Nonequilibrium Systems in Natural Water Chemistry

6 Transport of Organic and Inorganic Materials in Small-Scale Ecosystems 1

E A R N E S T F . G L O Y N A , Y O U S E F A. YOUSEF, and T H O M A S J. P A D D E N

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Center for Research in Water Resources, T h e University of Texas at Austin, Austin, Tex. 78712

T h i s p a p e r d e s c r i b e s some studies o n the transport of b i o degradable a n d nondegradable materials through a system of f l o w i n g and n o n f l o w i n g research flumes. A v a r i e t y of r a d i o n u c l i d e s and d y e s w e r e u s e d as tracers.

The uptake a n d

release o f p o l l u t a n t s a n d b i o m a s s o f v a r i o u s varieties o f t y p i c a l b o t t o m sediments, r o o t e d plants, w e r e m o n i t o r e d i n t i m e a n d space a l o n g a m o d e l r i v e r (200-ft-long w h i c h s i m u l a t e d the e c o l o g i c a l e n v i r o n m e n t .

flume)

Laboratory

a n d a q u a r i a studies s i m u l a t e d c l o s e d ecosystems.

Responses

of the t o t a l ecosystem a n d its c o m p o n e n t s to

instantaneous

a n d c o n t i n u o u s releases of p o l l u t a n t s w e r e

investigated.

Generalized mathematical relationships have been developed to d e s c r i b e the transport o f v a r i o u s m a t e r i a l s a l o n g a m o d e l flume.

À s m a l l - s c a l e ecosystem ( r e s e a r c h

flume)

has b e e n u s e d successfully t o

investigate t h e t r a n s p o r t p h e n o m e n a of r a d i o n u c l i d e s a d d e d as d i s s o l v e d i n o r g a n i c s a n d t o s t u d y a n d evaluate t h e parameters affecting a stream w h e n i t is s u b j e c t e d to o r g a n i c stresses. T h e r e s e a r c h flume ( F i g u r e 1) is 200 ft l o n g , 2 ft d e e p , a n d 2.5 f t w i d e w i t h a center r e m o v a b l e p a r t i t i o n p r o v i d i n g t w o 1.25-ft-wide c h a n nels. T h e i n t a k e c a n b e p r o v i d e d e i t h e r w i t h p o t a b l e w a t e r o r w i t h w a t e r f r o m a c o n t r o l reservoir r i c h i n p h y t o p l a n k t o n . T h e p h y t o p l a n k t o n p o p u l a t i o n c a n b e c o n t r o l l e d b y d i l u t i o n w i t h p o t a b l e w a t e r as system s i m u l a t i o n m a y r e q u i r e . F l o w c a n b e c o n t r o l l e d f r o m 0 to a p p r o x i m a t e l y 2 0 0 liters p e r m i n u t e p e r c h a n n e l a n d d e p t h s c o n t r o l l e d f r o m 0 to 2 ft. B o t t o m sediments w e r e o b t a i n e d f r o m n e a r b y L a k e A u s t i n , a n d p l a n t s , w h e n u s e d Present address: Department of Civil Engineering, Florida Technological University, Orlando, Fla. 1

181 Hem; Nonequilibrium Systems in Natural Water Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1971.


182

NONEQUILIBRIUM SYSTEMS IN N A T U R A L

Figure 1.

WATERS

Model river

i n the e x p e r i m e n t a t i o n , w e r e species c o m m o n to l o c a l streams a n d ponds. T h e p r e d o m i n a n t p l a n t s w e r e MyriophyUum, phora, the

a n d Spirogyra.

flume.

Chara,

Potamogeton,

Cfodo-

F i g u r e 2 i n d i c a t e s the h y d r a u l i c characteristics of

T h e s h a d e d p o r t i o n of F i g u r e 2 p o r t r a y s the g e n e r a l area i n

w h i c h e x p e r i m e n t a t i o n has b e e n c o n d u c t e d . I n s t r u m e n t a t i o n o n t h e flume consisted of p H meters, d i s s o l v e d o x y g e n p r o b e s ( g a l v a n i c ) , p y r h e l i o m e t e r s , a n anemometer,

and a

paper-

p u n c h tape d a t a a c q u i s i t i o n system. T h e studies o n the flume w e r e c o n d u c t e d to d e t e r m i n e t h e effects of specific e n v i r o n m e n t a l factors o n t r a n s p o r t a n d to specifically d e t e r m i n e the p h y s i c o c h e m i c a l characteristics of the e c o l o g i c a l system i n o r d e r to better u n d e r s t a n d the factors t h a t react to p o l l u t i o n a l stress.

