Albert W. Alexander and Fernando J. Muzzio
Department of Chemical and Biochemical Engineering, Rutgers University, Piscataway, New Jersey, U.S.A.
BACKGROUND
In the manufacture of many pharmaceutical products (especially tablets and capsules), dry particle blending is often a critical step that has a direct impact on content uniformity. Tumbling blenders remain the most common means for mixing granular constituents in the pharmaceutical industry. Tumbling blenders are hollow containers attached to a rotating shaft; the vessel is par-tially loaded with the materials to be mixed and rotated for some number of revolutions. The major advantages of tumbling blenders are large capacities, low shear stresses, and ease of cleaning. These blenders come in a wide variety of geometries and sizes, from laboratory scale [<16 quart (qt.)] to full size production models (>500 ft3). A sampling of common tumbling blender geo-metries includes the V-blender (also called the twin-shell blender), the double cone, the in-bin blender, and the rotating cylinder.
There are currently no mathematical techniques to predict blending behavior of granular components without prior experimental work. There-fore, blending studies start with a small scale, try-it-and-see approach. The first portion of this chapter is concerned with the following typical problem:
a 5-ft3- capacity tumble blender filled to 50% of capacity and run at 15 rpm for 15 minutes produces the desired mixture homogeneity. What conditions
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should be used to duplicate these results in a 25-ft3blender? The following questions might arise:
1. What rotation rate should be used?
2. Should filling level be the same?
3. How long should the blender be operated?
4. Are variations to the blender geometry between scales acceptable?
Unfortunately, there is no generally accepted method for approaching this problem; therefore, ad hoc approaches tend to be the rule rather than the exception.
Further complicating the issue is that rotation rates for typical commer-cially available equipment are often fixed, obviating question (1) and suggesting that, under such conditions, true dynamic or kinematic scale-up may not be possible.
GENERAL MIXING GUIDELINES Defining Mixedness
Before specifically addressing scale-up of tumbling blenders, this section discusses some general guidelines that cover the current understanding of the important issues in granular blending. The final objective of any granular mixing process is to produce a homogenous blend. But even determining mixture composition throughout the blend is a difficulty for granular systems.
As yet, no reliable techniques for on-line measuring of composition have been developed; hence, granular mixtures are usually quantified by removing samples from the mixture. To determine blending behavior over time, the blender is stopped at fixed intervals for sampling; the process of interrupting the blend cycle and repeated sampling may change the state of the blend. Once samples have been collected, the mean value and sample variance are deter-mined and then often used in a mixing index. Many mixing indices are avail-able; however, there is no ‘‘general mixing index,’’ so the choice of index is left to the individual investigator (1). Once a measure of mixedness has been defined, it is then tracked over time until suitable homogeneity is achieved.
Ideally, this minimum level of variance would stay relatively constant over a sufficiently long window of time. This procedure is simple in concept, but many problems have been associated with characterization of granular mixtures (2).
One dangerous assumption is that a small number of samples can suffi-ciently characterize variability throughout the blend. Furthermore, sample size can have a large impact on apparent variability. Samples that are too small can show exaggerated variation, while too large a sample can blur concentration gradients. Unlike miscible fluids, which, through the action of diffusion, are continually mixing on a microscale, granular blends only mix when energy is
inputted into the system. Hence it is paramount that a sufficient number of samples is taken that represents a large cross-section of the blender volume.
Another concern is thinking that standard sampling techniques retrieve samples that are truly representative of local concentration at a given loca-tion. Thief probes remain the most commonly employed instrument for data gathering. These instruments have been demonstrated to induce sometimes large sampling errors as a result of poor flow into the thief cavity or sample contamination (carryover from other zones of the blender) during thief inser-tion (2). Care and skepticism have to be employed whenever relying on thief probes data. One method to assess blend uniformity and blend sampling error is given in PDA Technical Report No. 25 (3).
Finally, the degree of mixedness at the end of a blending step is not always a good indicator of the homogeneity to be expected in the final product. Many granular mixtures can spontaneously segregate into regions of unlike composi-tion when perturbed by flow, vibracomposi-tion, shear, etc. Once a good blend is achieved, the mixture still must be handled carefully to avoid any ‘‘de-mixing’’
that might occur. The second half of this chapter deals with the scaling of flow from blenders, bins and hoppers, and the effect of segregation during handling.
Mixing Issues in Tumbling Blenders
Mixing in tumbling blenders takes place as the result of particle motions in a thin cascading layer at the surface of the material, while the remainder of the material below rotates with the vessel as a rigid body. Current thinking describes the blending process as taking place by three essentially indepen-dent mechanisms: convection, dispersion, and shear. Convection causes large groups of particles to move in the direction of flow (orthogonal to the axis of rotation) as a result of vessel rotation.
Dispersion is the random motion of particles as a result of collisions or interparticle motion, usually orthogonal to the direction of flow (parallel to the axis of rotation). Shear separates particles that have joined due to agglomeration or cohesion and requires high forces. While all mechanisms are active to some extent in any blender, tumbling blenders impart very little shear, unless an intensifier bar (I-bar) or chopper blade is used (in some cases, high shear is detrimental to the active ingredient, and is avoided). While these definitions are helpful from a conceptual standpoint, blending does not take place as merely three independent scaleable mechanisms. However, attentive planning of the blending operation can emphasize or de-emphasize specific mechanisms and have significant impact on mixing rate.
