Rochester Institute of Technology
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Theses
Thesis/Dissertation Collections
1970
Diffusion of the thiosulfate ion out of photographic
film during washing
Kenneth Haring
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Recommended Citation
Haring, Kenneth, "Diffusion of the thiosulfate ion out of photographic film during washing" (1970). Thesis. Rochester Institute of
Technology. Accessed from
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ROCHESTER INSTITUTE
of TECHNOLOGY
Diffusion of the Thiosulfate Ion Out
of Photographic Film During Washing
A thesis submitted in partial satisfaction of the
requirements for the degree Master of Science
in Photographic Science and Instrumentation
by
Kenneth Robert Haring
Under the supervision
o~
Professor B. H. Carroll
~ ~ 3 1 197()
1970
Burt H. Carroll
Ronald Francis
Name Illegible
DIFFUSION
OF THE THIOSULFATE ION OUT
OF PHOTOGRAPHIC FILM DURING WASHING
ABSTRACT
The thiosulfate ion does not
freely
diffuse out of a hardened photographic gelatin
emulsion.
Salts in the washing water displaces
the adsorbed thiosulfate ions and allows them to
The effect
freely diffuse out of the emulsion.
of temperature upon the diffusion of the thiosul
fate ion is on the order of other diffusion pro
The type and amount of hardening also
cesses.
affects the diffusion of thiosulfate.
The diffu
sion of thiosulfate out of the emulsion is fastest
when a non-hardening fixer is used.
The use of
an alum hardening fixer results in slower diffusion
than with formaldehyde prehardening.
-
When
fixing
is
for
agent
it from the
the
cause
the
rate
image
silver
fiTLm
the
thiosulfate
controling
The
fusion
rate
to
with
film is
ion
out
free
or
retention
an
the
coefficient.
or
change
of
the
thiosulfate
of
problem
to
do
usual
The
so
gelatin,
removal
the
which
diffusion
the
for
a
in time,
of
with
upon
as
removing
will,
method
rate
dependent
diffusion
Anything
a
of
sodium
this
is
the
step.1
temperature.
by
The
water.
the
diffusing
shown
Failure
fade.
the
upon
be
such
of
constant
depends
the
began.
emulsion
by washing
film,
photographic
thiosulfate leaves
of
began using
photographers
the
can
be
The
expressed
value
this
of
entity and medium,
that
impedes free
in the diffusion
thiosulfate
ion
by
by
as
dif
a
constant
well
as
diffusion
constant.
gelatin
will
Adsorption
would
be
impedement.
The
purpose
of
this
investigation is
1
1 9. 3 n 8 1
to
derive, by
means
of
constant
during
sion
to
the
express
in the
wash
ion
effects
the
of
tion
*-
after
Higgins^
put
are
diffusion
equation'
The
of
a
and
the
simplified
one
starting
with
order
second
law.
where:
^>C/
=
concentration,
and
type,
solution
three
specified.
Blyumberg
of
an
a
of
initial
emulsion,
an
=
but
equation
James
not
equa
and
valid
Davydkin"
studied
a
getting
derived
they
of
^^
time, D
differential
boundary
similar
Davydkin,
t
and
an
,
is
diffusion
known
as
a
Fick's
*-
=
diffusion
distance
partial
and/or
Choosing
and
x
=
/")
changing
Hickman
by
and
equation
=.
and
law.
types
for all
photographic
of
emulsion,
second
differential
partial
c
an
salts
Elsden^
form
state
For this
.
Fick's
equation
constant,
For the
into
used
diffusion
but the
mentioned
emul
hardening.
of
by
work
Blyumberg
1.0x10
of
second
Early
steady
thiosulfate
constant
general
the washing
washing,
for changing concentrations.
the diffusion
emulsion
had been reached.
continuous
is then
temperature,
equilibrium
forward
of
water
washing technique
studied
they
photographic
static
studied
water
Spencer
the
a
constant
and
into
have been conducted.
materials
the
wash
image density,
water,
Several investigations
Warwick-'
leaving
The diffusion
washing.
for the diffusion
expression
thiosulfate
the
of
an
model,
a mathematical
for the
2
of
must
be
conditions
conditions
adapting
equation
to
those
them to
changing
used
diffusion
this,
by
out
concentration
may be derived.
film
The
three
and
washing procedure.
