Yang Fluidization, Solids Handling, and Processing

386 Fluidization, Solids Handling, and Processing

as long as binder is present in sufficient amounts at the point of contact. The rate of coalescence is independent of granule kinetic energy and binder viscosity and critically hinges, instead, on the distribution of binder—this regime is referred to as non-inertial or St N granulation.

From Eq. (20) it is evident that the Stokes number, St, is proportional to (aU0 /μ). Two immediately apparent examples of this regime are the granulation of fine powders where a is smaller then say, 10 µm and high temperature agglomeration where particle surface viscosities, due to material softening, are 104–106 poise are not uncommon. Another conclusion can be drawn for the case when a large granule or binder droplet is surrounded by fines as shown in Fig. 12c and 12d. As mentioned above, the equivalent size a is taken in this case to be the size of the smallest particles resulting, even for large relative velocities, in small values of the Stokes number. For these small values, all collisions between fines and the large granule take place in the noninertial regime and, as long as binder is present on the surface, the granule will collect fines and grow preferentially. This kind of behavior is strongly supported by actual industrial practice in the operation of fluidized beds and pan granulators.

Further support for the existence of the above regime can be drawn from examining the implication of adding too much binder to the powder and hence increasing the binder thickness layer h. This results, as can be seen from Eq. (22), in a corresponding increase in the critical Stokes number,St*, and thus is an extension of the non-inertial regime to higher relative velocities and/or higher particle sizes; this can yield over-granulation and total defluidization of the bed if it is carried too far.

As granulation proceeds in the fluid bed and as granules grow in size, so do the granule Stokes numbers, since St is an increasing function of a. When granules have reached sufficient size such that some values of the Stokes number equals or exceeds the critical value St* in certain regions of the granulator, coalescence will become impossible while in others, especially in regions of low bubble activity, particles will continue to coalesce and grow (see Fig. 23b). In this regime, granule kinetic energy and binder viscosity (and/or surface tension), will begin to play a role. In this “inertial” or StI regime of granulation, increases in binder viscosity or decreases in granule kinetic energy will increase the rate of coalescence by lowering the corresponding Stokes number, as traditionally expected.

As granules grow still further, local Stokes numbers exceed the critical value St* or St/St* → ∞ (see Fig. 23c), so that granule growth is no longer

Coating and Granulation 387

possible and the so called coating regime or StC granulation is achieved. This regime implies that a constant state of bed hydrodynamics dictated by the excess gas velocity in the fluidized bed will determine a theoretical growth limit by coalescence where only coating is possible. Only very limited growth is possible in this regime and this may be due only to layering of remaining fines in the bed and to collection of small binder droplets. The existence of this regime at high gas velocities, high granule circulation rates and nonviscous, rapidly solidifying binders is exploited in fluid bed coating as described in Sec. 2.

3.4Experimental Support and Theoretical Predictions

Since the value of the Stokes number, St, increases with increasing granule size, the granulation of an initially fine powder should exhibit characteristics of all three granulation regimes as time progresses. This was indeed demonstrated by the author and coworkers (Ennis et al., 1991; Tardos et al., 1991) who showed that growth rates in a fluid bed granulator were independent of binder viscosity up to a critical size, where presumably granulation switched to the inertial regime. During the same experiment, the transition to the coating regime occurred for a constant excess gas velocity with larger granules generated with a binder of higher viscosity. The surprising conclusion of these and other similar experiments was the relative “shortness” of the inertial regime, i.e., the relatively rapid transition of the granulation process from the regime where all collisions were effective (non-inertial) to the final regime where no collisions were effective (coating) except the collection of fines and binder droplets by larger granules as explained above.

Prediction of Critical Sizes. In order to use the above model for actual predictions, it is necessary to assign values to the relative velocity U0; this is, at the present level of knowledge, an extremely difficult task since, due to bubble motion (and perhaps the presence of fixed and moving internals in a fluid bed such as, for example, draft tubes) the particle movement in a fluidized bed is extremely complex. Some crude estimates of the relative velocity between particles have been made (Ennis et al., 1991) and these were expressed as

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where UB is the bubble velocity, DB is the bubble diameter and δ is the dimensionless bubble spacing. Using the above velocities and the conditions shown in Fig. 23, one can calculate the limiting granule sizes when the process crosses over the boundaries between different granulation regimes:

A schematic representation of the different regimes, their characteristics and the transition sizes are shown in Fig. 24. It can be seen that only in the inertial regime does binder viscosity, surface tension, or both have a significant effect on coalescence rates. As an illustration of the above classification and of the critical sizes calculated from Eq. (25), results from a fluid bed granulation experiment are reproduced here (Ennis et al, 1991). During this work, fine glass powder was granulated using two polymeric binder solutions which had similar surface tensions and very different viscosities: the CMC-Na(M) binder = 1.7 poise while the PVP = 0.36 poise. The results are shown in Fig. 25; three regimes of granulation are clearly observed. For the initial several hours with average granule diameters less then about 800 microns, similar rates of growth were observed for both binders, i.e., the granulation proceeded in the non-inertial regime where growth rates are independent of viscosity. In the later half of the granulation, lower binder viscosity (PVP) granule growth began to slow compared to CMC-Na, implying transition to the inertial regime (see Fig. 25). Finally PVP granule growth began to level off somewhat in excess of 900 microns indicating a transition to the coating regime. At the same time CMC-Na binder growth continued unabated, indicating non-inertial granulation throughout the run due to the higher viscosity of the binder.

