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 Updated: 28 December 2015 Print version Lecture #32 Toxics: Volatilization, Photolysis, Hydrolysis and Biodegradation: Recapitulation and Simplified Forms (Chapra, L41, L42, L43 & L44) David Reckhow CEE 577 #32 1 The two film theory p g p i Interface c i c l David Reckhow CEE 577 #32 2 1

CEE 577 Lecture #32 12/28/2015 Two film model  Flux from the bulk liquid to the interface   ( ) J K c c l l i l  Flux from the interface ot the bulk gas K Mass transfer  g  ( ) J p p g g i velocities (m/d) RT a  And the K’s are related to the molecular diffusion coefficients by: D D  l  g K K l g z z l g David Reckhow CEE 577 #32 3 Two film theory (cont.)  We want to be able to relate flux to bulk air and water concentrations  interface concentrations cannot be directly measured   p     g J v c   v l   H e  to do this we must substitute expressions for the interface concentrations David Reckhow CEE 577 #32 4 2

CEE 577 Lecture #32 12/28/2015 Whitman’s 2 film model (cont.)   According to Henry’s law: p H c i e i  And relating this back to the bulk concentration   ( ) J K c c l l i l J   l c c    now combining, we get: i l J K     l l p H c   i e l K l K     g ( ) J p p J RT J      g g i g a l RT p H c   a g e l   K K g l J RT   g a p p i g K g David Reckhow CEE 577 #32 5 Whitman’s 2 film model (cont.)   p    g  c  l 1   H RT  And re ‐ arranging   e a J K H K l e g      And recall: p p    g   c     g J v c l   1   H  v l e   H v J e v  now solving and equating the fluxes, we get (pg. 371 in text): 1 1 RT   a v K H K The net transfer v l e g velocity across the air- water interface (m/d) David Reckhow CEE 577 #32 6 3

CEE 577 Lecture #32 12/28/2015 Whitman’s 2 film model (cont.) H   Which can be rewritten e v K   v l K    as: H RT l e a  K  g  Now, applying it to Contaminant toxicants Environment specific specific  p g  0 ' K H  or g e v K  c l =c d v l  ' K K H Where, H e ’=H e /RT l g e Unitless Henry’s Law Const  And converting to the appropriate units: dc     V v A c J v v c v s d dt d David Reckhow CEE 577 #32 7 Volatilization: Parameter estimation  Liquid film mass transfer coefficient (m/d) 0 . 25   32  and    K K H K K Compound , , l O a l l O 2   2 MW molecular weight  Gas film mass transfer coefficient (m/d) 0 . 25  18   168   K U g W   MW Wind velocity (mps)    0 . 25  or 346 K U MW g W David Reckhow CEE 577 #32 8 4

CEE 577 Lecture #32 12/28/2015 Volatilization: lakes  For lakes, correlations with K a cannot be used  Wind velocity (U w in m/s) drives liquid phase   resistance D    0 . 17 l For K l in m/d K C U    l d w   l  Where: C d is the drag coefficient (~0.001), D l is the diffusivity of the toxicant in water, and  l is the kinematic viscosity of water (0.01 cm 2 /s)  0.017 K DU For K l in m/s  This reduces to: l l w  1470* For K l in m/d K DU l l w From Thomann & Mueller, 1987 Thus, the 0.017 coefficient 9 David Reckhow CEE 577 #32 essentially has the units: s/cm 2 . correction correction (atm m 3 gmol -1 ) Figure 20.4, page 373 in text. David Reckhow CEE 577 #32 10 5

CEE 577 Lecture #32 12/28/2015 Effect of U w and H e  Chapra, pg. 730 David Reckhow CEE 577 #32 11 Box and Whisker Plots  Useful for summarizing non ‐ ideal data distributions Thickness is proportional to the square root of the number of outlier observations x Median Upper data range Lower data range Upper quartile Lower quartile David Reckhow CEE 577 #32 12 6

CEE 577 Lecture #32 12/28/2015 Summary of sorption & volatilization effects  Assume  T a =283 K  M=200 g/mole  U w = 5 mph  v s =91 m/yr  Assimilation refers to general rate of removal David Reckhow CEE 577 #32 13 Summary: pesticides  Chapra, pg.735 David Reckhow CEE 577 #32 14 7

CEE 577 Lecture #32 12/28/2015 Summary: PCBs  Chapra, pg.736 David Reckhow CEE 577 #32 15 Summary: PAHs  Chapra, pg.736 David Reckhow CEE 577 #32 16 8

CEE 577 Lecture #32 12/28/2015  To next lecture David Reckhow CEE 577 #32 17 9