The pro

c e d u r e u s e d w a s to estimate the u p t a k e a n d release rates of r a d i o n u c l i d e s , to e s t a b l i s h the effects of o r g a n i c a n d i n o r g a n i c p o l l u t i o n loads o n r a d i o n u c l i d e m o v e m e n t , a n d to relate a l l of these factors i n t o a b a s i c p r e d i c t i o n model.

Radionuclides including

β 5

Ζη,

5 8

Co,

1 3 7

Cs,

8 5

Sr,

1 0 6

R u , and

5 1

Cr

w e r e i n t r o d u c e d i n t o the flume u n d e r different e n v i r o n m e n t a l c o n d i t i o n s . A close f o l l o w - u p of the r a d i o a c t i v e flume w a s m a i n t a i n e d as the r a d i o n u c l i d e s d i s p e r s e d l o n g i t u d i n a l l y a n d transversely. C o n t i n u o u s m o n i t o r i n g of r a d i o a c t i v i t y i n the w a t e r p h a s e , s e d i m e n t ,

a n d biomass

m a i n t a i n e d b y s a m p l i n g a n d use of r a d i o n u c l i d e d e t e c t i o n

was

equipment.

Hem; Nonequilibrium Systems in Natural Water Chemistry Advances in Chemistry; American Chemical Society: Washington, DC, 1971.

6.

Transport

GLOYA E T A L .

Transport

of

of Materials

in Ecosystems

183

Radionuclides

T h e t r a n s p o r t characteristics o f r a d i o n u c l i d e s i n flowing ecosystems w e r e e s t a b l i s h e d t h r o u g h a series of step-wise (a)

operations:

l o g i c a l l y e n u m e r a t i n g t h e v a r i o u s processes w h i c h o c c u r i n a

model river ( b ) i s o l a t i n g i m p o r t a n t processes b y u s i n g a q u a r i a a n d m o d e l r i v e r studies (c)

synthesizing logical mathematical models using the above infor-

m a t i o n i n c o n j u n c t i o n w i t h p a r a m e t r i c studies


(d)

p r o g r a m m i n g of t h e p r e d i c t i o n m o d e l i n c o m p u t e r l a n g u a g e t o

e v a l u a t e the r e l a t i v e i m p o r t a n c e o f factors affecting r a d i o n u c l i d e transport. T h e basic transport equation developed b y S h i h a n d G l o y n a ( J ) w a s used.

10 I

Figure 2.

1.0 DEPTH (ft) I

0.5

I

0.1

I

I

0.385 0.179 0.1 HYDRAULIC RADIUS

Hydraulic

characteristics

0.02 L_l

0.0286 of model river


184

NONEQUILIBRIUM

SYSTEMS

IN

NATURAL

WATERS

c o n c e n t r a t i o n of a p a r t i c u l a r r a d i o n u c l i d e i n the

flowing

where =

c

stream at a n y p o i n t (x)

(t)

X

=

distance i n d i r e c t i o n of

u

=

average v e l o c i t y of

f*

=

mass or surface area of the i t h sorbent per u n i t v o l u m e of

=

mass or area transfer coefficient for phase i

=

a transfer f u n c t i o n r e l a t i n g the c o n c e n t r a t i o n of a c t i v i t y i n

=

the specific a c t i v i t y i n the i t h p o s i t i o n of the n - s o r p t i o n

the z o n e of G,(c) Downloaded by TUFTS UNIV on June 3, 2018 | https://pubs.acs.org Publication Date: June 1, 1971 | doi: 10.1021/ba-1971-0106.ch006

at t i m e flow

flow

flow

the w a t e r to the e q u i l i b r i u m l e v e l of a c t i v i t y i n phase i phases T h e first t w o terms i n the e q u a t i o n define the m i x i n g characteristics a n d d i l u t i o n , w h i l e the t h i r d t e r m establishes the u p t a k e a n d release b y the v a r i o u s a q u a t i c masses. L o n g i t u d i n a l d i s p e r s i o n coefficients, D

x

values, i n the absence of b i o

mass w e r e c a l c u l a t e d for velocities r a n g i n g f r o m 0.33 to 3.30 f t / m i n . D

x

The

values c a l c u l a t e d f r o m the t i m e - c o n c e n t r a t i o n curves of the R h o d a -

m i n e Β d y e studies, u n d e r v a r i o u s flow c o n d i t i o n s i n the

flume,

follow

a n e m p i r i c a l r e l a t i o n s h i p i n the f o r m D

x

= 3.26w 0

(2)

607

where u D

x

= =

the average v e l o c i t y i n f t / m i n the l o n g i t u d i n a l d i s p e r s i o n coefficient i n f t / m i n 2

Discrepancies between nonsorptive dye a n d radionuclide movement were observed.