1
)
conditions
The base
to
vious
the film is
thiosulfate
The
2)
of
initial
such
that
the
none
is
a model
on
to be
assumed
concentration
throughout
stant
based
used were
the
imper
penetrates
it.
be
con
to
assumed
film thickness
of
prior
the
to
washing.
After washing starts,
3)
surface
is
a
valid
water
The
of
the film is
assumption
changes
equation
resulting
for
concentration
for the
with
the
turbulent
and
spray
washing.
diffusion
the
at
This
zero.
rapid
in
presented
br
to
assumed
associated
derivation is
actual
the
appendix
The
A.
is:
constant
,z
D
where:
=
diffusion constant,
=
der
of
the
derived
It is
for D.
The
of
value
for D
R
and
actuality,
equal
term
term R
The
to
first have
containing
arises
out
of
concentration
a
emulsion
infinite
an
the
thick
series
mathematical
equation
converging infinite
to
get
for the
This
little
the
cases
studied,
is because the
effect
on
the
R
can
series
value
of
expression
alternately solving
is
desired accuracy
an
rearranging
containing D.
series
D is determined iteratively,
until
1.0.
=
average concentration,
t
time, "c
initial concentration, and R is a remain
ness,
c^
1
=
=
In
reached.
be
assumed
terms
R.
to be
after
the
Experimental
The
data
experimental
the parameters
on
was
setup
that
stored
with
as
in
This
the water.
bottle
a
An
to force
the
emulsion
The
fiTLm
not
have
simple
It
of
the
emulsion
Whether
exposed
fixing
time
then
and
backing
time
wiped
film
fixing, the
with
with
was
clean
a
a
wash
through
water
spray
was
Recon
Duplicating
it does
and
it is
because
type films
there
that
a
relatively
receive
some
was
harden
manufacture.
not,
the film
water
in the
was
first
placed
31
for I4.
minutes
before
being
placed
to
fixing
bath
twice
was
in
at
in the
the
clear.
piece
was
moisture
surface
damp filter
taken for
The
in
CO2
to the
rate
constant
7
about
of
pH
applied
was
was
water
dissolved
of
duplicating
during
with
a
many
for washing
principally because
possible
or
as
the film sample.
chosen
it took the film to
t he fiTLm
the
The
bath.
After
then
rinsed
a
at
Kodak HC-110 developer diluted 1
25C
psi
The
to
70mm Kodak Aerial
was
is
5
nozzle.
Because
emulsion.
in.
enter
the
experimental
used
was
water
adjusted
of
out
of
was
gelatin
treatment it
rough
ing
any
side
used
Film type 8lj.27
and
pressure
the water
The
gather
eliminate
necessary because
"Spra-Rite"
Brinks F-0
onto
air
would not
bottle
was
up to
set
designed to
Distilled
hardness
a plastic
NaOH,
and
possible.
water
was
the equation.
of
simple
quite
variables
so
procedure
of
filter
paper
analysis
k
to
blotted from
The base
paper.
and
dried.
determine
A
sample
the initial
was
of
thiosulfate
hole punch.
mond
For initial
having
shaped
started
washing
diameter
was
thiosulfate
a
was
tration figures.
mg./In^
of
aera
to
get
it
taken,
sion
in the film
then correlated
another
punching
sodium
blade
viewing it,
off
while
with
a
time
consuming process,
micrometer
for the
tion.
was
other
the
average
As
determined.
was
The
sample
concen
expressing them in
by
concentration
sample
of
still
determined
by taking
the
with
wet,
Since
sample
was
a
razor
difficult
time
other
every
a
determined
was
and
the
The
taken duringyaLwashing.run..
samples
a
a microscope
under
this
done
was
emul
interpola
by
.