Most tumbling blenders are symmetrical in design; this symmetry can be the greatest impediment to achieving a homogeneous mixture. The mixing rate often becomes limited by the amount of material that can cross from one side of the symmetry plane to the other (4–8). Some blender types have been built asymmetrically (e.g., the slant cone, the offset V-blender), and show
greater mixing proficiency. Furthermore, by rocking the vessel as it rotates, the mixing rate can also be dramatically increased (9). Asymmetry can be
‘‘induced’’ through intelligent placement of baffles, and this approach has been successfully tested on small-scale equipment (7,10–12) and used in the design of some commercial equipment. But, when equipment is symmetrical and baffles unavailable, careful attention should be paid to the loading pro-cedure as this can have an enormous impact on mixing rate.
Non-systematic loading of multiple ingredients will have a dramatic effect on mixing rate if dispersion is the critical blending mechanism. For instance, in a V-blender, it is preferable to load the vessel either through the exit valve or equally into each shell. This ensures that there are nearly equal amounts of all constituents in each shell of the blender. Care must be taken when loading a minor (1%) component into the blender—adding a small amount early in the loading process could accidentally send most of the mate-rial into one shell of the blender and substantially slow the mixing process.
Smaller blenders entail shorter dispersal distances necessary for complete homogeneity, and thus may not be as affected by highly asymmetrical loading.
As a final caution, the order of constituent addition can also have significant effects on the degree of final homogeneity, especially if ordered mixing (bond-ing of one component to another) can occur within the blend (13).
Intershell flow is the slowest step in a V-blender because it is dispersive in nature while intrashell flow is convective. Both processes can be described by similar mathematics, typically using an equation such as
s2¼ AekN ð1Þ
where s2is the mixture variance, N the number of revolutions, A an unspe-cified constant, and k is the rate constant (6,14). The rate constants for con-vective mixing, however, are orders of magnitude greater than for dispersive mixing. Thus, unequal loading across the symmetry plane places emphasis on dispersive mixing and is comparatively slow compared to top-to-bottom loading, which favors convective mixing.
Process Parameters
When discussing tumbling blender scale-up, one parameter consideration that arises is whether rotation rate should change with variations in size. Previous studies on laboratory scale V-blenders and double cones have shown that, when far from the critical speed of the blender, the rotation rate does not have strong effects on the mixing rate (6,7) (the critical speed is the speed at which tangential acceleration due to rotation matches the acceleration due to gravity). These same studies showed that the number of revolutions was the most important parameter governing the mixing rate. An equation was derived by assuming that the mixture went through a specific incremental increase in mixedness with each revolution (either by dispersion or convection). While this approach has
been shown to be successful at modeling increasing in-mixture homogeneity, no scaling rules have been determined for the rate constants that govern this equa-tion, and it remains an open question for further inquiry.
Given a geometrically similar blender and the same mixture composi-tion, it would seem obvious that the fill level should also be kept constant with changes in scale. However, an increase in vessel size at the same fill level may correspond to a significant decrease in the relative volume of particles in the cascading layer compared to the bulk—this could accompany a large decrease in mixing rate. It has been shown in 1 pint v-blenders that running at 40% fill brings about a mixing rate that is nearly three times faster than at 60% fill (6). Thus, although fill level should be kept constant for geometric similarity, it may be impossible to match mixing rate per revolution across changes in scale if the depth of the flowing layer is a critical parameter.
SCALE-UP APPROACHES
In the literature, the Froude number (Fr O2R/g; where O is the rotation rate, R the vessel radius, and g is the acceleration from gravity) is often sug-gested for tumbling blender scale-up (15–18). This relationship balances gravitational and inertial forces and can be derived from the general equa-tions of motion for a general fluid. Unfortunately, no experimental data have been offered to support the validity of this approach. Continuum mechanics may offer other dimensionless groups if a relationship between powder flow and powder stress can be determined. However, Fr is derived from equations based on continuum mechanics, but the scale of the physical system for blending of granular materials is on the order of the mean free path of individual particles, which may invalidate the continuum hypothesis.
A less commonly recommended scaling strategy is to match the tangential speed (wall speed) of the blender; however, this hypothesis also remains untested (Patterson–Kelley, personal communication, 2000).
We now look at our general problem of scaling the 5 ft3using Fr as the scaling parameter: the requisites are to ensure geometric similarity (i.e., all angles and ratios of lengths are kept constant), and keep the total number of revolutions constant. With geometric similarity, the 25 ft3blender must look like a photocopy enlargement of the 5 ft3blender. In this case, the linear increase is (51/3) or a 71% increase. Also, for geometrical similarity, the fill level must remain the same. To maintain the same Fr, since R has increased by 71%, the rpm (O) must be reduced by a factor of (1.71)1/2¼ 0.76, corresponding to 11.5 rpm. In practice, since most blends are not particularly sensitive to blend speed, and available blenders are often at a fixed speed, the speed closest to 11.5 rpm would be selected. If the initial blend times were 15 minutes at 15 rpm, the total revolutions of 225 must be maintained with the 25 ft3scale.
Assuming 11.5 rpm were selected, this would amount to a 19.5-minute blend time. Although this approach is convenient and used often, it remains empirical.