whitman 2 layer (film) model applies

In cases of high turbulence on air and water sides, “new” and and water parcels displace “old” air and water parcels, Surface Renewal Model applies.

In both models, mixing forces dissipate rapidly below 1mm on air side and 0.1 mm on water side

So, Boundary Layer thicknesses are: ~1000 m – air~100-200 m – water

In both models, gas penetration is rapid (high injection velocities) at interface and equilibrium is achieved and assumed (thus we can use KH)

Overall: Limitations to transfer are provided by both boundary layers

Influence of KH on Dominant Process

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Large Compounds Small compoundsPolar Compounds Non-Polar Compounds

Surface Renewal Model

Figure from Schwarzenbach, Gschwend and Imboden, 1993

Surface Renewal Model

Eddies

Non-renewed Surface

Renewed Surface

Parcels of Air and water are mixed to interface where exchange occurs (instantaneously).

Surface Renewal Model

F = ( 1 / (1/ ( r * Dw )1/2 ) + (1 / (KH’ (r * Da)1/2) ) * ( Cw – Ca / KH’ )

Mass transfer coefficient Conc. gradient

(or, water parcel renewal rate)

where r = water parcel renewal rate (t-1)

Dw, Da = molecular diffusion coefficents

vtot = [ ( 1 / ( rw Dw )1/2 ) + 1 / (KH’ (ra Da)1/2) ]-1

vw = ( rw Dw )1/2 va = ( ra Da )1/2

Surface Renewal Model: Continued

Conceptually, describes turnover of parcels of air and water at interface

Dominant exchange process is renewal or exchange of parcels

no diffusive exchange in boundary layers ( diffusive exchange at interface)

size of boundary layer is not important

Account for time varying diffusion

vw = ( rw Dw )1/2 va = ( ra Da )1/2

where rw = renewal rate for water parcels (sec-1)

ra = renewal rate for air parcels (sec-1)

Conceptually ==> when r, then z and thus F .

Surface Renewal Model: Continued

F = Kol * ( Cw – Ca H*)

resistance to mass transfer * conc. gradient

1 / Kol = ( 1 / ( rw Dw )1/2) + ( 1 / H* ( ra Da )1/2)

1 / Kol = 1 / kw + 1/ (H* ka)

un-measurable parameters: rw, ra

Where do these two models leave us?

F = Kol * ( Cw – Ca / H)

Whitman two film model un-measurable parameters: zw & za

Surface renewal model un-measurable parameters: rw, & ra