The
analysis
chemical
repeatable,
accurate,
and
it
was
edge
eyepiece.
sample
1/i|. inch
a
taken to determine the
was
the
of
which
After
thiosulfate.
thickness
slice
having
a
dia
was
inch.
square
holes.
more
thiosulfate
sample
The
the hole
with
necessary to increase the
was
were
very thin
thickness
from
by
anhydrous
concentration
punch
taken
were
a
of
done
thickness.
and
hole
samples
At the time that the
was
1/61*.
of
circular
used
samples
concentrations,
concentration
This
size.
an
progressed
washing
All
concentration.
give
objective
for the thiosulfate has
sensitive
results.
to
small
For these
to be
concentrations,
reasons
the method
Q
of
Warburton
method
the
tion
of
and
Przybylowicz
Crabtree
and
10
The
Ross.
thiosulfate from the film
of
KI
and
KH2P0j,.
was
instead
used,
procedure
sample
in
a
Sodium borohydride
1
is
g/1
of
to
the
extract
each
solution
solu
is
then
to the
added
extract
sulfide.
Ferric
tions
then
ar
to
solution
sulfate
added
and
which
the
reduce
p-dimethylaminoaniline
the formation
causes
to
thiosulfate
of
solu
methylene
blue.
The amount
was
6D
measured
665
at
with
mji
The
mined.
of
the concentration
and
th
calibration
This
condition
centration
of
The
sulfate.
absorbance
readings
1620
computer
equation
equation
to
(because it
of
to
experimental
for
long
set
equal
continue.
to 0.001
This
a
"A.FX'k-r-By
17:
on-
"4
that
so
con
thio
The
concentrations
on
concentrations
and
a
IBM
an
line
linear
cubic
for the
closely fit the data)
the
360
computer
constant.
concentration
of
If,
the
the data
because
thiosulfatp
determined to b negative,
the
that
is
--pEc :.
of
cases.
straight
an
computer
order
of
.'4
'44-4 [P.
.v
y.
it
calculations
magnitude
OTsruO'
'7''.t.e
in
condition
other
technique
squares
diffusion
was
value
i;
to
1
micrograms
in both
same
IBM ; Systems
the
so
done
(See figures 1&2)
an
error,
times
wash
The
15
equations,
most
data.
compute
was
the instrument.
of
thiosulfate
for the high initial
concentration
used
two
give
below
least
a
using
With the aid 7 on
was
scale
the
was
known
of
deter
only to determine the initial
procedure
correlated
samples
thiosulfate
diluted
was
thiosulfate in the film.
were
low
the
for lower concentrations,
was
the
of
spectrophotometer
solution
off
go
used
was
the film
for high concentrations,
was
blue
not
the
of
One
methylene
th reading did
by
Coleman Junior Spectrophotometer Model
a
for two conditions.
which
blue formed
methylene
was
could
smaller
than
20
25
CONCENTRATION
1
fig.
the
smallest
obtain
and
for washing
setup
was
image
and
conventional
silver
was
optieal^
u*i|ig
wash
a
water
studied
density
of
fiTLm
0.3
and
(Kodak SH-1 )
exposed
film
a
1.0.
with
,
a
conducted
of
image
was
an
studied
formaldhyde
the non-hardening
7
no
(Kodak
developed to
Film hardness
(Kodak F-2i+)
with
bath
were
effect
and
The
conditions.
experiments
The
designed
were
hardening fixing
temperatures.
with
several
25 C using
at
acid
non-hardening fixer
prehardener
for
From this base,
F-5 formula).
other
Ito
35
runs
experimental
constants
basic
at
30
NB2S2O3
concentration.
non-negative
diffusion
a
jig
High Concentration Calibration Curve
Th washing setup
to
-
fixer,
and
.60
-
.50
-
.ko
W
o
.30
o
-
.20
-
.10
6
5
^
hardening
acid
hardening
A
used
and
of
the
agents
salt-water
after
with
an
mental
were
fixer that
pg
9
Na2S203
than the
wash
standard
2
of
densities
washing
on
g/1
replicated
of
the
at
twice
contained
F-5 fixing bath
optical
salt-water
runs
-
2 Low Concentration Calibration Curve
fig.
an
8
7
CONCENTRATION
0.3
of
film
and
diffusion
least once
variability.
