Dispersing Powders in Liquids, Part 1, by Ralph D. Nelson, Jr.
When you pour a powder out of a container onto a flat surface,
you often find that it is agglomerated into clumps. Some clumps
fall apart under their own weight as they tumble, while others
may not break unless they are hit with a hammer. The term {\sl
particle} means an assemblage of solid matter which translates
and rotates as a rigid unit, with no translational or rotational
motion of the constituent parts with respect to the whole.
Before attempting to disperse a powder in a liquid, you should
determine the structure of the starting powder and get a clear
description of what sort of particle size and structure is
required in the end-use application. Many discussions between
marketing representatives, plant supervisors, technical support
people, particle size analysts, and academic researchers suffer
from great confusion because of differences in nomenclature or
conceptualization of the structure of the solid particles.
The term "particle" is used very loosely, and it may be used to
refer to either a single crystal or a loosely bound clump of
smaller units. It does not imply that anything is either
nonporous or agglomerated or dispersed to the maximum extent.
Many other terms in slurry technology are also used loosely, so
you must be quite careful to establish at the beginning of a
discussion just what others mean for each term. Drawings can be
very helpful for describing the structures found for the starting
powder, intermediate states, and the final dispersion.
Levels of Particle Structure
There are often several levels of structure in a clump. Small
primary particles are often cemented together by rather strong
forces to form medium-size aggregates which are bound by moderate
forces to form large agglomerates. These may be collected by
weak forces into large and tenuous flocs. As we go from lower to
higher level structures, the strength of bonding decreases, the
void (nonsolid) fraction within the clump boundaries increases,
and the degree of structural complexity increases.
People who are not familiar with slurry technology often do not
realize how complex a clump of particles can be. They may
believe that a single pass through a low energy process such as
screening breaks the feed material down to fundamental particles.
This is rarely the case. More experienced workers know that while
loosely bound clumps may be broken up by a low energy process to
moderate size particles, these are usually agglomerates of
still smaller particles. The specialist will always insist upon
examining the powder with a microscope (or electron microscope)
so as to determine the structure in detail. The purpose of this
section is to discuss the most common particle structures and to
describe how they are formed in industrial processes.
The terminology for describing the structure of particles often
seems somewhat confused because there are a wide variety of
different structures that can be formed from the wide variety of
chemical compositions in this world. The terms listed below
describe structures typical of different regions in the continuum
of bond energies and contact areas that may be formed. There are
no sharply defined dividing lines between the regions. Many
specialists use variants of the terminology presented, since what
one specialist considers to be a relatively weak bond may be
considered by others to be a relatively strong bond.
Fundamental Particles
Fundamental particles are the lowest level of structure --
having the highest degree of crystal lattice or structural
homogeneity, the highest density, and the lowest void fraction
For crystalline materials the fundamental particles are single
crystal domains. It is important to note that even a particle
that looks like a single, nonporous, unagglomerated crystal may
in fact be made up of several single crystal domains; for
example, magnetic particles are generally made up of microdomains
with different orientations. The boundaries and orientations of
these domains change in response to exposure to an external
magnetic field.
For noncrystalline solids we can define the fundamental
structural elements to be those regions that are homogeneously
solid (with no voids down to the atomic packing level) and
cut from the solid continuum into relatively convex shapes by
imaginary cut-planes of minimum area. Thus, the regions on each
side of a pore would be separate fundamental units and a porous
or sintered clump would be a high-level structure made up of
many fundamental units.
Fig. 2.1a -- Varieties of Single Particle Structure
Twins and Mosaics
Twinned crystals are made up of two (relatively perfect) crystal
domains that are joined at a plane which forms a symmetry
element. Thus there is a large angle between the major axes of
the two crystal domains. Twins are usually formed during the the
initial precipitation of a solid. The exterior of a primary
particle usually grows by addition of solution material at kinks
or shelves or screw dislocations in the surface, so the exterior
atomic plane is not flat. Rapid growth about a dislocation can
produce a twinned crystal. Polarized light microscopy can
usually distinguish twinned crystals from single crystals.
Mosaics are made up of multiple crystal domains which have only
small differences in angle between their major axes so that the
crystal planes meet at the grain boundary (also called a
domain boundary) with only a small mismatch in lattice
parameters. In those cases where these domains have dimensions comparable
to the wavelength of x-rays (0.001 to 10 nm), then the broadening of lines
in an x-ray powder diffraction pattern can be used to characterize the size
of the grains that make up the mosaic.
Semicrystalline polymeric materials have regions of crystallinity
adjacent to regions of amorphous (glassy) structure. These may
be considered to be mosaics. A polymer chain that is part of the
crystalline region may also be part of the amorphous region, so the
regions may be bound together very strongly along the plane
separating the two regions, with little or no void fraction.
Aggregates and Porous Particles
An aggregate is a clump of fundamental particles that are
strongly bonded through a region that is not planar or involves
some voids, so there is significantly imperfect contact between
the particles. See Chapter 1 for a discussion of differences
between European and American terminology. Aggregates may be
crystals joined across rough faces, porous materials, clumps of
particles held together by extensive precipitation bridges or
heavily sintered structures for which the cross sectional area of
the regions joining the fundamental particles is larger than the
surface area which is exposed to void space.
A precipitation bridge forms when precipitation occurs at
the point where two particles make contact in a floc or a packed
bed of material. A heteroprecipitation bridge or
gel bond forms when a solid different from the core particle
precipitates at the contact points. This may occur when a
coating agent is applied to an incompletely dispersed slurry or
when a soluble salt precipitates out during the drying of a
filtercake.
