Lecture 7, Particles in Surface and Water and Exchange of Volatiles between Air and WaterConrad (Dan) Volz, DrPH, MPHBridgeside Point100 Technology DriveSuite 564, BRIDGPittsburgh, PA 15219-3130office 412-648-8541: cell 724-316-5408: Fax [email protected], Environmental and Occupational Health, University of Pittsburgh, Graduate School of Public Healthhttp://www.pitt.edu/~cdv5/; Director-Center for Healthy Environments andCommunitieshttp://www.chec.pitt.edu;Director, Environmental Health Risk Assessment CertificateProgramhttp://www.publichealth.pitt.edu/interior.php?pageID=82Types of Particles• Mineral- clay aluminosilicates, Iron and manganese hydroxide-approximated density~2.6/cc.• Organic-plant material, dead bacteria and algal cells as well as decaying aquatic organisms. • Anthropogenic- sewage biosolids, overflow particles and deposition of industrial emissions. See figure 2-11.Particle Settling• Average settling velocity is approximated by Stokes Law;шf= (2/9)g(рs/рf– 1)r2/ηfwhere шf is the settling velocity[L/T], g is acceleration due to gravity, рs is solid density and рfis fluid density, ris the particle radius and η is the kinematic viscosity(the ratio of the viscosity to the density of the fluid).R is meant to be hydrodynamically equivalent diameter (so non-spherical particles can be assessed).See figure 2-11 for settling velocitiesCounterbalance of settling and Fickian Processes• As particles settle they become more concentrated so there is a Fickian transport upward to counteract the downward settling.• The downward flux density due to settling must equal the upward flux density of diffusion at equilibrium so;Jstokes=C шf=Jfickian= D dC/dx so by differentiating and rearrangingC=Co e-(шf/D)x -the concentration of particles in the water column follows an exponential decay from the bottom upward. Go over Example 2-3The Air-water Interface• For volatiles (i.e. most solvents and fuels) water-to-air exchange is really the most significant mechanism of removal from surface water. Quite often this removal process is used formally to drive solvents from water through aeration. • Chemicals in the atmosphere, dependant on concentration can also go from air to water.• The concentration of a dissolved gas (or vapor) in a surface water at equilibrium with the atmosphere (C equil) is determined by its concentration in air (Ca) and its Henry’s law constant: Cequil = Ca/H, H is dimensionless.• If the concentration in water (Cw) > Cequil, the chemical agent will volatilize into the atmosphere with a flux density given by: J [M/L2T] = –kw(Cw – Ca/H) where the gas exchange coefficient (kw), [L/T] depends on the water flow and air movement above the surface. Flux denity is – into air and + if into water.• Note that in the case of volatiles stemming from anthropogenic activity, the term involving Ca will at least initially be zero and unless atmospheric conditions include low inversions should be essentially thought of as 0 (unless the control volume is small). So the gas exchange coefficient is also called the piston velocity when Ca is 0.The Air-water Interface• As reality lies somewhere between the conceptualized ideal physical models (i.e. the “thin film” and “surface renewal” models) the presently available procedures for estimating flux and/or kw purely by calculation are unreliable.• Thin layer model (figure 2-14)-turbulent diffusion is assumed in both the air and water phases except within a few micrometers from the interface, so transport occurs in this thin stagnant film by molecular diffusion (Ficks first law). Equation 2-32 is the general case and we use 2-29 if H is >> 0.01 (most volatile chemicals) and 2-31 if H<< 0.01 as in the case of PAH or pesticides.• In the surface renewal model it is assumed that small parcels of water are brought to the surface through turbulence and the average time each parcel spends on the surface determines the gas exchange rate.• In practice, the best estimates of kw are obtained with measurements involving a tracer gas (e.g. propane) since the ratio of the gas exchange coefficients of two volatiles can be approximated, but an explicit choice of model must be made.• In the surface renewal model: kA/kB = DA/DB (ratio of the square root of the molecular diffusion constants)   [(MW)B/(MW)A] where the D are the diffusion coefficients in water and the MW are the relative molecular masses/weights.• However, in the case of the thin film model: kA/kB = DA/DB  (MW)B/(MW)Awhere the D and Mr are the sameEx. 2-6:Ex. 2-6:• kTCE/kpropane = MWpropane/ MWtce= 44/131  kTCE = (44/131)  3.0  10-3 = 1.7  10-3 {cm/s}• J = –1.7  10-3 {cm/s}  1.0  10-3 {g/cm3} = –1.7  10-6 {g/cm2/s}Volatilization from Pure Liquids• This is of concern when a fuel or solvent has been spilled to produce a non-aqueous floating slick on the surface of water or the ground.• Faster than volatilization of agents dissolved in water as permeation of a “stagnant” film of water at the surface is not required, only a stagnant air film need be overcome.• The (molar) concentration of the agent at the base of the stagnant air layer (in contact with the spill) is argued to be given by: Ca = (PMw)/RT where P is the vapor pressure, Mw is the molar mass, Ris the gas constant and T the absolute temperature.• The rate of volatilization (flux density) is then given by:• J = –kaCa = –(Da/a)•Ca • Where ka is the air-side gas exchange coefficient, Da the molecular diffusion coefficient of the agent in air and a the thickness of the hypothetical film of air;Example 2-8• Benzene VP= 0.12 atm at 20 degrees C. Use 2-38 to find the stagnant air film [benzene] = 0.4 g/L• An approximate value for ka ≈ 3300 {cm/hr} [Eq. 2-36]• [Eq 2-39] J = –3300 {cm/hr}  0.4  10-3 {g/cm3} = –1.3 g/(cm2-hr)Volatilization from Pure Liquids• In practice, ka depends quite strongly on the wind velocity and somewhat (for larger slicks) on the size – as advection from upwind contributes to the local concentration, decreasing the concentration gradient at a downwind point.• Also, the forgoing supposes the spilled agent floats, or does not seep into the ground – but note that halogenated solvents, for example, are more dense than water.Relationships involving a first-order