8
amount
of
F-5
each
on
the
KI
with
1.0
and
no
to
NaCl
image
was
silver
study the
constant.
All
effect
of
to determine experi
Results
Some
the
of
is presented in
data gathered in
appendix
B.
diffusion
equation
should
diffusion
constant
for free
decrease,
when
constant
with
plotted
tim
on
of
Substituting
give
a
constant
diffusion.
log-log
a
found.
was
few
a
the
the
experiments
data into
for the
value
Instead,
scale,
of
the
linear
a
the diffusion
(See figure 3 below)
1-10"
3-10 -7
-
o
1
1
_
10
o
a
o
Fixer:
F-5
Temperature:
25C
Density: 0.0
8
3-10'
m
_l_
10
30
1 00
300
TIHB
fig,. 3 Non-Saltwater
In
rithms
order
to
(samples from the
tion but
with
the
times
wash
technique.
same
different
were
This
seconds
Washing
facilitate
the diffusion
of
-
1000
data interpretation the loga
constants
piece
wash
of
regression
film
times
by
correlated
for
)
a
analysis
9
each
and
and
washing
initial concentra
the logarithms
regression
was
run
done
of
analysis
on
an
IBM
Systems 360 Model 91
eters
of
which
may be
a
The
rearranged
a
exception
constant
A
plot
fusion
of
constant
60
about
to:
seconds
to
tha
with
D
=
and
the
also
exponential
(figure ij.)
to be
then
goes
to
the
=
a
+
b In
slope
plotted
in figure 3
saltwater
washes.
dif
that the
shows
for
a
period
exponential
the
of
relationship
constant
a
param
t*3
a
b is
and
the
give
the form In D
time is for the
the data
appears
results
of
line for the data is
diffusion
log-log
equation
is the intsrcept
regression
The
line
straight
where:
The
computer.
of
tim
relationship.
"'"
"1
3-10-6!-
r
Density
-
X
0
-
x
-
0.0
0.3
1.0
Fixer:
I
o
4)
gxx
F-5
X
Temperature:
X
25C
0
1-10
8
CVJ
*
X
X
S3
\
IS
GO
53
0
O
o
3-10
0
*
K
-7
M
CO
E>
fx.
&<
0
s
*
1
o*
0
"
-10
"
X
1
100
30
10
TIME
fig.
k
Saltwater
^>
~L
Washing
10
-
seconds
300
1000
t
The
effect
is
constant
and
figure
there is
no
image
in figure
shown
k
the
of
for the
definite
silver upon
5 for
non-saltwater
saltwater washing.
to
pattern
This indicates that image
no
upon
1
^-6
As
the data
density.
effect
the diffusion
can
be
seen
regards
to
has little
or
with
silver
washing
th diffusion constant.
IT
T
Density
to
.
-
o.O
o-
0.3
x-
1.0
*
x
S
3-10-7
X
*
x2
O
Eh
Eh
O
ol
3
Eh
X
CO
8
x
*
1-10-7
o
Fixer:
H
03
F-5
_
Temperature:
fe
25C
H
3-10
-8
_
-L
100
30
10
TIME
5
fig.
As mentioned,
a
straight
lines
straight
This
is
regard
various
log-
are
log
quite
similar
to
the
similar
of
in
slope
for the
but
runs
the
are
Image Silver
diffusion
th
temperature.
temperature
seconds
relationship
especially true
is
slope
line
of
most
-
Washing
Non-Saltwater
1000
300
The
for
most
of
lines
are
spaced
regression
data has
These
time.
with
the
temperature data
plotted
11
constant
data.
where
apart
lines
in figure 6.
the
with
for the
1-10"
6 Tes^erature Variation
fig.
