Note: Descriptions are shown in the official language in which they were submitted.
~2~ 3
--1--
FIBER OPTIC PROBE AND METHOD FOR
DETERMINING THE SIZE AND/OR
CONCENTRATION OF MATERIALS IN SUSPENSION
This invention relates to a fiber op-tic
probe that is particularly useful for in-situ detec-
tion and measurement of the intensity of light scat-
-tered by particles sus~ended in a -transparent or
translucent fluid medium. This invention also relates
to the in-situ measurement of the size and/or concen-
tration of solid particles, immiscible li~uid droplets,
or gas bubbles in suspension in the fluid medium.
In the practice of many chemical processes
proper control of the process requires detection of
the presence of a suspended phase in the reaction medium
and determination of its concentration, particle size,
or both. An example of such a process is one in
which crystals are to be formed in a reaction li~uid.
Detection of the onset of crystallization usually
is necessary to control the process in such manner
as to yield crystals of the desired size and purity.
Detection of the onset o~ crystallization currently
is accomplished by visual monitoring of the reaction
medium, detection of the exotherm resultin~ from the
heat of crystallization, or detection of an increase
34,420-F -1-
-2- ~5~7~3
of the -turbidity of the reaction medium as a result
of the presence therein of crystals. These known
methods often lack sufficient sensitivity and dynamic
range for proper process control.
Numerous other methods exist for measuring
the size and concentration of solid particles in
suspension, but nearly all require removal of a sample
of the suspension for examination and thus are not
generally applicable to the measurement of li~uid
droplets or gas bubbles. These known methods also
are unsuitable for the measuremen-t of solid par-
ticles in those instances in which the size and/or
concentration undergoes changes unless the caus~ of
the changes can be terminated abruptly on removal
of the sample from the suspension.
A fiber optic probe constructed in accor-
dance with the invention makes use of the phenomenon
-that light traversing a transparent or translucent
fluid medium containing particles whose refractive
index differs from that of the medium results in
the scattering of some of the light. This effect
is known as Tyndall scattering. The fraction of
the light scattered per unit of light path length
depends on the surface area of the particles, the
refractive indices of the medium and the particles
(or, if the particles are opaque, on the reflectivity
of the particle surface), and upon the relative
sizes of the particles with respect to the wavelength
of the illuminating ligh-t. At relatively low particle
concentrations, the scattered light fraction is sub-
stantially linear with the concentration, assuming the
34,420-F -2-
~25 Ei7~3
other factors to be relatively constant. At rela-
-tively high concentrations, however, both the illu-
minating light and the scat-tered light are attenua-ted
by secondary scat-tering, resulting in non-linearity
of the collected sca-ttered light with concentration.
A probe according to -the invention employs
one or more optical fibers for transmitting light
from a source to a continuous phase reac-tion medium
so as to illuminate a predetermined area or zone
thereof. The probe also employs one or more op-tical
fibers to collect light scattered by particles in
the illuminated zone and transmit such collected light
to a detector. The use of optical fibers enables the
illuminating light source and the collected light
detec-tor to be located at safe distances from the
medium being monitored.
Both sets of fibers, i.e., the illuminating
light fibers and the scattered light collecting fibers,
are enclosed in a single fluid tight probe housing
having a transparent window at one end which confronts
the medium to be examined. The material from which
the housing is made is one which can withstand the
heat and constituency of the medium so as to be capable
of immersion in the medium itself and at any desired
area and depth thereof. The optical fibers are so
oriented to the longitudinal axis of the probe housing
that -the longitudinal axes of the illuminating light
fibers intersect -the longitudinal axes of the collected
light fibers at a common point on the longitudinal
axis of the housing. This arrangement provides an
ade~uate ~one of illumination and an adequate illu-
minated field of view.
34,420-F -3-
~5~7~3
6469~-3722
--4--
More particularly, the invention resides in a
.~ethod for determinin~ in situ the size and
concentration of moving, light reflective particles
present in a fluid medium, said method comprising:
(a) illuminating a zone of said medium with
light capable of being transmitted by said medium and
reflected by said particles;
(b) collecting light reflect by said particles
and measuring the intensity of such collected light;
(c) determining both the average intensity
value and the variation in intensity value of the
collected light;
(d) using both of the values obtained in step
(c) to compute a first value indicative of particle size
and a second value indicative of particle concentration;
and
(e) comparing the values obtained in step d
with corresponding values obtained by the in situ
application of steps (a), ~b), (c) and (d) to at least
one other like medium containing like particles.
