Air / Water Gas ExchangeProcesses of Air / Water ExchangeSlide 3Stagnant Boundary Layer Model of Air / Water Exchange – Whitman Two Film ModelTwo Film ModelTwo Film Model- ContinuedTwo Film Model- “Velocities”Steady State FluxTwo Film Model- Important FactorsFilm Resistance in Whitman ModelAir – Water Exchange MechanismsInfluence of KH on Dominant ProcessSurface Renewal ModelSlide 14Slide 15Surface Renewal Model: ContinuedSlide 17Where do these two models leave us?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 CwAppropriate 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 ExchangeDepiction 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, 1993Processes 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, 1993Stagnant Boundary Layer Model of Air / Water Exchange –Whitman Two Film ModelFigure from Schwarzenbach, Gschwend and Imboden, 1993Two Film ModelFigure from Schwarzenbach, Gschwend and Imboden, 1993Net Flux = Kol * (Cw – Ca/H*)resistance to transport * Concentration gradient relative to equilibriumH* is “dimesnionless” Henry’s Law Constant at ambient temperature1/ 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 thicknessun-measurable parameters: zw, zaTwo Film Model- ContinuedFw = - 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) zaCw/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. gradientFnet= (+) 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-3Defining “Partial Transfer Velocities:vw = Dw / zw& va = Da / za1 / vtot = 1 / vw + 1 / va KH’Resistance analogy:1 / Rtot = 1 / Rw + 1 / RaTransfer dominated by layers:vw << va KH’ ==> vtot ~= vwvw >> va KH’ ==> vtot ~= va KH’1 / vw ~=~ 1 / va KH’ ==> Both phases importantSteady State FluxFigure from Schwarzenbach, Gschwend and Imboden, 1993Two Film Model- Important Factorsza & 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-1Da ~ 0.1 cm s-1then, diffusion times ~ seconds  a-w exchange is rapid ( & increased with greater turbulence)Film Resistance in Whitman ModelFlux = vtot (Cw – C*)where C* = Ca / KH1/ vtot = 1 / vw + RT / H va( kol ) ( kw ) ( ka )Compounds exhibiting liquid phase resistance:O2, CO2kw = 2-10 cm hr -1Compounds exhibiting gas phase resistance:H20 ka = 200 to 2000 cm hr-1Dominant phases for resistance to transfer:Resistance = ( RT kw ) / ( KH ka ) = 0.024 * 0.005 / KHso Resistance = 0.00012 / KH @ 25 oCKH >~ 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 phaseAir – Water Exchange Mechanisms4 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 interfaceExchange is instantaneous at the air-water interface.In cases where effectively no mixing occurs in boundary layers,Whitman 2 layer (film) model appliesIn 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 sideSo, Boundary Layer thicknesses are: ~1000 m – air~100-200 m – waterIn 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 layersInfluence of KH on Dominant ProcessFigure from Schwarzenbach, Gschwend and Imboden, 1993Large Compounds Small compoundsPolar Compounds Non-Polar CompoundsSurface Renewal ModelFigure from Schwarzenbach, Gschwend and Imboden, 1993Surface Renewal ModelEddiesNon-renewed SurfaceRenewed SurfaceParcels of Air and water are mixed to interface where exchange occurs (instantaneously).Surface Renewal ModelF = ( 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 coefficentsvtot = [ ( 1 / ( rw Dw )1/2 ) + 1 / (KH’ (ra Da)1/2) ]-1vw = ( rw Dw )1/2 va = ( ra Da )1/2Surface Renewal Model: ContinuedConceptually, describes turnover of parcels of air and water at interfaceDominant exchange process is renewal or exchange of parcels no diffusive exchange in boundary layers ( diffusive exchange at interface)size of boundary layer is not importantAccount for time varying diffusionvw = ( 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