The contact points between primary particles can deform under
pressure to increase the area of contact between particles in a
packed bed. Sintering occurs when surface material migrates to
broaden the contact area and fuse the structures of two
originally distinct particles. This is called
thermal sintering or pressure sintering according to which
variable was used to produce the effect. Sintering is most
commonly applied to amorphous materials such as glasses or
metals. The surface migration rate increases exponentially with
temperature, and sintering can occur within reasonable contact
times at (absolute) temperatures as low as 70% of the solid's
melting point.
Fig. 2.1b -- Varieties of Clump Structure
Agglomerates or Strong Flocs
A strong floc is a clump of particles with large areas in
close proximity but not in intimate contact. Direct contact may
be prevented by surface roughness, a scale of reaction products,
or an adsorbed coating of surfactant or vehicle molecules. Even
though the interparticle bonding here is weaker than for direct
lattice bonds, it can hold such flocs together up to quite high
shear. Since these tight flocs are held together over large
contact areas, they have a small void fraction.
Weak Flocs
Aggregates and agglomerates have rough surfaces, so when they
collide, the area available for direct contact is limited. The
bonding energy that can be attained per unit mass is low.
Bonding will also be weak if the particles have thick coatings
that prevent the particles from getting close enough to attract
strongly or if the interparticle forces are inherently weak (as
for nonpolar polymer particles dispersed in an organic liquid).
Weak flocs usually have rather open structures with high void
fractions. Light stirring can redisperse weak flocs, and the
weight of sediment in a settling mass can break the bonds between
the particles, allowing them to collapse into a more compact
configuration.
Tangles
Long fibers have extended, flexible structures that can twist
about to become entangled to hold the particles together
mechanically. The void fraction of such tangles is generally
high. Although the attraction between the fibers may be weak, an
essentially infinite time would be required for the random motion
in a stirred slurry to bring them into configurations that would
enable them to disengage from the tangle. This complex
configuration dependence for deagglomeration means that the
particles are entropically agglomerated rather than
enthalpically agglomerated.
Adsorbed-Vapor Agglomeration
The flow and clumping of hygroscopic powders are critically
dependent on the relative humidity. Clumping is dependent on the
partial pressure of any vapor that could be adsorbed, but water
vapor is most common cause of agglomeration by adsorption. A
hygroscopic (water-adsorbing) solid adsorbs water, often as
a surface film that increases the bonding between particles. The
strength of agglomeration depends on the relative humidity of air
and its diffusion into the powder. Since a vapor is best
adsorbed or condensed at contact points, fine powders with many
contact points per unit mass are more sensitive to humidity than
coarse particles are. At high humidities so much moisture is
adsorbed that liquid bridges form.
The adsorbed water may dissolve the surface or any residual salts
deposited on the surface. If this solution later evaporates, the
dissolved material will reprecipitate to form precipitation
bonds. Several options that may reduce the sensitivity to
humidity are to
- Chemically treat the surface to make it less
hygroscopic.
- Coat the powder with a small amount of
hydrophobic liquid. First check to see that this liquid does not
by itself cause unacceptable clumping.
- Disperse over the core powder a small
amount of a hydrophobic shield powder that is at least ten
times smaller in diameter than the first. The shields act as an
anticaking agent by preventing contact between the surfaces
of the core particles. The shield particles are chosen so that
they will not condense or sinter.
Liquid-Bridge Agglomerates
Particles may be held together in agglomerates by a liquid that
wets the contact points. Some examples are
1) liquid in a filtercake
2) water wetting the particle contacts in a damp storage bin
3) oil drops added to agglomerate coal particles in a coal-water slurry.
Fig. 2.2 -- Shoreline on a Liquid Bridge
When a liquid drop wets the contact point between two spheres of
equal diameter dp [m] as in Fig. 3, the shoreline
length [m] (one for each sphere) of the solid-liquid-gas contact is
lshore = 
dp
sin 
shore
where shore [rad] is the angle defined
by a line drawn from the particle-particle contact point to one particle's
center and then to a point on the shoreline for that particle. The total
agglomerative force due to liquid bridging Fagglom [N]
depends on shore, the contact angle
[rad] (the angle between the surface tangent
and the liquid tangent at the shoreline), and the surface tension
of the liquid 
l [N/m].
Rigorous analysis produces two terms that sum to approximately
Fagglom = Fcoh + Fsurf
dp l
cos
Fcoh is the cohesive (negative) force based on the curvature
of the liquid-vapor meniscus. It is a complicated function,
but for small values of , the term
Fcoh Fagglom
(1 - sin i) / cos
dominates the sum (Hunter 1987 [see reference list] pages 287-290).
Fsurf is the component of l
(along the shoreline of both particles) in the direction of the line
of particle centers.
Fsurf = Fagglom sin2
and is small until is rather large.
Fagglom depends strongly on the particle diameter
and only weakly on the amount of liquid in the meniscus
(related to $).
Solid-Bridge Agglomerates
Particles of one material may become cemented together by the
solids that precipitate as liquid evaporates during tray drying
of wet filtercake or spray drying of a slurry. Because the
surface tension causes the last remaining solution to be held as
liquid bridges rather than as droplets on particle surfaces, the
solids precipitate in the places best suited to cause cementation
of the particles into a clump. Many medicinal and agricultural
powders use water-soluble binders to provide solid bridges in
tablets and granules.