Probes constructed in accordance with the
invention are illustrated in the accompanying drawings,
wherein:
Figure l is a fragmentary sectional view of one
embodiment and taken on the line l-l of Figure 2;
Figure 2 is an end elevation view of the
embodiment of Figure l;
Figure 3 is a view similar to Figure l, but
taken on the ~ine 3-3 of Figure 4 and illustrating
another embodiment;
34,420-F -4-
- ~256~3 64693-3722
.~
-4a-
Figure 4 is an end elevational view of the
embodiment of Figure 3;
Figure 5 is a view similar to Figure 3, but
illustrating a further embodiment; and
Figure 6 is a diagrammatic illustration of the
manner in which a probe according to the invention may
be used.
34,420~F -4a-
~2S~7~3
A probe constructed in accordance with the
embodiment of Figure 1 is generally designated by
reference number 1 and comprises a hollow, cylindri-
cal, elongate housing 2 formed of a metal ox some other
suitable material capable of immersion in a fluid
medium that is to be monitored. Hereinafter the
fluid medium sometimes will be referred to as the
sample. The housing 2 has external threads 3 at
one end thereof. Fitted into the threaded end of
the housing 2 is a support 4 having a flange 5 which
is seated on the free end of the housing. Adjacent
the flange is a groove 6 in which is accommodated a
sealing ring 7 so as to provide a fluid -tight joint
between the support and the interior of the housing.
The support 4 also is provided with an annular sroove
8 on which is seated another seal 9.
Seated upon the support 4 and the annular
seal 9 is a transparent window 10 of suitable thickness,
such as 2 mm, and formed of a suitable material, such
as glass, quartz, sapphire, and the like. The support
4 and the window 10 are maintained in an assembled
relationship by means of a cap 11 having an internally
threaded bore 12 in which the threaded end of the
housing 2 is accommodated. The cap has a flange 13
which overlies and seats upon the marginal edge of the
window 10.
The opposite end of the housing 2 is
exteriorly threaded as at 14 for accommodation in a
correspondingly threaded skirt 15 of a cap 16. A
suitable seal 1~ is interposed between the end of the
housing 2 and the cap 16.
34,420 F -5-
5L~5~7~3
--6--
The cap 16 is provided with three axially
extending openings 18 which are radially and cir-
cumferentially spaced at uniform distances about the
longitudinal axis 19 of the housing 2. The circum-
ferential spacing between each opening 18 is preferably120 although it will be obvious that other spacings
for the openings are practical.
Extending through each of the openings 18 is
an optical fiber 20 o~ preferably uniform diameter.
Suitable seals 21 provide a fluid tight connection
between the cap 16 and the fibers 20. The fibers
extend through the housing and have corresponding ends
fixed in openings 22 formed in the support ~. The
openings 22 also are preferably radially and cir-
cumferentially spaced uniformly about the axis 19 ofthe housing, but unlike the openings 18, the axes of
the openings 22 converge in a direction toward the
adjacent end of the housing. The angle of conver-
gence may vary, as will be explained. The fibers
20 extend through the openings 22 and abut the inner
surface of the window 10. Preferably, a thin coat-
ing 23 of an optical coupling gel or oil having a
refractive index similar to -that of the fibers and
the window is in-terposed between the window and the
confronting ends of the fibers to reduce reflection
losses at the fiber/window interface.
At least one of the fibers 20 has its
free end located in a position to receive light
from a source and transmit such light through the
window 10 to illuminate a zone of a fluid sample.
The remaining fibers may be coupled to one or more
light detectors as will be explained in more
34,420-F -6-
~567~
--7--
de-tail hereinafter. For the time being, however, it
is sufficient to state that the longitudinal axes of
all of the fibers 20 intersect one another and the
longitudinal axis 19 of the probe 1 at a common point
24 which lies on the longitudinal axis of the probe
beyond the outer surface of the window 10. The diameter
of the illumina-ting fiber is such that a substantially
cylindrical beam of light 25 passes through the window
into the sample. The diameter of -the collec-ting light
fibers preferably corresponds to that of the illumina-
ting fiber so that, when an imaginary cylinder along
the extended axes of the light collecting fibers 25a
intersect with the light beam 25, there is formed a
field of view 2~ having the configuration of two
back-to-back cones. The significance of this will be
explained hereinafter.
