The two film theory p g p i Interface c i c l David Reckhow CEE - - PDF document

CEE 577 Lecture #32 12/28/2015 1 Lecture #32 Toxics: Volatilization, Photolysis, Hydrolysis and Biodegradation: Recapitulation and Simplified Forms

(Chapra, L41, L42, L43 & L44)

David Reckhow CEE 577 #32 1

Updated: 28 December 2015

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The two film theory

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Interface pi pg cl ci

CEE 577 Lecture #32 12/28/2015 2

Two film model

 Flux from the bulk liquid to the interface  Flux from the interface ot the bulk gas

 And the K’s are related to the molecular

diffusion coefficients by:

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J K c c

l l i l

  ( )

J K RT p p

g g a g i

  ( ) Mass transfer velocities (m/d)

K D z

l l l



K D z

g g g



Two film theory (cont.)

 We want to be able to relate flux to bulk air and

water concentrations

 interface concentrations cannot be directly measured

 to do this we must substitute expressions for the

interface concentrations

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         

l e g v

c H p v J

CEE 577 Lecture #32 12/28/2015 3

Whitman’s 2 film model (cont.)

 According to Henry’s law:  And relating this back to the bulk concentration  now combining, we get:

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p H c

i e i



p H J K c

i e l l l

       

l l l i l i l l

c K J c c c K J     ) (

g a g g i i g a g g

K RT J p p p p RT K J     ) (           

l l l e g a g g

c K J H K RT J p

Whitman’s 2 film model (cont.)

 And re‐arranging  And recall:  now solving and equating the fluxes, we get (pg.

371 in text):

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1 1 v K RT H K

v l a e g

 

The net transfer velocity across the air- water interface (m/d)

g e a l l e g

K H RT K J c H p            1

         

l e g v

c H p v J

J c H p v

l e g v

          1

CEE 577 Lecture #32 12/28/2015 4

Whitman’s 2 film model (cont.)

 Which can be rewritten

as:

 Now, applying it to

toxicants

 pg0  cl=cd

 And converting to the

appropriate units:

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       

g l a e e l v

K K RT H H K v

Contaminant specific Environment specific

d vc

v J  

d s v

c A v dt dc V  

' ' e g l e g l v

H K K H K K v  

Where, He’=He/RT

Unitless Henry’s Law Const

• r

Volatilization: Parameter estimation

 Liquid film mass transfer coefficient (m/d)  Gas film mass transfer coefficient (m/d)

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25 . ,

32

2

       MW K K

O l l

25 .

18 168        MW U K

W g

Compound molecular weight Wind velocity (mps) and

H K K

a O l



2

,

 

25 .

346



 MW U K

W g

• r

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Volatilization: lakes

 For lakes, correlations with Ka cannot be used  Wind velocity (Uw in m/s) drives liquid phase

resistance

 Where: Cd is the drag coefficient (~0.001), Dl is the diffusivity of the

toxicant in water, and l is the kinematic viscosity of water (0.01 cm2/s)

 This reduces to:

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w l l d l

U D C K           17 .

0.017

l l w

K DU 

From Thomann & Mueller, 1987

1470*

l l w

K DU 

For Kl in m/s For Kl in m/d For Kl in m/d

Thus, the 0.017 coefficient essentially has the units: s/cm2.

correction

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Figure 20.4, page 373 in text. (atm m3 gmol-1) correction

CEE 577 Lecture #32 12/28/2015 6  Chapra, pg. 730

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Effect of Uw and He Box and Whisker Plots

 Useful for summarizing non‐ideal data

distributions

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x

Thickness is proportional to the square root of the number of

• bservations

Median Lower data range Upper data range

• utlier

Upper quartile Lower quartile

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Summary of sorption & volatilization effects

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 Assume

 Ta=283 K  M=200 g/mole  Uw = 5 mph  vs =91 m/yr

 Assimilation refers to general rate of removal

Summary: pesticides

 Chapra,

pg.735

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CEE 577 Lecture #32 12/28/2015 8

Summary: PCBs

 Chapra,

pg.736

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Summary: PAHs

 Chapra,

pg.736

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CEE 577 Lecture #32 12/28/2015 9  To next lecture

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