I n some experiments w h e r e 9 0 - 1 0 0 %

of R h o d a m i n e Β

passed t h r o u g h the flume after one d a y f r o m release, o n l y 5 - 2 5 % of 5 8

Co,

1 3 7

water.

C s , and

8 5

S r a d d e d at the i n l e t w a s d e t e c t e d i n the exit

T h e r e t e n t i o n of r a d i o n u c l i d e s w a s p r i m a r i l y o w i n g to

c o n c e n t r a t i o n b y sediments a n d biomass Surface

Concentration

by Bed

6 5

Zn,

flume surface

(1,2,3,4,5,6,7,8).

Sediments

D i s s o l v e d r a d i o a c t i v e ions i n a q u a t i c systems are extracted f r o m the w a t e r b y b e d sediments.

T h e s e r a d i o n u c l i d e s are c o n c e n t r a t e d at the

s e d i m e n t surface a n d t h e n diffused i n t o the l o w e r layers of b o t t o m s e d i m e n t . T h e rate of transfer is d e p e n d e n t o n contact t i m e , e n v i r o n m e n t a l c o n d i t i o n s , a n d p h y s i c o c h e m i c a l characteristics of the sediments.


The

6.

Transport

GLOYA E T A L .

of Materials ι ι 1111


τ—ι—ι

II 0.1

Figure 3.

ι

in Ecosystems

1 — ι — ι ι ι 1111

ι ι I ι 1111 ι ι—ι I n u l 1.0 10 CONTACT TIME (days)

185

1—ι—Γ

1

1—LJ 50

Concentration of radionuclides by bottom sedi ments in nonflowing ecosystems

surface d i s t r i b u t i o n coefficients, K values [ t h e specific a c t i v i t y p e r u n i t 8

area o f b e d s e d i m e n t d i v i d e d b y t h e specific a c t i v i t y p e r u n i t v o l u m e o f w a t e r (i.e., d p m / c m

d p m / c m ) ] , a r e u s e f u l parameters t o c o m p a r e

2

3

the r e l a t i v e c o n c e n t r a t i o n o f r a d i o n u c l i d e s b y s e d i m e n t surface area. T h e K

8

values w e r e m e a s u r e d i n a q u a r i a studies f o r v a r i o u s r a d i o n u c l i d e s as

s h o w n i n F i g u r e 3. I t w a s o b v i o u s that K values i n c r e a s e d w i t h c o n t a c t 8

t i m e ; c e r t a i n r a d i o n u c l i d e s s u c h as

1 3 7

C s a n d S r appear to follow a n 8 5

exponential relationship (linear o n l o g - l o g coordinates).

Previous inves

tigations ( 7 ) i n d i c a t e d t h a t the c o n c e n t r a t i o n o f S r b y sediments s i m i l a r 8 5

to those u s e d i n e x p e r i m e n t s d e s c r i b e d h e r e i n f o l l o w e d t h e e q u a t i o n K

8

= 5.07 · 70

(3)

64

where Τ K

8

=

contact t i m e ( d a y s )

=

( d p m / c m ) -f- ( d p m / m l ) 2

T h e affinity o f b o t t o m sediments o b t a i n e d f r o m L a k e A u s t i n t o r a d i o n u c l i d e s released i n s t a n t a n e o u s l y i n the flume f o l l o w e d the o r d e r 6 5

Zn >

5 8

Co >

8 5

S r . T h e m a x i m u m uptake of

1 3 7

1 3 7

Cs >

C s d i d not exceed 2 4 %

of released a c t i v i t y .


186

NONEQUIL1BRIUM

SYSTEMS

IN

N A T U R A L

WATERS

A s r a d i o n u c l i d e s concentrate o n the s e d i m e n t surface, t h e y t e n d to diffuse t o d e e p e r d e p t h s .