Boltaks1^
fusion
said
that the thermal dependence
be
can
constant
Diffusion Constant
of
expressed
D
as:
I),
=
e
a
of
dif
-E/RT
diffusion constant, D= diffusion con
stant base, E = thermal activation energy,
R = gas constant, and T = Kelvin temperature
where:
the
Taking
D
=
logarithm of the
natural
In D
The
+
Y
=
a
X
=
1/T.
the
of
log
tJae
is
now
bX assuming Y
Th
of
the
diffusion
temperature
th
=
activation
1/T.
slop
equal
temperature
lng
witji
The
equation
'to
=
lb-
In
equation:
E/RT
in the form
In D,
a
=
In
of
C,
energy E may be
constant
The
-E/R
studied
D
graph
straight
a
b
-E/R,
found
against
will
=
by
the
be a
and
plotting
reciprical
straight
and
the
intercept
was
not
very
12
line
line
being In D
great
and
as
,
figure 6
the
shows
spacing
For these reasons,
logarithm
or
be
can
energy
of
the diffusion
approximation
Figure 7
shows
a
diffusion constant,
gives
A
computer
intercept
an
Using
-2.68*102
the
of
gas
=
-6.37
constant
and
R
of
proper
order
ttt-
for
a
th
the
natural
about
120
seconds
versus
the
reciprical
at
of
analysis
a
activation
of
of
slope
1.987
thermal activation energy
approximate
This is
a
D
of
regression
varies.
constant
of
plot
approximately midway into the wash,
temperature.
an
an
only
made.
the
of
-E/R
cal/K
of
diffusion
data
the
5.3
=
gives
kilocalories.
process.
r
CO
S3
O
w
CO
g
-15.11.
h
Fixer:
u
F-5
o
Density:
3
3
0,0
-15.6
<
i.
1
RECIPRICAL
fig.
The
different
fixer,
a
7
Activation
effect
of
Energy
emulsion
conditions.
The
F-5
with
modified
TEMPERATURE
Plot
hardness
standard
30
25T K
29H K
303 K
WK
g/1
13
of
was
tested
Kodak F-5
potasiisum
-under
acid
four
hardening
alum
instead
of
and
tji
l5g/l,
non-hardening fixer (Kodak F-2i|_),
a
formaldehyde prehardener
a
fixer
ent
normal
all
were
tried.
xperimental
runs
(Kodak SH-1 )
with
th F-2ij.
The regression lines for the differ
ar
presented
in figure 8.
~
T
1
1
Fixer
F-5
F-24
3 10
-6
SH-1 &F-24
4
F-5 2X Hard
10"
*v_
1
z
o
o
o
3 10 -7
to
10"
1
10"
3
240
60
15
TINE
8
fig.
The
the
Effect
main
emulsion
slower
the
of
effect,
the
Hardening
as
smaller
diffusion
-
of
seconds
on
expected,
is
the
the
Diffusion Constant
is
the more
diffusion
thiosulfate
1ft
960
hardening
constant
ion
out
of
or
the
of
the
The
emulsion.
in diffusion
use
Doubling
the diffusion
slows
prehardening the
by
alum
results
non-harden
in the F-5
For the formaldehyde
2 times.
the
of
the
with
potassium
about
slope
than
slower
the
fixer
hardening F-5
acid
8 times
about
ing F-2I). fixer.
the
of
line is
regression
steeper
and
the decrease in diffusion from non-hardening is
not
very
the
F-5 fixer (emulsion
for
both),
The
great.
but
emulsion
with
between the diffusion
to be
more
the F-5 fixer.
to
same
allows
as
wet
|i
the
with
emulsion
The difference
then decreases
hardening
adsorbed
strongly
th
leaves
initially
constants
t,Jie formaldehyde
was
approximately I4.O
thickness
the thiosulfate
3 times faster than
that
hardness
initially
indicating
thiosulfate
the
ion
the gelatin.