Figure 3 discloses a probe la which cor-
responds to the probe 1 excep-t that the probe la has
a window lOa having a convex outer surface lOb and
the flange 13a at the free end of the cap 11 is
configured to accommodate and seat upon the con-
cave surface. The greatest thickness of the window
lOa is at the longitudinal axis 19 of the probe
and may be about 3 mm in thickness. Ano-ther dif-
ference between the probes 1 and la is that thesupport 4a of the latter has four openings 22a therein
instead of three. The openings 22a are uniformly
radially and circumferentially spaced about the longi-
tudinal axis 19 of the probe la and the longitudinal
axes of the fibers converge and intersect one
another and the axis 19 at a common point 24a. The
angle of convergence with respect to the axis 19 is
about 20. The intersection point 24a does not
34,420-F -7-
~256~3
extend beyond the convex outer surface lOb of the
window lOa, but instead coincides therewith.
Accomm~dated in each of the openings 22a
is one of the optical fibers 20. Two diametrically
opposed fibers are coupled to one or more li~ht
sources for transmitting ligh-t beams 25a through
the window lOa into the sample, whereas the other
two fibers are associated with one or more light
detectors for transmitting thereto light scattered
by particles in that zone of the sample ad~acent the
point 24a.
As is apparent from Figure 3, the resulting
field of view 26a at the intersec-tion of the fiber
axes and the housing axis is su~stantially conical
in configura-tion with the base of the cone coinciding
with the convex outer surface of the window lOa.
The field of view 26a, therefore, is less than
the field of view 26 produced in the embodiment
of Figure 1.
It is not necessary to use a window having
a convex external surface to obtain a conical field
of view like that indicated at 26a.
In the embodiment shown in Figure 5, the
window lOa has a flat outer surface and a peripheral
flange 27 which underlies a flange 13b at the free
end of a cap llb. Between the flanges 13b and 27
is an annular seal 28. A support 4b is similar to
the supports 4 and 4a and underlies the inner surface
of the window lOb and is provided with openings 22b
for either three or four optical fibers 20 whose
34,420-F -8-
~2567~3
g
longitudinal axes converge and intersect one another
and the longitudinal axis l9b at a common point 24b
located at the outer surface of the window lOb, as a
conse~uence of which the field of view 26b is conical
and has its base at the outer surface of the window.
In the application of any of the disclosed
probes for use, optical fibers which are to transmit
light into the sample have those ends which are remote
from the sample optically connected to a suitable
light source 29 as shown in Figure 6. Such fiber or
fibers hereinafter will be referred to as the illu-
minating fiber or fibers. The remote ends of the
remaining fibers are connected to one or more suitable
light detecting and intensity measuring devices 30
1~ and 31, respectively. Such remaining fibers herein-
after will be referred to as the light collecting
fibers. For convenience of illustration only one
illuminating fiber and one light collecting fibex
are shown in Figure 6.
A suitable source of light is a light
emitting diode (LED), a laser diode, a continuous
wave (CW) gas laser, an incandescent lamp, and a
spectral lamp. Suitable detectors 30 include
photodiodes and photomultipliers. A suitable inten-
sity measuring device 31 is a photometer. The
preferred detection and measuring devices comprise
a photodiode and a transimpendance amplifier the
output from which is coupled to a suitable control
computer 32 or the like which is operable to control
the process.
34,420-F -g_
67~
-10-
More particularly, a sui-table source 29 of
light is a Honeywell Model SPX 4689-04 GaAl~s light
emitting diode ~LED) which emits light at a wavelength
of about 0.8 micron and -this is suitable for use in
suspensions of particles of about one micron or
greater in diameter. The light source may be ener-
gized by a Hewlett-Packard Model 6181C DC power source.
