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					                       Transport

                          You are on a train to NYC.
                          You are stirring the milk into your
                          coffee.




The train and everything in it are moving toward
NYC via directed or advective transport
As you stir, the milk is moving via turbulent
diffusion. This is a random process.
                          Flux
 Gradient flux law:




Flux: mass            transfer or   Concentration
per unit              exchange      gradient
area per              velocity      (ng/m3)
unit time             (m/day)
(ng/m2-day)
                      aka mass
                      transfer
                      coefficient
           Fick’s First Law
One example of a gradient flux law is Fick’s First Law:




Relates the diffusive flux (Fx) of a chemical
to its concentration gradient (dC/dx) and its
molecular diffusion coefficient (D)
          Fick’s Second Law



The local concentration change with time (dC/dt) due to a
diffusive transport process is proportional to the second
spatial derivative of the concentration (concentration
gradient)
            Turbulent diffusion
In contrast to molecular diffusion, which arises due to
thermal molecular motions, turbulent diffusion is based on
the irregular patterns of currents in water and air.
Turbulent vs. laminar flow is defined by the Reynold’s
number:



   d = spatial dimension of the flow system or objects around which
   the flow occurs (m)
   v = typical flow velocity
   f = dynamic viscosity of the fluid (kg/m-s)
   rf = density of the fluid (kg/m3)
For laminar flow Re < 0.1
             Turbulent diffusion

the effect of the turbulent velocity component on the
transport of a dissolved substance can be described by an
expression which has the same form as Fick’s first law:




   the molecular diffusivity (D) is now replaced by the
   turbulent or eddy diffusion coefficient, E
   E >>> D
                    anisotropy
in natural systems, turbulent diffusion is usually anisotropic,
    meaning that the magnitude of E depends on the direction.
horizontal diffusion is usually much greater than vertical
    diffusion because:
1. natural systems extend horizontally
2. often the system (ocean, atmosphere) is density stratified
      Transport through boundaries
                         (Chapter 19)
What is a boundary = surface at which properties of a system
  change extensively or, discontinuously (interface)
   air-water interface
   sediment-water interface
   epilimnion - hypolimnion (thermocline)
   stratosphere – troposphere (tropopause)
What to boundaries do?
1. control the transport of energy and matter
2. control chemical process triggered by the contact of two
   systems with different chemical composition
What is the boundary condition?
may be defined by a value (i.e. concentration) or by a flux (i.e.
   mass flux across the boundary per unit time)
What types of boundaries are there?
1. bottleneck
2. wall
3. diffusive
classified according to the shape of the diffusivity (D) profile
                              bottleneck boundaries
                     bottleneck
                                                  bottleneck = mass
Diffusivity D(x)




                                                  crossing must squeeze
                                                  itself through a zone in
                                    turbulent     which transport occurs
                                    diffusion
                                                  by molecular diffusion
                                                  (usually interface)
                                    molecular
                                    diffusivity
                   distance
                                                  example:
                                                  air-water interface
                                                  Like a toll booth on the
                                                  turnpike
                              wall boundary
                       wall                   at a wall boundary, a zone
                                              characterized by turbulent
                                              diffusion encounters a
Diffusivity D(x)




                                              zone in which transport is
                                  turbulent
                                              dominated by a much
                                  diffusion   slower process, such as
                                              molecular diffusion
                                  molecular   example:
                                  diffusion
                   distance                   sediment-water interface
                                              Like an icy stretch of road
                              diffusive boundary
                      diffusive
                      boundary
                                          at a diffusive boundary,
                                          diffusivity is of similar
Diffusivity D(x)




                                  C (x)   magnitude on either side
                                  D (x)   diffusivity may be
                                          molecular or turbulent
                                          example:

                   distance               troposphere – stratosphere
                                          boundary (tropopause)
Air – Water Exchange
       (Chapter 20)
 Inputs and outputs of SPCBs (kg y-1)

                        Atm dep      Volatilization
                        18-48          317-846
                                                           Advection to
                                                           Atlantic 130-190
       CSOs 67-146
   Stormwater 36-140          NY/NJ Harbor
     STP effluents 32         Estuary
Advection from
 Hudson River
   260-470                                                 Dredging
                                                           150-290
                           Storage in sediments
                                 147-307              Totten 2005
               Air – Water Exchange
 the air-water interface can be thought of as a bottleneck
 boundary
 (if one phase is stagnant we can think of it as a wall boundary)

 We already know, from our discussions of mass transfer, that
 the equation for the air-water exchange flux (Fa/w) should look
 like this:

where va/w is a mass transfer coefficient or air-water exchange
velocity (m/s)
the second term describes the fugacity gradient and the
direction of air-water exchange:
   Net air-water exchange flux




sometimes we divide this into the absorption flux
(“gross gas absorption”):




and the volatilization flux:
              total exchange velocity
the total exchange velocity can be interpreted as
resulting from a two-component (air/water) interface
with phase change. if water is the reference state, then:



           (two resistances in series)
va typically is about 1 cm/s
vw typically is about 10-3 cm/s
Critical Kaw

          thus if Kaw << 10-3
          (dimensionless) or 0.025
          L bar/mol then the air-side
          resistance (va) dominates
          if Kaw >> 10-3
          (dimensionless) or 0.025
          L bar/mol then the water-
          side resistance (vw)
          dominates
             both phases important



air-phase                            water-phase
controlled                           controlled
va derived from evaporation of water

