All the material in a blender will not always be exposed to uniform shear, however. Agglomerates are found in a 300-L vessel
after mixing for 256 revolutions at 9 rpm (see Figure 3). Though the blending process achieves a nearly satisfactory level
of gross homogeneity, some samples show high active concentrations caused by the presence of drug agglomerates. These agglomerates
are readily destroyed by the mill. Samples obtained at the discharge of the mill show a general improvement in the quality
of the blend and the disappearance of drug agglomerates (see Figure 3).
Figure 3: Concentration profiles before and after milling.
The use of mills at the discharge should not be regarded as a universal solution, however. If the blend is highly inhomogeneous,
the stream traversing the mill will exhibit differences in composition as a function of time. Lacking back-mixing capacity,
a mill cannot eliminate such insufficiencies in homogenization. Typically, an additional mixing stage is required after milling
to ensure sufficient homogeneity, although, in such cases, care should be taken to ensure that agglomerates do not re-form.
Shear rate and scale-up of the process
One of the most complex problems in powder blending is the scale-up of an operation that involves cohesive powders. The customary
theoretical approach to this problem is to develop a dimensionless version of the equations that govern the flow in a specific
geometry (5). As a result, one obtains several dimensionless groups, and experiments can help determine which of those groups
are relevant for the specific conditions of operation. The behavior of free-flowing particles is determined mainly by gravitational
and centrifugal forces, and the main criterion to scaling up such a process is the Froude number (6). Constitutive interparticle
forces are involved in the blending process of cohesive powders, however. The scale-up for the latter process is much more
complex, and a rigorous method for such a process has not been established.
Mixing in a tumbling vessel takes place in the flowing layer, and the rest of the material simply follows the motion of the
container. Not surprisingly, a body of research is focused on understanding the behavior of this layer (7, 8). The study of
the dynamics of avalanches has led some researchers to propose universal granular-flow properties applicable not only to blenders,
but to numerous other systems (9). Correlations between the systems' subunits can be described either by an exponential correlation
or by a power-law correlation. The exponential law implies the use of a characteristic length scale, whereas power-law systems
are scale-free. Data on granular avalanche behavior of granular processes can be applied to fit both of these categories.
For free-flowing materials, a theory successfully uses half of the length of the flowing layer as a scaling parameter (10).
These theories can be difficult to apply to cohesive systems under practical conditions. A substantial problem is how to account
for the effect of cohesion on powder flow. The problem is extensive, and only a brief discussion is provided in this article.
In simple terms, a cohesive powder can be defined as a material in which the adhesive forces between particles exceed the particle weight by at least an order
of magnitude. In such systems, particles no longer flow independently; rather, they move in ''chunks'' for which characteristic
size depends on the intensity of the cohesive stresses. The size of the chunks introduces an internal, material-dependent
length scale that plays a role in flow scale-up (e.g., in determining whether a blend will flow easily into a tablet press die).
The effective magnitude of cohesive effects depends primarily on two factors: the intensity and nature of the cohesive forces
and the packing density of the material (which determines the number of interparticle contacts per unit area). This dependence
on density is the source of great complexity. Cohesive materials often display highly variable densities that depend greatly
on the immediate processing history of the material. In spite of this complexity, a few guidelines can be offered within a
fixed operational scale:
- Slightly cohesive powders mix faster than free-flowing materials.
- Strongly cohesive powders mix much more slowly than free-flowing materials.
- Strongly cohesive powders often require externally applied shear (e.g., in the form of an impeller, an intensifier bar, or a chopper).
- Baffles attached to vessels do not increase shear substantially.
Because there is no systematic means to measure cohesive forces under practical conditions, the effects of cohesion on scale-up
have been studied rarely. The most important observation is that cohesive effects are much stronger in smaller vessels, and
their effect tends to disappear in larger vessels. The reason is simple: although cohesive forces are surface effects, the
gravitational forces that drive flow in tumbling blenders are volume effects. Thus, as the scale of the blender increases,
gravitational forces grow faster, thus overwhelming the cohesive forces. This effect also can be explained by remarking that
the characteristic chunk size of a cohesive powder flow is a property of the material, and thus, to a first approximation,
it is independent of the blender size. As the blender grows larger, the chunk size–blender size ratio decreases. Both arguments
can be expressed mathematically in terms of a dimensionless cohesion number, Πc:
in which σ is the effective (surface averaged) cohesive stress (under actual flow conditions), ρ is the powder density under
flow conditions, g is the acceleration of gravity, and R is the vessel size. The group σ = (σ ÷ ρg) is the aforementioned chunk size, which can be defined more rigorously as the internal length scale of the flow. Thus, as
R increases, Πc decreases, explaining why scale-up of powder-blending operations often succeeds in spite of limited understanding of cohesive
For processes in which shear entails effects as difficult to predict as overlubrication, overconfidence can lead to devastating
process failures. For blenders with intensifier bars and other moving internal parts, the long-established practice has been
to match the linear (tip) speed of the moving element, and this approach has been used successfully in numerous practical
situations. For blenders without internal moving parts, experience clearly indicates that both shear rates and total shear
per revolution increase as the blenders become larger. This effect is supported by ample data showing more frequent overlubrication
and less frequent agglomeration in larger tumblers (2, 11). Unfortunately, the method outlined above has so far failed to
produce reliable criteria for scaling of shear rates. Though a scaling approach leading to confident design would be greatly
desirable, the safest approach at the moment is to seek an empirical correlation between tablet properties and operational
Even though the effects of shear in blending processes are not understood completely, several reproducible observations provide
guidance for process design and scale-up.
Tumbling blenders provide low shear intensity, especially in small-scale devices. Baffles do not substantially increase shear.
When blending cohesive APIs, the main process risk is the survival of particle agglomerates that can cause superpotent tablets
to occur. Using de-lumping steps can greatly help alleviate this problem, provided that the agglomerates do not re-form during
subsequent blending and lubrication.
During lubrication, process risk can be caused either by very short process times, which can lead to the inhomogeneous distribution
of the lubricant, or the application of excessive shear, which might reduce lubricity, adversely affect powder flowability,
and decrease tablet hardness and solubility. Practitioners must be careful to find an optimum process time. Maintaining such
an optimum setting through process scale-up is not trivial because shear rates for tumbling blenders increase for larger systems.
It should be emphasized that a better understanding of the role of shear in process design and scale-up is long overdue. A
fundamental limitation is the lack of well-defined experimental systems for which samples are sheared uniformly at a controlled
rate to allow systematic quantification of the effects of shear on blend and tablet properties. The development of such a
system is actively under way at various institutions, including Rutgers University. Promising results have been obtained and
are currently being checked for reproducibility.