A suitable detector 30 is a Math Associates Model
E-5100 silicon PIN photodiode. A suitable measuring
device/amplifier 31 is a UDT model lOlA amplifier
manufactured by United Detector Technology. A suitable
control/computer 32 is an Intel single board computer
Model SBC-80/24. Each optical fiber may be a plastic
clad silica fiber having a core diameter of 0.6 mm. A
source of such fibers is Quartz Products Corporation.
If light other than that intentionally
transmitted to the sample is present, an optical
filter 33 can be interposed between the collecting
fiber end and the detector 30 so as to exclude from -the
latter light having wavelengths o-ther than those
emitted by the light source.
If a high degree of ambient light exclusion
is required, the light source 29 may be a monochro-
matic CW gas laser, a laser diode, or a spectLal lamp,
and the filter 33, 29 may be a narrow band pass filter
or a monochromator.
In ~se, the probe l may be inserted via
conventional tube fittings into a vessel 34 containing
the sample 35 to be examined for the presence of
particles or the probe may b~ immersed in the medium
at any desired location within the latter.
34,420-F -10-
2567~,3
Although the term "particles" is used
herein, such term is intended to encompass all forms
of materials present in discontinuous form in a reaction
medium. Thus, the term "particles" is intended to
apply to materials such as liquid dropl~ts in a
gas or in an immiscible liquid, gas bubbles in a
liquid, or solid particulate in a gas or liquid.
The embodiment shown in Figure 1 is pre-
ferred for use in the monitoring of samples containing
low concentrations o~ particles. This is because a
sample containing a low concentration is less turbid
than one having a greater concentration, as a conse-
quence of which there is less obstruction to penetra-
tion to penetration of the sample by the illuminating
light beam. Thus, the light beam 25 is capable of
illuminating a relatively large volumn of the sample
as compared to the probe design 43 e.g. Figure 3
or 5.
The field of view 26 is determined by pro-
jecting the imaginary cylinder 25a of the lightcollecting fiber 20 beyond the outer surface of the
window 10 so that it intersects the light beam 25.
Any particles in the field of view 26 will reflect
or scatter some of the light and some of the scattered
light will be collected by the light collecting fiber
and will be transmitted by the latter to the detector
and intensity measuring devices.
In those instances in which the co~centration
of particles in the sample is relatively high, the
probe la of ~igure 3 or 4 is preferred. In such case
the light beams 25a emitted by the illuminating fibers
34,420-F -11-
12 ~5~7~
have a relatively shallow penetration into the sample,
but the field of view 26a commences at the exterior
surface of the window, thereby enabling light scattered
by par-ticles in the field of view to be collected
by the light collecting fibers.
The sensitivity of probes constructed accor-
ding -to the invention is dependent upon (1) the amount
of light conducted to the field of view, (2) the
efficiency with which the light scattered by the
particles in the sample is collected and transmitted
to the detector, and (3) the efficiency with which
light other than that scattered by the particles
(extraneous light) is excluded.
For detection of very small concentrations
of particles (in the parts per million to parts per
billion range) exclusion of extraneous light is the
most important consideration. A major source of
extraneous light results from reflection of the illu-
minating light at the in-terface between -the sample and
the window. Typically 10 5 to 10 2 Watts (W) of light
are used to illuminate the sample. The reflection
at the window-sample interface is typically about
0.1 to 1 percent, or 10 4 to 10 8 W, and varies with
the refractive index of the sample. The scattered
light collected from very low concentrations of
particles may be as low as 10 13 W, Accordingly it
is necessary to exclude virtually all of the reflected
light.
The geometry of the probes disclosed herein
has been selected to yield maximum exclusion of reflected
light consistent with otherwise acceptable performance.
34,420-F -12-
-13- ~2567~3
This is accomplished by choosing the angle be-tween
the longitudinal axes of the fibers and the longi-
tudinal axis of the probe, the radial spacing of the
fibers from the longitudinal axis of -the probe, the
circumferential spacing between the fibers, and the
window thickness so that light reflected from the
window does not fall on any of the collecting fiber
ends. Typically, these factors are so selected that
such reflected light falls either along the probe
axis or on that side of the probe axis opposite the
illuminating fiber and bet.ween adjacent collecting
fibers. By positioning the illuminating fibers
diametrically opposite one another, light reflected
from one such fiber is least likely to fall on a
light collecting fiber.