Kaw (water) = 2.3  10-5, so air
side resistance dominates
wind speed is important
va increases linearly with wind
speed up to ~8 m/s
va (water) = 0.2u10 + 0.3
where u10 is the wind speed
(m/s) at 10 meters
   vw derived from tracers with high KH
O2, CO2, He, Rn, SF6
Influence of wind speed,
but also wave field




  Liss and Merlivat 1986



 See Table 20.2
 for equations
         Air-water exchange models
              for lakes, oceans
Whitman Two-Film Model (1923)
   considers two bottleneck boundaries, stagnant films on the air and
   water side of the interface where transport occurs by molecular
   diffusion

Surface Renewal Model
   interface is described as a diffusive boundary. parcels of air or water
   undergo a/w exchange to eqbm, then are replaced (air is replaced more
   often than water b/c less viscous)

Boundary Layer Model (Deacon, 1977)
   considers changes in turbulence and molecular diffusivity (due to
   changes in T) separately
Whitman two-film
model
       Whitman Two-Film Model
each stagnant boundary layer has a characteristic thickness :




If we assume that the layer thickness is the same for all
chemicals then we can easily convert the transfer velocity
for water or CO2 to a velocity for our chemical:
            Diffusivity
In air:




In water:
Air-water exchange in flowing waters
Physics of boundary now influenced by both wind and
water movement
Turbulence in rivers is primarily introduced by shear at the
bottom
Water side: vw is affected by flow
Air side: va is not affected by flow
Two models:
   Small Eddy Model (Lamont and Scott, 1970)
   Large Eddy Model (O’Connor and Dobbins, 1958)
small

 vs.

large

eddy
             Small Eddy Model
The turbulent eddies produced by water flowing over the rough
bottom are small compared to the depth of the river
(bottom is smooth and/or river is deep)




Sciw = Schmidt number = vi/Diw = viscosity/diffusivity
vw = kinematic viscosity of water
u* = shear velocity
h = water depth
            Large Eddy Model
The turbulent eddies produced by water flowing over the rough
bottom are large compared to the depth of the river
(river is shallow and/or bottom is rough)




 Constant ~ 1
 u = mean flow velocity of river
 h = mean river depth
                  Summary
We have moved from the smooth flow (small eddy)
regime to the rough flow (large eddy) regime.
At even rougher flow, bubbles (foam) are formed
which further enhance air-water exchange.
Note that when we apply either the large or small eddy
model, we necessarily assume that air-water exchange
is enhanced (greater than the stagnant flow models).
Thus the vw we calculated from either the large or
small eddy model must be greater than the vw we
get from the stagnant two-film model!
Study Site
             Need:
             • Large fetch
               upwind of
               site
             • Easy access
             • Power
      Description of the Micrometeorological Technique

• Uses two systems to determine turbulent fluxes in the near
  surface atmosphere:
   – Aerodynamic Gradient (AG) Method
       • determine profile of wind speed, temperature and water vapor,
         which along with concurrent measurements of PCB air
         concentration at two heights are use to determine vertical fluxes of
         PCB emanating from the water column.

   – Eddy Correlation system
       • directly measure fluxes of momentum, sensible heat and latent heat,
         which can be used for correction of PCB concentration profile for
         non-adiabatic conditions.
   Calculation of Fluxes and va/w
• Vertical PCB fluxes (FPCB) were calculated
  using the Thornthwaite-Holtzman equation :
                         k = von Karman’s constant
                         u* = friction velocity Need
                         C1 = upper concentration
                                                measurabl
                         C2 = lower concentration
                                                e conc
                         z1 = upper height      gradient!
                         z2 = lower height

• Every term can be measured except C , which
  is the atmospheric stability factor. C can be
  determined from M, H, and W which are the
Micrometeorological
   Measurement
                         PCB Concentration gradients
                    6




                    5




                    4




Concentration ng m-3 3

                                                       Upper Sample
                                                       Lower Sample
                    2




                    1




                    0




                                    PCB samples
                          Results: PCB fluxes
                      Low MW congeners            Heavier congeners
                 25   have higher fluxes due      volatilize more slowly b/c
                      to higher Cw and faster     they are sorbed to solids
                 20                               and have slow va/w
                      va/w
Fluxes pg/m2 s




                 15

                 10

                  5

                  0
                      101+89+90
                          24+27




                          52+43
                          47+48



                          70+76
                             63
                             15
                             18

                             25
                             28
                             22
                             53


                             42
                             64


                             55
                             91
                            7+9
                            5+8




                            110
                            154
                            147
                            146
                            132
                        138+163
                            159
                            157
                            178
                            185
                            177
                        172+192
                              1
                              3




                                      PCB Congeners
                        MTC m/d



                                 0
                                 2
                                 4
                                 6
                                 8
                                12
                                14

                                10
                    1
                 7+9
                   11
                   17
                   25
            20+21+33
                   53
                   49
                   42
                                     PCB MTC




                   40
                70+76

Congeners
                                               Results: va/w




                93+95
            101+89+90
                  151
                  153
              138+163
                  157
              174+181
                  180
How to use va/w
        It’s hard to use net flux, because it is
        dependant on both Ca and Cw, and is
        not, therefore, pseudo first order
        with respect to either of them.


 By dividing the flux in to the
 absorption and volatilization fluxes,
 you can model each as a pseudo first
 order process.
  Pseudo first order rate constants

To obtain a pseudo first order rate constant, you need to get
va/w into units of 1/time:

Mass lost = volatilization flux times surface area




To convert to concentration change, divide by volume:



Define a pseudo first order rate constant kaw = va/w/d (d = depth)

				
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posted:8/15/2011
language:English
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