Page 179 - Instrumentation Reference Book 3E

Analysis methods that measure terminal velocity 163
characteristics of the settling medium with over a 20-second period centerd around the selected
time and depth are then measured. times to minimize errors caused by the disturbance
(b) The particles and settling medium are mixed at the pipette tip. The results yield a cumulative
as in (a) and measurements are then made on masdtenninal velocity distribution which can be
the sediment collecting at the base of the fluid converted to mass size, etc., as already discussed.
column. With suitable choice of liquid; the method can be
(c) The particles are introduced at the top of the used for particles ranging in size from about
fluid column and their arrival at the base of 1 - 100 pm. The conditions should be controlled
the column is monitored. to be Stokesian, Le., laminar flow, and of course
the terminal velocity is appropriate to the fluid
Group (a) is sometimes termed incremental, i.e., conditions, i.e., it depends on the liquid density
increments of the sedimenting fluid are analyzed. and viscosity which are also dependent on tem-
Group (b) is sometimes termed cumulative perature.
referring to the cumulative effect on the bottom
of the column.
Group (c) is also cumulative, but it is some- Density-measuring methods Several techniques
times distinguished by the term “two-layer,’’ Le., involve the measurement of the density of the
at the initiation of the experiment there are two fluidlparticle mixture at different times or at dif-
separate fluids, the upper one thin compared with ferent depths at the same time. Initially, after
the lower and containing all the particles; the mixing, the density is uniform and depends on
lower one clear. the fluid, the particle densities, and the mass con-
centration of particles. After a period of sedimen-
11.8.1.1 Increnzental methods tation, the density varies with depth.
One method of measuring the density uses a
Consider at time t = 0 a homogeneous distribu- hydrometer. This is complicated by allowance hav-
tion of particles containing some special ones ing to be made for the change in the overall height
with terminal velocity V. Ignoring the minute of the fluid caused by the immersion of the hydro-
acceleration period, after a time tl all the special meter tube. Also, any intruding object causes
particles will have fallen a distance h = Vt1. The a discontinuity in the settling medium, some
concentration of those special ones below the particles settling on the upper surface of the hydro-
depth h will have remained unchanged except on meter bulb, none settling into the volume immedi-
the bottom. Above the depth h, however, all the ately below the bulb. Motion around the bulb is
special particles will have gone. The same argu- not vertical. These problems tend to outweib the
ment applies to any sized particle, except that the basic simplicity of the method.
values of 12 and Yare obviously different. A neat method of hydrometry which overcomes
It follows that a measurement of the concen- the overall height problem uses a number of indi-
tration of all the particles at depth I? and time t is vidual hydrometers, commonly called divers. Each
a measurement of the concentration of those par- consists of a small body which is totally immersed
ticles with a termina: velocity less than V, and we in the fluid, but with its density individual!y
have therefore a method of measuring the cumu- adjusted so that after the preselected time, the
lative distribution. divers will be distributed vertically within the sedi-
The folllowing methods use this general principle. menting column, each at the depth appropriate to
its density. Accurate measurement of the positions
Andreasen’s pipette This consists of a relatively yields the required information. The main problem
large ( N 550ml) glass container with a pipette in this case is being able to see the divers.
fused into its ground-glass stopper. A 1 percent A specific-gravity balance can be used. The
concentration of the sample, suitably dispersed in change with time in the buoyancy of a ball sus-
a chosen liquid, is poured into the container to a pended from one arm of a balance at a fixed
set level exactly 200 mm above the lower tip of the depth again gives the information required.
pipette. Means are provided to facilitate the with-
drawal of precise lOml aliquots from the con- Photosedi~ientntion In a photosedimentometer,
tainer via the pipette. the sedimentation is observed by a lamp and
After repeated inversions of the container to give photocell system (see Section 11.3). The observa-
thorough mixing, the particles are allowed to sedi- tion distance is small and for particles greater in
ment. At preselected times after this, e.g., 1 minute, size than about 15 pm, the value of K, the scatter-
2 minutes, 4 minutes, etc., lQml samples are with- ing coefficient, progressively reduces from 2 to 1.
drawn and their solids content weighed. Cor- We know that
rections are applied for the change in depth as
samples are removed. Samples are removed slowly optical density D = 0.4343 KaIA