T h e surface c o n c e n t r a t i o n a n d m i g r a t i o n r e l a

t i o n s h i p s of r a d i o n u c l i d e s f o l l o w a n e m p i r i c a l r e l a t i o n s h i p = ColO-"

C

8d

(4)

where C

8d

=

C

80

=

specific a c t i v i t y of r a d i o n u c l i d e p e r g r a m at d e p t h d i n core specific a c t i v i t y of r a d i o n u c l i d e at surface

ρ

=

p e n e t r a t i o n coefficient

T h e p e n e t r a t i o n coefficient

varies i n v e r s e l y w i t h contact t i m e .


the c o n t a c t t i m e increases, the v a l u e of ρ decreases.

As

Penetration depth

i n d i c a t e d i n T a b l e I is t h a t d e p t h i n w h i c h 9 9 . 9 % of the a c t i v i t y i n the s e d i m e n t core w a s c o n c e n t r a t e d d u r i n g the i n d i c a t e d contact t i m e . T h i s d e p t h has v a r i e d b e t w e e n 2 c m for Table I.

6 5 6 8 1 3 7 8 6 1 0 6

Zn Co Cs Sr Ru

Concentration

Z n a n d 13.5 c m for

1 3 7

Cs.

Penetration Depth for Various Radionuclides in Bottom Sediments

Contact Time j Days

Radionuclide

6 5

Penetration

17 17 30 32 30

Coefficient p, Cm-1 1.38 0.70 0.22 0.43 0.60

of Radionuclides

by

Penetration, Depth 2.0 4.0 13.5 7.3 5.2

Plants

S o m e p r e v i o u s studies, s u c h as those c o n d u c t e d o n the C l i n c h R i v e r , h a v e i n d i c a t e d that b i o m a s s m a y b e n e g l e c t e d i n a mass b a l a n c e analysis of r a d i o n u c l i d e s ( I , 4).

H o w e v e r , w h e n the biomass w a s extensive i n

t h e flume, a significant p o r t i o n of the r a d i o n u c l i d e w a s r e t a i n e d , at least temporarily (Figure 4).

P l a n t s s o r b e d r a d i o n u c l i d e s i n the o r d e r i n d i

cated. 5 8

Co >

6 5

Zn >

8 5

Sr >

F i g u r e 4 also shows that p l a n t s released than

5 8

C o and

6 5

1 3 7

1 3 7

Cs

C s and

8 5

S r at a faster rate

Zn.

R a d i o n u c l i d e t r a n s p o r t i n a n aqueous e n v i r o n m e n t p r o b a b l y is r e l a t e d to c o m m u n i t y m e t a b o l i s m ( 9 ) .

T h e c o n c e n t r a t i o n of r a d i o n u c l i d e s

increases i n the p l a n t b i o m a s s , w i t h a n a c c o m p a n y i n g loss f r o m w a t e r or s e d i m e n t , w h e n the p h o t o s y n t h e s i s - t o - r e s p i r a t i o n

(P/R)

r a t i o exceeds

o n e ( F i g u r e 5 ). W h e n this r a t i o f e l l b e l o w one, a net g a i n of r a d i o n u c l i d e s i n the s e d i m e n t a n d w a t e r a c c o m p a n i e d b y a loss i n p l a n t s w a s o b s e r v e d .


6.

GLOYA

E T

Transport

AL.

of Materials

in

Ecosystems

187

H o w e v e r , the role of c o m m u n i t y structure i n the t r a n s p o r t of r a d i o n u c l i d e s is not as t h o r o u g h l y u n d e r s t o o d . Mathematical

Modeling

S h i h a n d G l o y n a ( 7 ) presented a n a n a l y t i c a l s o l u t i o n for E q u a t i o n 1 d e s c r i b i n g instantaneous releases of r a d i o n u c l i d e s , a s s u m i n g d i s p e r s i o n i n t h e l o n g i t u d i n a l d i r e c t i o n a n d s o r p t i o n b y sediments a n d biomass.

A

l i n e a r r e l a t i o n s h i p b e t w e e n specific a c t i v i t y i n sediments a n d plants as c o m p a r e d w i t h t h e specific a c t i v i t y i n w a t e r s e e m e d to exist, p r o v i d i n g


E q u a t i o n 5. f

t

= K[G(c)

-

(5)

C)

T h e s o l u t i o n of E q u a t i o n 5 for sediments is

whereas t h e s o l u t i o n of E q u a t i o n 5 for plants is

K

~ t

t

K,(P.)

l n

( 7 )

where Κχ a n d K

2

=

mass transfer coefficients (time)

30 f

1

1

for sediments a n d p l a n t s

1

1

1

1

1

1

Γ

TIME

Figure 4.

