246
G. Schroeder, E. Êemer=Samson0v
microns
thick.
The thickness depended upon the rate of
stirring.
If
we
assume
for
our
ponds on calm nights,
a
100 micron thick laminar
surface
layer below which eddy diffusion (which is orders of magnitude greater than
molecular
diffusion) is dominant,
then we can solve for the value of
the
diffusion coefficient in
First Law of diffusion:
J = —D 8c/8x
,
(2)
where J is flux, D is the diffusion coefficient and ÔC/ôX is the concentra—
tion gradient of the diffusing substance across the laminar layer.
Substituting
the
observed rates of oxygen loss
from.
supersaturated
fish
ponds and the corresponding values of DO
supersaturation
(Schroeder
1975) for J and ÔC/ôX in Eqn.
2 gives an average value of D, the diffusion
coefficient of oxygen across the laminar pond surface layer, of 2 x 10_5 cm
sq/sec.
The
coefficient of oxygen in water at 20° C
has
been
neasured to be 2 x
cm
sq/sec (Kanwisher 1963).
The
agreement between diffusion theory and observation has important
implications
for
transfer
of all gases across
the
pond/air
interface.
Because of the laminar boundary layer,
when DO is low, diffusion of oxygen
from
the atnosphere into the pond can supply only a few ppm DO
daily.
To
increase
the transfer rate,
the landnar layer must be broken
and
oxygen
introduced by convection (e.g., the vigorous stirring of a paddle wheel).
C — Annonia diffusion
Ammonia
in
the
water column is necessary for
algal
and
microbial
heterotrophic
production of protein.
Ammonia is also potentially toxic at
concentrations
exceeding a few ppm.
Values of D vary inverse1y
with
the
square root of the molecular weight (MW) of the diffusing substance.
Hence
the
value
of D for ammonia (MW = 17) is similar to that of oxygen
(MW
=
32).
Consider a one meter deep, 28° C, freshwater pond with pH 8. For these
conditions, 7%
of
the ammonia is in the un—ionized,
gaseous
forn1
(Boyd
1982).
Based
on
the above values of D and X and recalling
that
transfer
rates are also dependent upon the solubility of the gas in water, the daily
loss
of
ammonia by diffusion into the atmosphere can account for
of
the total amount of amnonia in the water column.
For 2 ppm
ammonia,
this
would
account
for
200 mg loss/ sq m/day.
Using l5—N as
a
tracer,
Ian
Fillary (IRRI,
Los Banos,
Philippines, personal comm.) measured losses of
0.4
to
2 gn1anncnia/sq m/day from paddy water (18 to 34° C;
pH 8
to
9)
initially containing 14 ppm amnonia.
Considering the estimates of
laminar
film
thickness and solubility coefficients and the differences in
concen—
trations,
our
calculated
value of 10% loss is consistent with
Fillary's
measured values.
D — Carbon dioxide diffusion
Carbon
dioxide also has potential for diffusion across the
water/air
interface.
A
complexity in considering flux of carbon dioxide into
water
from
the
atmosphere is its removal as a dissolved gas as it
converts
to
roni2ed carbonates. As with ammonia, only the un—ionized, dissolved form of
the gas affects diffusion between the atnosphere and the
water.
Kanwisher
(1963)
estimated
that
the average time for a
dissolved
carbon
dioxide
nclecule to diffuse through a 100 micron layer is <2 seconds.
Roughton and
G. Schroeder, E. Êemer=Samson0v
microns
thick.
The thickness depended upon the rate of
stirring.
If
we
assume
for
our
ponds on calm nights,
a
100 micron thick laminar
surface
layer below which eddy diffusion (which is orders of magnitude greater than
molecular
diffusion) is dominant,
then we can solve for the value of
the
diffusion coefficient in
First Law of diffusion:
J = —D 8c/8x
,
(2)
where J is flux, D is the diffusion coefficient and ÔC/ôX is the concentra—
tion gradient of the diffusing substance across the laminar layer.
Substituting
the
observed rates of oxygen loss
from.
supersaturated
fish
ponds and the corresponding values of DO
supersaturation
(Schroeder
1975) for J and ÔC/ôX in Eqn.
2 gives an average value of D, the diffusion
coefficient of oxygen across the laminar pond surface layer, of 2 x 10_5 cm
sq/sec.
The
coefficient of oxygen in water at 20° C
has
been
neasured to be 2 x
cm
sq/sec (Kanwisher 1963).
The
agreement between diffusion theory and observation has important
implications
for
transfer
of all gases across
the
pond/air
interface.
Because of the laminar boundary layer,
when DO is low, diffusion of oxygen
from
the atnosphere into the pond can supply only a few ppm DO
daily.
To
increase
the transfer rate,
the landnar layer must be broken
and
oxygen
introduced by convection (e.g., the vigorous stirring of a paddle wheel).
C — Annonia diffusion
Ammonia
in
the
water column is necessary for
algal
and
microbial
heterotrophic
production of protein.
Ammonia is also potentially toxic at
concentrations
exceeding a few ppm.
Values of D vary inverse1y
with
the
square root of the molecular weight (MW) of the diffusing substance.
Hence
the
value
of D for ammonia (MW = 17) is similar to that of oxygen
(MW
=
32).
Consider a one meter deep, 28° C, freshwater pond with pH 8. For these
conditions, 7%
of
the ammonia is in the un—ionized,
gaseous
forn1
(Boyd
1982).
Based
on
the above values of D and X and recalling
that
transfer
rates are also dependent upon the solubility of the gas in water, the daily
loss
of
ammonia by diffusion into the atmosphere can account for
of
the total amount of amnonia in the water column.
For 2 ppm
ammonia,
this
would
account
for
200 mg loss/ sq m/day.
Using l5—N as
a
tracer,
Ian
Fillary (IRRI,
Los Banos,
Philippines, personal comm.) measured losses of
0.4
to
2 gn1anncnia/sq m/day from paddy water (18 to 34° C;
pH 8
to
9)
initially containing 14 ppm amnonia.
Considering the estimates of
laminar
film
thickness and solubility coefficients and the differences in
concen—
trations,
our
calculated
value of 10% loss is consistent with
Fillary's
measured values.
D — Carbon dioxide diffusion
Carbon
dioxide also has potential for diffusion across the
water/air
interface.
A
complexity in considering flux of carbon dioxide into
water
from
the
atmosphere is its removal as a dissolved gas as it
converts
to
roni2ed carbonates. As with ammonia, only the un—ionized, dissolved form of
the gas affects diffusion between the atnosphere and the
water.
Kanwisher
(1963)
estimated
that
the average time for a
dissolved
carbon
dioxide
nclecule to diffuse through a 100 micron layer is <2 seconds.
Roughton and