The amount of light collected and trans-
mitted by the collecting fibers is approximately
proportional to (1) their total cross-sectional
area (i.e., the product of the number of collecting
fibers and the cross-sectional area of each), (2) the
inverse of the square of the distance between the ends
of the fibers and the intersection of their axes, and
(3) the angle between the illuminating fiber(s) and the
collecting fibers(s). The optimum angle was found
experimentally to be between about 20 to 25~ for
particles with diameters between 0.2 and 200 microns,
but angles between about 10 and 30 yielded sensi-
tivities within about 30 percent of the maximum.
A radial distance from the fiber to -the
longitudinal axis of the probe of two to three times
the fiber diameter was found to yield satisfactory
results for three and our fiber probes in which the
34,420-F -13-
~2S6~3
-14-
angle be-tween the longitudinal axes of the fibers and
the longitudinal axis of the probe is between 10 and
25. The choice of the circumferential spacing between
the illuminating fibers and the collecting fibers also
represents a compromise between sensitivity and extra-
neous light reflection, with relatively small spacing
(less than 90) yielding better extraneous light rejec-
tion, but poorer sensitivity than larger spacing ~over
90). In practice, a circumferential spacing of the
fibers of from 60 to 120 performs well.
Assuming that the circumferential spacing
between the fibers and the ratio between the fiber
diameter and the distance to the longitudinal axis of
the probe is constant, the sensitivity is approximately
proportional to the fiber diameter. This results from
the fact that both -the cross-sectional area of the
fibers and -the sguare of the distance to the inter-
section are proportional to the square of the fiber
diameter, while the depth of field (i.e., the length of
the region in which the fields of view of the illu-
minating fibers and the collecting fibers overlap)
increases with the fiber diameter. Plastic clad silica
fibers having a core diameter of from 200 to 600
microns are most suitable. The larger diameters (about
600 microns) perform slightly better and are easiest to
handle and are thus preferred. Fibers with larger core
diameters are more expensive however and require probes
of a larger diameter, due to their large bending radii,
and are thus less desirable.
The diameter o~ the illuminating fibers may
be identical to each other and to that of the collec-
ting fib~rs. When used in conjunction with LEDs or
34,420-F -14-
~2567~
- --15--
extended light sources, such as incandescent lamps or
spectral lamps, smaller fibers will generally transmit
less light to the sample and larger fibers increase the
extraneous light more than they increase the illumina-
tion of the region viewed by the collection fibers.
When focused beams from CW lasers or laser diodes are
used for illumination, fibers with core diame-ters
smaller than those of the collection fibers are pre-
ferred because their use results in less extraneous
light due to the smaller diameter of the reflection
from the window sample interface. Further, the depth
of field of the probe is reduced, due to the smaller
diameter of the illuminating light beam, which results
in increased dynamic range. Illuminating fibers with
core diameters of from 100 to 300 microns perform well
in conjunction with laser light sources and 600 micron
diameter collecting fibers.
The number of collecting fibers employed
represents a compromise between sensitivity and
expense. One collecting fiber is sufficent for most
applications, but more are advantageous for appli-
cations requiring high sensitivity.
One illuminating fiber is sufficient to
collect the light from a light emitting diode, laser,
or laser diode, whereas two or more are advantageous
for collecting light from extended sources.
Probes with more than the minimum number of
fibers required for the measurement provide redundancy
which is advantageous in case of fiber breakage.
34,420-F -15-
-16- ~2S6~13
The present invention also relates to a
method for measuring either the size or concentration, or
both simultaneously, of particles, immiscible liquid
droplets, or gas bubbles suspended in a fluid medium
employing the apparatus hereinbefore described. For
convenience, the term "particle~s)" as used hereinafter
in the description and claims means solid particulate
material, gas bubbles, or liquid droplets. The
measurements can be performed in-situ within closed
reactors, pipes, or other process equipment. It thus is
suitable for process control applications.
The method is applicable to suspensions which
are stirred, agitated, or flowing, or in which the
particles otherwise are set in motion as, for example,
suspensions in which the particles are moving under
the influence of gravity.
The method comprises illuminating a zone of
a fluid medium containing moving, light reflective
particles with light of a constant intensity and
collecting and measuring a portion of the light
reflected by the particles. The average intensity
and the variance of the intensity of the collected
reflected light are computed. The size and con-
centration of the particles are determined by
comparison of the computed values with values
resulting from identical measurements of a like
medium containing like particles of known size and
concentrations.