Radionuclide

uptake by aquatic ρ fonts


188

NONEQUILIBRIUM

SYSTEMS

I N NATURAL

Ι—Γ

Τ

12.5 x l O V 25

WATERS

PLANTS I: fi ^ Z n A C T I V I T Y

20

10.0 x I0

4

7.5 χ I 0

4

15 μ

5-OxlO

4

10

2.5xl0

4

5

65

y\ ^

C0 (P/R) RATIO 2

ί8)

la/ \

0

20 30 April


20

10 20 June

10 20 Moy

30 7 July

BOTTOM SEDIMENTS

1.2 cr.

1.0 0.8

V-o^' (5) -^.^Zn^ACTIVITY C K

( 7 )

ο ο

Co

58

ACTIVITY

_ l

S

3 2 I 0 20 30 April

J

L

-I 0.6 0.4 0.2 L 0

1.2 1.0 0.8 \ _ / 17) \ 0.6 \ _ 0.4 Co58 IN WATER \ ^0 2 J L 0 10 20 30 7 10 20 31 June July May v

TIME

Figure 5.

Co and Zn activity in pfonts, sediment, and water as related to the P / R ratio (C0 metabolism) 58

65

2

K

s

and K =

e q u i l i b r i u m c o n c e n t r a t i o n coefficients f o r sediments

Cs

and C =

a n d plants specific a c t i v i t y i n sediments a n d p l a n t s a t t i m e t

C

p

w

p

=

specific a c t i v i t y i n w a t e r phase

V a l u e s o f K f o r v a r i o u s isotopes are p r e s e n t e d i n F i g u r e 3. V a l u e s 8

of K d e r i v e d f r o m the flume experiments agree w i t h the p u b l i s h e d c o n p

c e n t r a t i o n coefficients o f r a d i o n u c l i d e s b y e d i b l e p l a n t s (10).


6.

Transport

GLOYA E T A L .

of Materials

189

in Ecosystems

E q u a t i o n s 6 a n d 7 w e r e u s e d to d e t e r m i n e t h e mass transfer coeffic i e n t K i a n d K f o r sediments a n d p l a n t s . D e t a i l e d studies o n S r s h o w e d 8 5

2

that K i values r a n g e d f r o m 0.0045 a n d 0.011 h r f o r flow c o n d i t i o n s h a v 1

i n g a R e y n o l d s n u m b e r o f 2440 a n d 3700, r e s p e c t i v e l y (7). F l u m e studies also i n d i c a t e d t h a t K

for

p

8 5

S r r a n g e d f r o m 664 to 683 d p m / g r a m p e r

d p m / m l a n d values o f K v a r i e d f r o m 0.0126 to 0.0322 h r " w i t h a n a v e r 1

2

age of 0.022 h r " ( I ) . 1

B y determining D , K x

u

a n d K , i t w a s possible to p r o g r a m a s o l u t i o n 2

for E q u a t i o n 1 a n d v e r i f y i t t h r o u g h r e p e a t e d flume experiments.


Influence of Organic

Pollutional

Stresses on

Transport

A n o r g a n i c l o a d m a y influence t h e t r a n s p o r t o f other p o t e n t i a l p o l lutants.

