Air / Water Gas Exchange The 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 Water K H = P a /  w C w 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 solution Sheltered systems with more or less constant water and atmospheric conditions Inappropriate for : Large Lakes Flowing rivers Spills in both rivers and lakes Oceans ( 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 model Wave 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 = K ol * (C w – C a /H*) resistance to transport * Concentration gradient relative to equilibrium H* is “dimesnionless” Henry’s Law Constant at ambient temperature 1/ K ol = ( 1/ K w + 1/ (K a H*) ) = (1 / D w / z w ) + (1/ D a / z a H*) where D w = diffusivity in water D a = diffusivity in air z w = water film thicknessz a = air film thickness un-measurable parameters: z w, z a

Two Film Model- Continued F w = - D w ( C w/a – C w ) / z w So, at steady state: F w = - D w ( C w/a – C w ) / z w = -D a (C a – C a/w ) / z a = F a Flux total = Fw = Fa since: K H ’ = C a/w / C w/a ( mol / L air / mol / L water ) then:D w (C w -C w/a ) / z w = D a (K H ’ C w/a - C a ) z a C w/a = ( ( D w / z w ) + ( D a / z a ) C a ) / ( ( D w / z w ) + ( D a K H ’ / z a ) ) F overall = 1 / ( z w / D w ) + (z a / D a K H ’) * ( C w - C a / K H ’) mass transfer coefficient (cm/hr) * Conc. gradient F net = (+) then water ====> air b/c (C w > C a / K H ’) F net = (-) then air ====> water b/c (C w < C a / K H ’)

Two Film Model- “Velocities” Flux total = v tot * ( C w – C a / K H ’) mol m -2 sec -1 = m sec -1 * mol m -3 Defining “Partial Transfer Velocities: v w = D w / z w &v a = D a / z a 1 / v tot = 1 / v w + 1 / v a K H ’ Resistance analogy: 1 / R tot = 1 / R w + 1 / R a Transfer dominated by layers: v w v tot ~= v w v w >> v a K H ’ ==> v tot ~= v a K H ’ 1 / v w ~=~ 1 / v a K H ’ ==> Both phases important

Steady State Flux Figure from Schwarzenbach, Gschwend and Imboden, 1993

Two Film Model- Important Factors z a & z w : higher turbulence (wind, flow ===> decreasing thickness) H: Temperature, Ionic Strength ( x 2-3 for every 10 o C) Surface films (surfactants) additional barrier & additional resistance. The time needed for average molecule to cross film / boundary layer:  w ~= z w 2 / D w = z w / v w  a ~= z a 2 / D a = z a / v a if: z w ~ 5x10-3 cm z a ~ 5 x 10-2 cm D w ~10-5 cm s -1 D a ~ 0.1 cm s -1 then, diffusion times ~ seconds  a-w exchange is rapid ( & increased with greater turbulence)

Film Resistance in Whitman Model Flux = v tot (C w – C*) where C* = Ca / K H 1/ v tot = 1 / v w + RT / H v a ( k ol ) ( k w ) ( k a ) Compounds exhibiting liquid phase resistance: O 2, CO 2 k w = 2-10 cm hr -1 Compounds exhibiting gas phase resistance: H 2 0k a = 200 to 2000 cm hr -1 Dominant phases for resistance to transfer: Resistance = ( RT k w ) / ( K H k a ) = * / K H soResistance = / 25 o C K H >~ atm m3 mol-1 ===> resistance is 95 % in water phase K H 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 ~  m – water In both models, gas penetration is rapid (high injection velocities) at interface and equilibrium is achieved and assumed (thus we can use K H ) Overall: Limitations to transfer are provided by both boundary layers

Influence of K H on Dominant Process Figure from Schwarzenbach, Gschwend and Imboden, 1993 Large Compounds Small compounds Polar 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 * D w ) 1/2 ) + (1 / (K H ’ (r * D a ) 1/2 ) ) * ( C w – C a / K H ’ ) Mass transfer coefficientConc. gradient (or, water parcel renewal rate) where r = water parcel renewal rate (t -1 ) D w, D a = molecular diffusion coefficents v tot = [ ( 1 / ( r w D w ) 1/2 ) + 1 / (KH’ (r a D a ) 1/2 ) ] -1 v w = ( r w D w ) 1/2 v a = ( r a D a ) 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 ˆ no diffusive exchange in boundary layers ( diffusive exchange at interface) ˆsize of boundary layer is not important Account for time varying diffusion v w = ( r w D w ) 1/2 v a = ( r a D a ) 1/2 where r w = renewal rate for water parcels (sec -1 ) r a = renewal rate for air parcels (sec -1 ) Conceptually ==> when r , then z  and thus F .

Surface Renewal Model: Continued F = K ol * ( C w – C a H*) resistance to mass transfer * conc. gradient 1 / K ol = ( 1 / ( r w D w ) 1/2 ) + ( 1 / H* ( r a D a ) 1/2 ) 1 / K ol = 1 / k w + 1/ (H* k a ) un-measurable parameters: r w, r a

Where do these two models leave us? F = K ol * ( C w – C a / H) Whitman two film model un-measurable parameters: z w & z a Surface renewal model un-measurable parameters: r w, & r a