Upon illumination of a zone of a trans
parent or translucent medium containing particles
which are at least as large as the wavelength of the
34,420-F -16-
-17- ~6~3
illuminating ligh-t, and which have a refractive index
different from that of the medium, a fraction of the
light is reflected. The fraction of the incident
light reflected from an illuminated zone of fixed
volume within the medium depends on the size and
number of particles present in that zone and on the
refractive indices o~ the particles and the medium.
If the intensity of the illuminating light is not
constant throughout -the illuminated zone, or if the
efficiency of collection of the reflec-ted light
is not constant throughout, the intensity of the
detected light (i,e., the collected, reflected light)
from a par-ticle will depend on the position of the
particle within the zone. If the particles are in
motion, rather than stationary, the number and
positions of particles in -the illuminated zone will
vary with time, thereby resulting in random fluc-
tuations in the intensity of the detected light. The
magnitude of these fluctuations will depend on the
size and number of particles present.
In a case in which a dilute suspension
of monosized particles is illuminated by light of
constant intensity, the fraction of light reflected
from each par-ticle may be considered a constant.
Thus, fluctuations in the intensity of the detected
light will be due to the statistical variations in
the number and positions of particles in the illu-
minated zone. In this ins-tance, the average (mean)
intensity of the detected light (X) and the variance
(V) of the intensity of the detected light are given
by:
X = A* (C/D) Equation 1
V = B* (CD) Equation 2
34,420-F -17-
~L256';7~3
-18-
where D is the particle diameter, C is the particle
concentration, and A* and B* are quantities whose
values depend on the refractive index or reflectivity
of the particles, the intensity of -the illuminating
light, the size of the illuminated zone, and the
geometry of the illuminating and light collecting
optics. A* and B* thus are constants for a par-
ticular combination of particle material, sus-
pendin~ medium, and optical system.
Equations 1 and 2 can be solved simultaneously
for the concentra-tion i~C) and diameter (D) to yield:
C = A (XV)1/2 Equation 3
V 1/2
D = B X Equation 4
where A and B are constants which are related to
A* and B* by the equations:
1 1/2
A = A*B* Equation 5
A* 1/2
20B = B* Equation 6
If a suspension of particles o known size
and concentration is obtained, the size and concen-
tration of like particles of unknown size and concen-
tration suspended in a like medium can be determined
by measuring the mean and variance of the intensity
of light reflected by the known and unknown sus-
pensions, respectively, usin~ the same measuring
apparatus for both suspensions, and applying Equation
3 and Equation 4.
34,420-F -18-
-19~ 567~3
Because Equation 3 is independent of the
particle size and Equa-tion 4 is independent of con-
centration, it is possible to determine either the
size or the concentration independently.
The determination of particle size in a
medium does not necessarily require that the average
concentration of the particles in the illuminated
zone be the same as that of the entire medium. It
is only necessary tha-t the particles in that zone be
representative. Thus, the invention is applicable
to particle size determination in processes in which
the particle concentration is not constant throughout
the medium.
If s-table samples of known particle size
and concentration are no-t available, as always is the
case for gas bubbles, and often for liquid droplets,
the calibration must be performed external to the
process equipment. This sometimes can be accom-
plished by making light reflection measurements
simultaneously with other measurements, such as
photography-image analysis, which yields measures
of the concentration and particle size.
If a suspension of known particle size and
concentration is not available, the relative sizes
and concentrations of the particles in two suspensions
of the same material in the same medium still can be
determined. If Xi and Vi represent the average intensity
and variance, respectively, of the detected light
from one sample, and Ci and Di represent the concen-
tration and average particle si7.e of the particles inthat suspension, and if Xj, Vj, Cj, and Dj represent
34,420-F -19-
-20- ~2S~3
the same variables in a second suspension of the same
material in the same medium, then:
Ci XiVi 1/2
Cj XjVj Equation 7
Di X~ l/2
Dj XiVj Equation 8
The direction, i.e., smaller or larger, and
the relative magnitude of changes in the concentration
and of the average size of particles, in a single
suspension, also can be determined by repeatedly
measuring the average intensity and variance of the
collected liyht and applying Equations 7 and 8.