F o r example, the reducing environment created b y organic

p o l l u t i o n m a y cause the r e d u c t i o n of h e x i v a l e n t

5 1

C r to t r i v a l e n t C r (3), 5 1

thus affecting t r a n s p o r t of these r a d i o a c t i v e ions, since sediments a n d biomass h a v e different c a p a c i t i e s f o r s o r b i n g C r V I a n d C r I I I . I n this c o n n e c t i o n , i t is possible to e v a l u a t e t h e influence of surface a e r a t i o n , w i t h o u t w i n d effects, a n d p h o t o s y n t h e t i c o x y g e n a t i o n . P r i o r to s i m u l a t i n g stream c o n d i t i o n s a n d d e t e r m i n i n g responses to i m p o s e d o r g a n i c loads, i t is d e s i r a b l e to investigate t h e i n d i v i d u a l factors that influence o x y g e n b a l a n c e , n a m e l y a t m o s p h e r i c r e a e r a t i o n , p h o t o s y n t h e t i c p r o d u c t i o n , r e s p i r a t i o n , a n d b e n t h i c u p t a k e of oxygen. T h e a e r o b i c or a n a e r o b i c c o n d i t i o n s of a stream m a y d r a s t i c a l l y influence t r a n s p o r t of ions, b u t the effect o f r e a e r a t i o n m a y b e difficult to m o n i t o r i n a stream. I n these i n v e s t i g a t i o n s , t h e first step w a s to d e t e r m i n e a t m o s p h e r i c r e a e r a t i o n o v e r v a r i o u s ranges o f depths a n d velocities. T h i s w a s a c c o m p l i s h e d i n a c l e a n c h a n n e l d e v o i d of sediment u s i n g p o t a b l e w a t e r . I n l e t d i s s o l v e d o x y g e n w a s c o n t r o l l e d b y a s o l u t i o n of N a S 0 2

3

with

cobalt

catalyst d i s p e n s e d f r o m c a r b o y s i n w h i c h a n i t r o g e n e n v i r o n m e n t w a s maintained. T h e nitrogen prevented assimilation of oxygen b y the solut i o n , t h e r e b y p r o v i d i n g r e a s o n a b l y consistent i n i t i a l d i s s o l v e d

oxygen

c o n d i t i o n s . D i s s o l v e d o x y g e n profiles a l o n g t h e l e n g t h of t h e flume w e r e t h e n o b t a i n e d . A b r i s k w i n d i n c r e a s e d a t m o s p h e r i c r e a e r a t i o n rate i n a s h a l l o w system as m u c h as 20 times t h e e x p e c t e d rate. T o e l i m i n a t e w i n d effect, a series o f baffles w e r e i n s t a l l e d a b o v e t h e flowing surface, a n d d a t a o b t a i n e d d u r i n g w i n d s e x c e e d i n g 5 knots w e r e d i s c a r d e d .

However,

e v e n w i t h these p r e c a u t i o n s , w i n d affected t h e a e r a t i o n , a n d i t w a s n e c essary to c o m p l e t e l y c o v e r t h e flume. I n a n a t u r a l system, t h e m a g n i t u d e a n d d i r e c t i o n of t h e w i n d w o u l d b e a major factor i n s t r e a m r e a e r a t i o n , b u t first t h e m i n i m u m surface transfer c o n d i t i o n m u s t b e met. F i g u r e 6 shows t h e r e l a t i o n s h i p b e t w e e n t h e r e a e r a t i o n coefficient ( k ) a n d V/H 2

15

w h e r e V is stream v e l o c i t y i n feet p e r s e c o n d a n d H is


190

NONEQUILIBRIUM SYSTEMS IN N A T U R A L WATERS

d e p t h i n feet. E a c h p l o t t e d p o i n t is a m e a n v a l u e of k for a g r o u p o f test 2

r u n s for a g i v e n v e l o c i t y a n d d e p t h . A n average of 17 test r u n s w e r e m a d e to e s t a b l i s h t h e v a l u e of e a c h p l o t t e d fc - E q u a t i o n s 8 a n d 9 d e s c r i b e t h e 2

best fit d e t e r m i n e d b y t h e least s q u a r e m e t h o d . Log k

= 0.703 L o g ^

2

fc =

2.98

2

"

V "

+

L o g 2.98

(8)

0.703

(9)


W h i l e these e q u a t i o n s are d e s c r i p t i v e of t h e flume, t h e y are r e a s o n a b l y close to t h e p r e d i c t i o n m o d e l d e r i v e d b y C h u r c h i l l , E l m o r e , a n d B u c k i n g h a m f r o m t h e i r a n a l y s i s of a t m o s p h e r i c r e a e r a t i o n of streams i n t h e Tennessee V a l l e y ( I I ) .

T h e C h u r c h i l l et al

f o r m u l a for p r e d i c t i o n of

at 2 0 ° C is

k

2

fc = 2

(10)

5.026

A s a n e x a m p l e of c o m p a r i s o n , T a b l e I I shows k

2

ι

ι ι ι ι 11|

1—ι—ι I ι ι 11J

predictions b y the

I

1

I I I II I

10.0

ce

UJ

Nonequilibrium Systems in Natural Water Chemistry

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