Conclusion
The
is
that tohe thiosulfate ion does
th
gelatin
adsorbed
of
to
washing.
film
emulsion
of
the
it,
as
soon
even
It is
not
known
by
adsorption
The difference
of
the
seen
in figure 8
emulsion
as
provides
for better
used
any formaldehyde type
of
this
might
with
time.
account
a
this
by
in
an
that
the
in these
changing
15
appears
after
of
to be
the
unhardened
start
of
gelatin.
prehardened
an
emulsion
thiosulfate ion.
experiments
of
out
interference
such
hardening during
for the
results
freely
formaldehyde
shows
adsorption
the duplicating film
seconds
occurs
for
but
used
15
as
diffuse
not
whether
free diffusion
slope
drawn from the
to be
conclusion
principal
If
had received
manufacture
then
the diffusion constant
In t heir study
1 P
Crabtree
have
emulsion
thiosulfate ion by
th
fact that in figure
remain
about
washing.
salt
Th
salt
thio
due to displacement
of
the
This
anion.
for the first
would
constant
minute
10.2%
firmly
each
NaCl
adsorbed
constant
takes
time.
16
and
KI)
on
the
the
to
saltwater
until
can
thiosulfate
explain
appears
of
displaces the thiosulfate
salt
and
of
constant
more
with
was
Henn, King,
removal
that the faster
the diffusion
time the diffusion
tionship
washing
l
concentration
displace the
saltwater
suggested
from th
sulfate
of
no
ions
the
low
longer
at
exponential
which
rela
APPENDIX A
Derivation
Fick's
law of diffusion
second
*%*
where:
Diffusion Constant
of
^c/b
D
=
is:1^
**
concentration, t
time,
constant, and x = distance
Film
=
c
=
model:
0)
D
diffusion
=
r
i
I
sfc
I
1 = emulsion
thickness
7777773
The base is
may be
X 0
tion
0.^*
=
x
gradient
penetrate
of
at
=
x
at
This
0
and
concentration
a
second
like Fick's
second
ditions
needed.
will
are
satisfy
is the
of
time t
the
=
The final
boundary
supply
of
is
a
function
the washing time
t,
above
that
and
differential
An initial
concentration,
equals
the
equation
boundary
and/or
partial
condition.
the
differential
partial
three initial
emulsion,
over
initial
con
equation
condition
the
entire
concentration
0.
requirement
condition.
fresh
order
The
concentra
thiosulfate will
no
concentration
base,
no
c0
boundary
specification
thickness
at
one
law,
therefore
The
equation
that there is
means
the distance x from the
TEn solving
differential
partial
into the base.
th initial
c0
th
by
expressed
This
impervious to thiosulfate.
to be
assumed
water
for
solution
With spray washing,
removes
may be
the
the thiosulfate
17
met
by
a
continuous
at
the
surface
of
the
tion
This may be
emulsion.
being
zero
at
=
x
expressed
1 for times
the
as
than t
greater
If it is assumed that the
concentration,
tion
of
x
Fick's law,
of
has
t,
and
and
are
examination
a
negative
the
assumed
sides
equal,
of
they
gives
The
t
>
0
that
othe
will
to
equal
are
technique
equation
a
of
into
one
vari
An
constant.
if both
equal
are
0
or
^
_
~~SC~
~~
-
be
can
this
o7
where:
-P
condition
can
concentration
boundary
Remembering that
OC
x
0 that
=
^d^=
0
it
^
satisfied
by
X
0
at
x
=
1 for
where
n
is
=
as:
that
condition
p
satisfied
at
only be
=
independently.
solved
if
be
the
by
functions
are
be
they
^
equations
the
func
?v
From the boundary
This
a
^7*x
^_
apparent
being
0.
