Dispersing Powders in Liquids, Part 1, by Ralph D. Nelson, Jr.
Measuring the PVD
Allen (see references) presents a comprehensive discussion
of the many methods for measuring particle size.
The ranges of diameter and concentration for which the major
techniques are applicable are given in Table 2.1. Note that
many of the methods require samples that are much more dilute
than commercial slurries. This can be a serious problem, since
both the liquid and the process used for diluting a
high-concentration plant sample to prepare a low-concentration
measurement sample may change the state of aggregation and hence
the particle volume distribution.
Table 2.1 -- Size Ranges for Various Methods of Particle Size Analysis
Method Diameter Limits Concentration
m volume %
----------------------- ------------- ----------
Wet Sieving 20 - 1000 0.1 - 25
Light Obscuration 10 - 1000 0.01 - 1
Gravity Sedimentation 0.6 - 1000 0.01 - 3
Electric Sensing Zone 0.6 - 100 0.01 - 0.1
Laser Scattering 0.1 - 100 0.1 - 1
Laser Diffraction 0.3 - 100 0.1 - 1
Autocorrelation Spectroscopy 0.01 - 10 0.01 - 0.1
Centrifugal Sedimentation 0.01 - 10 0.1 - 3
Sedimentation Field Flow 0.005 - 1 0.1 - 1
The Agglomerate Attrition Spectrum
The energy applied to disperse the powder can be a critical
element in particle size analysis. Most powders have distinctly
different types and strengths of bonds between the clusters at
different levels of aggregation. The weakest bonds are between
the largest particles, with progressively stronger bonds as the
sizes of the particles decrease. By using very small or very
large energies to disperse a powder we can produce samples that
appear to be made of very large or very small particles.
People requesting an analysis do not want to know how small we
can grind the particles, but rather what is the distribution that
characterizes the powder for their particular application.
One common preparation technique is to gently stir the powder
into the liquid and then place a beaker of the slurry in a weak
ultrasonic field (in an ultrasonic bath) for a few minutes. This
may be too harsh a treatment for weak flocs, and it may be too
gentle a treatment for agglomerates
If the sample is a granulated herbicide and the question is how
large the particles will be when poured out of the shipping
container, the dispersion procedure should be very gentle to
avoid breaking or attriting the grains during size analysis. If
the sample is pigment for an automotive paint and the question is
how large the particles will be after final sandmilling (the last
step before the paint is sprayed), we might have to use a shear
well beyond the capability of the ultrasonic bath.
The attrition spectrum is a plot of d50V and Bmid50V
against the shear rate, q [s-1]. This helps visualize
what happens to a clump as the shear rate increases
(Neduzhil). The d50V usually drops sharply over
a rather narrow range of shear rate as the bonds between
particles at one level of structure are broken. In this same
range the Bmid50V rises to a maximum, since the slurry is
then a mixture of two different levels of agglomeration.
Small changes in shear rate or time at shear will cause large
changes in observed PVD if the shear rate is near a maximum in
Bmid50V. If you want your dispersion procedure to be
robust (insensitive to the moderate variations expected from day
to day in laboratory or plant operations), you must specify a
shear rate well outside the region where d50V or Bmid50V
depend strongly on shear rate.
Since there is a continuum of possible shear rates, any
distinction between low, medium, and high is somewhat arbitrary,
but the following guidelines are useful for a low-concentration,
low-viscosity slurry in a laboratory beaker:
- A low shear rate is produced by stirring the
slurry with a hand-held paddle (tip speed 0.1 m/s).
- A moderate shear rate is produced by stirring at
moderate speeds with a motor-driven turbine (tip speed 1 m/s).
- A high shear rate is produced by stirring with a
high-speed disc (rim speed 10 m/s) or by pumping the slurry
through a small-diameter pipe.
- A very high shear rate is produced by using high
pressure to propel the slurry through a capillary tube.
To prepare an attrition spectrum you will need to obtain the
d50V and Bmid50V values for a series of dispersions,
each prepared at a different shear rate (or time at shear). Even
though you may not be able to compute the absolute shear rates for
the various samples in the series, useful insights can be gained
with such devices as a colloid mill run with at a series of
clearances between the plates, an ultrasonic probe run at a
series of voltages, or a disc mill run at a series of rotational
speeds.
Figure 2.4 (below) shows what the cumulative volume percent curves look
like for samples of an agglomerated powder in a slurry exposed
to a series of shear rates. The initial slurry mixed at low shear
fo a set time gives the PVD curve at the left. This slurry is then
expossed to higher shear for the same set time and analyzed again
to get the next curve to the left. This is repeated for a series
of ever-higher shear rates. The highest shear gives the curve at the left.
Fig. 2.4 -- PVD's for a Typical Slurry at a Series of Shear Rates:
2, 10, 20,30, and 45 s-1, highest shear gives the curve at left,
with the smallest sizes.
Figure 2.5 (below) shows the attrition spectrum for this same powder.
Values of d50V (line with diamonds) and Bmid50V
(line with triangles) are derived from the the curves in Figure 2.4.
Fig. 2.5 -- Attrition Spectrum for a Typical Material
Since the two curves become almost horizontal in the region
above 30 s-1 we can be assured that size analyses
of this powder will be consistent the lab procedure is written
to specify that the sample should be mixed at a shear rate of 40 s-1
for the time that was used in the attrition spectrum tests.
This will break most of the agglomerates, and small variations in shear rate
or time held at shear will not produce major changes in the results.