In some instances not all of the conditions
stated above will be met. For example, in some
industrial processes the size or concentration of the
particles may not fall within the range for which
Equation 1 and Equation 2 are valid. In these cases
the relationships among the size, concentration, mean,
and variance are complex and exact expressions relating
the variables cannot easily be derived. In such cases
multiple known suspensions, having particle sizes and
concentrations throughout the ranges of interest, may
be employed to determine empirical relationships which
will have the general form of nonlinear simultaneous
equations. If the average in-tensity and variance of
the detected light are monotonic functions of the
average particle size and concentration throughout the
range of interest, unique values for the concentration
and average particle size of an unknown suspension can
be obtained by inserting the measured values of -the
average intensity and the variance of the detected
light from the unknown samples into the empirical
equation thus obtained.
34,420-F -20-
-21- ~2S67~3
The concentrations and average diameters of
samples of polystyrene beads were determined by the
following procedure:
I. Calibration Samples
A plurality of samples o~ polystyrene beads
of known size were suspended in an aqueous sodium
chloride solution. Three different samples of beads,
having average diameters of 0.222 mm, 0.458 mm, and
0.621 mm, .respectively, were suspended in the solution
at concentrations of between 1.5 percent and 15 percent
by volume. The beads were set in motion by agitation
of the suspensions. Using the apparatus described
above, the intensity of the reflected light was
measured ten -thousand times at three millisecond
intervals for each suspension and the average (mean)
and variance of these measurements computed. This was
done thre~ times for each of the suspensions. Average
values for the mean and variance of each suspension
were then used to compute, by the method of least
squares, the cons-tants for the regression equations:
C = K1 (XV)1/2 + K2 Equation 9
V 1/2
D = K3 X + K~ Equation 10
II. Unknown Samples
Twenty-seven suspensions then were prepared
like the calibration samples, except that the diameters
of the beads were not known. The values of the mean
and variance of the intensity of the detected light
from each suspension were determined in a manner
identical to that used in the calibration procedure.
Measured values for the concentrations and average
diameters then were obtained by inserting the detected
34,420-F -21-
~256713
-22-
mean and variance values in-to the linear regression
Equations 9 and 10. The true average diameters of
the three samples were then determined by micropho-
tography. The measured and true values for the par-
ticle diameter and concentration of each unknownsuspension are set forth in the following Table:
TABLE
(Resul-ts from Illustrative Example)
Diameter Rel Concentration Rel
(microns) Error (Vol. %) Error
Sample Meas. True % Meas. True %
1 324 301 7.6 2.24 2.30 2.6
2 318 301 5.6 3.19 3.03 5.3
3 310 301 3.0 4.44 4.12 7.8
4 302 301 0.3 5.32 5.00 6.4
318 301 5.6 6.44 5.73 12.4
6 324 301 7.6 7.56 6.60 14.5
7 315 301 4.7 8.14 7.42 9.7
8 324 301 7.6 9.20 8.19 12.3
9 323 301 7.3 10.44 9.11 14.6
360 374 3.7 2.19 2.74 20.0
11 407 374 8.8 3.87 3.89 0.5
12 396 374 5.9 4.94 4.94 0.0
13 399 374 6.7 6.33 6.17 2.6
14 404 374 8.0 7.63 7.41 3.0
383 374 2.4 8.59 8.82 2.6
16 389 374 4.0 9.81 9.23 6.3
17 395 374 5.6 11.29 11.44 1.3
18 398 374 6.4 12.56 12.89 2.6
19 450 4~7 0.7 2.85 3.35 14.9
459 447 2.7 4.19 ~.50 6.9
21 436 447 2.5 5.33 5.91 9.8
22 430 447 3.8 6.43 7.15 10.1
23 450 447 0.7 7.66 8.19 6.5
24 439 447 1.8 8.59 9.51 9.7
448 447 0.2 7.86 10.74 8.2
26 444 447 0.7 10.75 11.96 10.1
27 456 447 2.0 12.06 13.22 8.8
34,420-F -22-
-23 ~25~7~
The disclosed embodiments are represent-
ative of presently preferred embodiments of the inven
tion, but are intended to be illustrative rather
definitive thereof.
34,420-F -23-