X(x)'Tit), then
concentration
must
P
JlL
is
=
solved
(2)
eq.
that
show
will
number
These
be
c
=
variables]-'
Substituting
Since both
form
general
(1), may
equation
separation of
able
a
concentra
=
(n
+
=
c
l/%)
-y^
an
z
integer.
Hie
initial
condition
-
that
18
D:
c
=
c
at
t
=
0 is incorp-
D
rated
sion
by evaluating
to
equal
needed
cw
%
the
is
^
x
<
with
respect
t
at
all
0
=
values
and
of
setting the
the integer
expres
n
are
concentration, it is necessary to
sum
the same
at
determined
0
rang
and
Multiplying
ing
Since
.
to give the
the expression
(3)
eq.
1
time incorporate
by evaluating
setting it
and
both
sides
to
over
x
by
0 to
=
x
=
0
over
.
(m+^lf-x
range
constant
a
t
at
to c
equal
/*r*
the
(ij.)
eq.
integrat
and
x
=
1:
j
fa Kn
of
The
right
side
m not
equal
to n.
xyxL(
of
eq.
to+y%)f
(5)
is
Setting
m
=
x
equal
n
and
s^(n+7z)fx
0 for
to
Evaluating
the limits
Substituting into
Equation
throughout
The
the
of
the
gives
analysis
the
concentration
film
is
U)
of
values
eq.
(5)
/
:
concentration
0
to
the film
An
sample.
obtained
Cs)
simplifing:
from x
emulsion
thiosulfate
centration
age
(6)
eq.
and
all
integrating
fr 4^fl/n;) 2^2J
up
x
=
gives
at
1
at
point
any time t.
an
average
con
expression
for the
aver
by integrating
19
any
the
concentra-
s
tion expression
eq.
dividing by
thickness.
the
(6)
over
the
emulsion
thickness
and
c^-jrf/cd.*.
Substituting
in
By rearranging
constant
be
can
Expanding
eq.
the
(6):
terms in
eq.
(7)
the diffusion
determined:
the
series:
TTX<1
777-6J?
11/*4r0_
Jf^t)
8 C0
Taking
the natural logarithm
Letting:
R
=
/+
$e
4^.*-
of
both
sides:
+4*
-*"%
+
.
Then
D may be
setting R
R
until
=
the
1
determined
and
then
desired
by
an
iterative
technique, first
alternately solving for D
accuracy is
20
reached.
and
then
APPENDIX B
Fixer F-5
Density
Time
0
Cone.
sec
1661.
"
15
30
"
60
"
0
"
lj.1.8
"
235.2
103.8
28.65
2ft0
"
3.14-5
I4.80
"
3.16
35.9
Density
"
14-3-3
"
120
"
54. 1
"
240
"
ij-6.9
"
540
14.7-7
"
720
Temp.
Cone.
Tim
15
30
60
120
240
480
720
sec
0
15
"
44*6
"
30
"
49.0
"
60
"
56.7
"
120
"
55.5
"
240
"
2.469"
54- 2
"
480
"
1.334"
49.2
"
720
172.7
"
83.22
"
24.20
"
6.94
45.9
"
"
42.8
"
"
14.667"
41.2
"
tt
1.838"
39.5
"
1.084"
42.5
"
Time
48.3 p
"
"
Thick.
"
184.8
"
Density
1820.
"
1^9.9
33.0C
pg/in2
0
n
199.1
126.3
44-5
Fixer F-5 2x Hard
No Salt
0.0
44.9 p
"
60
Fixer F-5
"
"
"
pg/in2
253.8
30
ii.3-3
2018.
"
"
"
1.902"
720
sec
15
p
Thick.
Cone.
Time
Thick.
21
2l|_.2C
Temp.
0.0
Density
pg/in2
265.8
n
120
Temp. 25.5C
0,0
No Salt
Fixer F-5
No Salt
1529.
307.9
"
261.9
"
"
5
C
pg/in2
"
"
24.
Thick,
Cone.
sec
"
No Salt
Temp.
0.0
"
168.7
85.96
12.27
"
32.0
"
37.1
"
"
"
"
4.108"
"
2.203"
31.4
34.4
34.4
34-3
36.2
p
"
"
"
"
"
"
Fixer F-2L).
Time
0
Cone.
1369.
sec
"
15
30
60
Temp.
0.0
Density
24.
5
C
Density
0
"
62.7 p
15
"
1.169"
65.2
"
30
"
0.303"
68.2
"
60
0.057"
66.3
"
120
120
Density
0.0
Temp.
Oonc.
Time
Temp.
Salt
25.0
C
Thick.
pg/in2
"
41.8
"
40.8
"
"
0.001"
40.9
"
"
1.274"
41.0
"
"
0.071"
4^-4
"
0.020"
41.8
"
6.05
"
3.04
Fixer
Salt
1161.
sec
480
F-5
No
Cone.
240
Fixer
F-24
0.0
Tim
Thick.
pg/in2
10.84
&
Fixer SH-1
No Salt
F
"
"
Salt
F-5
26.0C
Density 1.0
Thick.
Time
Temp.
24*5 C
Thick.
Cone.
pg/in2
0
sec
15
30
60
120
240
480
720
1707.
0
pg/in2
"
30.79
"
3.96
"
37.3 p
15
"
39.8
"
30
sec
"
0.180"
42.6
"
60
"
0.059"
42.8
"
120
"
0.055"
U4.2
"
240
"
0.042"
45.6
"
480
"
0.077"
46.9
"
720
22
"
1757.
30.78
"
38.5 p
"
"
2.061"
39.0
"
0.071"
44.3
"
0.165"
42.6
"
"
0.055"
44.6
"
"
0.159"
46.5
"
0.007"
46.5
"
"
"
BIBLIOGRAPHY
1
James, T. H.
Theory.
2Elsden,
C.
Higgins,
Fundamentals
Morgan & Morgan,
d.,
of
Photographic
New
Inc.,
York,
(1960)
166
p.
& G.
2nd
Photographic Journal.
-^Warwick,
American Photography.
4Hickman,
K.
C.
D.
62(N.S. 46)
& D.
p.
A.
57(N.S. 41 )
11
Spencer,
p.
31 7
p.
90
(1917)
(1917)
Photo graphic
Journal,
225 (1922)
c
^
James &
Higgins, Ibid
6Blyumberg,
I. B. & I, M. Davydkin, Zhurnal Nauchnoi i
Prikladnoi Fotografii i Kinematografii, 0(2) p. 81
?
B. & I. M. Davydkin, Uspekhi Naushnoi FotoAkademiya Nauk SSSR, Otdelenie Khimicheskikh.r
I.
Blyumberg,
rafii,
p.
(1962)
106
Moore, W. J., Physical Chemistry,
Inc., Englewood Cliffs, N. J.,
9Warburton,
and
C.
& E.
D.
Engineering,
1Crabtree,
(1963)
J.
& J.
F.
P.
10
3rd
p.
d.,
341
Prentice-Hall,
(1962)
Przybylowicz, Photographic Science
p. 86 (1966)
(2)
Ross, Journal of the Society
14 p. 419 (1930)
of
Motion
Picture Engineers,
1lBoltaks,
B.
I.,
conductors,
12Henn,
R.
13j0st,
W.,
trans, by J. I.
Academic Press,
Carasso, Diffusion in Semi
New York, p. 4 (1960)
W., N. H. King, & J. I. Crabtree,
Engineering, 7 p. 153 (1956)
Press
1^Rohsenow,
fer,
Solids, Liquids,
York, p. 75 (I960)
Diffusion in
Inc.,
New
Photographic
Gases, Academic
W. & H. Y. Choi, Heat, Mass and Momentum Trans
Prentice-Hall, Inc., Englewood Cliffs, N. J.,
306 (1961)
1^Sokoinikoff,
Physics
p.460
I.
and
S. & R. M. Redheffer, Mathematics of
Modern Engineering, McGraw-Hill, New
(1958)
23
York,