Using the characteristic parameters shown in the figure, critical transition diameters were calculated. The values obtained were 570 microns for transition from non-inertial to inertial and 1140 microns from inertial to coating, and are seen to be within a factor of 1.5–2 of the experimental data which, in view of the approximate nature of these calculations, is quite remarkable. The constant rate of growth in the non-inertial regime also implies that only growth by nucleation occurred and that coalescence (see Fig. 12) was not prevalent.

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To illustrate transition of growth from nucleation to coalescence, a result obtained by Ritala et al., (1986 and 1988) is shown in Fig. 26, while the characteristics of the binders used are given in the table above the figure. From the growth rate, which is seen to be independent of both viscosity and surface tension, one concludes that all granulation proceeded in the noninertial regime. The growth rate however increased significantly as soon as the liquid saturation reached values close to 100% (S = 1, capillary state) implying that, under conditions of high saturation, the granule surface became soft enough to allow large granules to stick and grow by coalescence. This was not possible in the run shown in Fig. 25 because binder was added very slowly and the condition of sufficient surface softening was never reached in any particular region of the spray zone.

An important point needs to be stressed here concerning control of the final granule size in an agglomerator. In the vast majority of cases, the process is run in the non-inertial regime, i.e., in the regime where granule growth is controlled by the presence of binder and hence final granule size is determined by the total granulation time. This means that granulation is stopped or quenched somewhere at or before the point where the large increase in growth rate occurs (for S < 1) as seen in Figs. 15 and 26. In fluid bed granulation, this is a preventive measure to avoid de-fluidization due to excessive granule growth and has the drawback of generating a wide particle size distribution of the produced granules. Clearly, allowing the bed to reach the coating regime would yield a much more uniform distribution but, due to the relatively low shear forces in the bed, this equilibrium diameter is usually much too large to maintain homogeneous fluidization. Many different proposals to increase shear forces in the fluid bed have been put forward lately, some by introducing agitators with others using jets, in an effort to let particles reach the critical coating size, aI-C, and thereby improve the size distribution of the product. The recent development of high shear mixer/ granulators (see, for example, Fig. 9b) which also employ fluidization are a good example of new machines which combine the advantages of both processes to ensure flexibility and uniform size.

Wet Granule Deformation and Break-Up. It would appear from the above analysis that once granules reach the critical size characteristic of the coating regime, any further increase in the Stokes number or relative velocity will maintain the size of the granules. This is certainly true for the case in which binder drying and solidification accompany growth and granule strength increases appropriately as large granules are formed. However, for this to

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happen, one has to tailor both the binder characteristics and the heating (or cooling) rate in the agglomerator very carefully so as to achieve the required properties in the optimal time frame. This is both desirable and possible, and an instrument and procedure are described in the next section to achieve this.

We present, in this section, a simplified model which accounts for the behavior of “green,” i.e., non-solid granules. It is assumed that these green or “wet” agglomerates, upon formation, possess only the strength imparted to them by the liquid bridges which assured coalescence in the first place. However, they have had no opportunity to strengthen significantly, either due to lack of time or to the fact that the binder did not become more viscous (for example, an oily surfactant which does not evaporate or solidify). In such cases, granule strengthening is achieved by liquids being absorbed into inner pores of the granules or by the addition, at the end of the granulation run, of adsorbing fine powders (flow aids) to serve as adsorption sites; these processes are usually quite slow. One is then left, within the shearing powder mass, with deformable granules which can grow by layering but which can also deform and break.

An example of this kind of granulation is given here from the work of Tardos et al. (1991), where the rapid transition from the non-inertial to the coating regime is shown and the conditions of granule deformation are measured. The experiment was performed by introducing large droplets of a very viscous binder (concentrated polymer solution) in a fluidized bed of glass powder. Due to the high viscosity of the binder droplet, it was possible to ensure that it remained intact in the powder and it captured fines in a noninertial layering mode (see Fig. 12d) until it was totally filled with powder; further growth was then achieved by layering in the coating regime. The maximum size of the granules obtained could be calculated from the equation:

where ad is the droplet size and ε is the powder void fraction. Equation (26) is based on the assumption that liquid fills all voids. It was found that keeping the binder concentration high enough (see Fig. 27), i.e., keeping the viscosity high and hence reducing the characteristic Stokes number, indeed yielded agglomerates of the calculated size. However, at lower concentrations (implying lower binder viscosities), only smaller granules could survive which were found to be spherical as were the larger granules. This was

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A somewhat more sophisticated version of the above experiment was carried out recently by Tardos and Khan (1995) and Tardos et al. (1997). To insure that the shear field in the granulator is constant and uniform, a fluidized bed Couette device was used in which a bed at minimum fluidization conditions was sheared between two concentric, rotating rough walled cylinders. Granules of glass powder using different viscosity Carbowax (PVP) solutions were formed, sheared in the device and subsequently allowed to solidify in a shear free environment. In addition to size and shape, the yield strength, τ0, of the wet or “green” granules was also measured separately. It was found that a dimensionless quantity defined as the ratio of inertial and yield forces called the Yield number

delimitates regions in which no deformation occurs and regions in which the granules are totally destroyed; the experimental data is given in Fig. 28. In

Eq. (28) and Fig. 28, Γ, is the shear rate, the parameter fsur is the fraction of surviving granules while Ddef is the coefficient of deformation which gives

Ddef = 0 for a sphere. The important finding here is that beyond a Yield number of about Y = 0.2, no “green” agglomerates survived.

The correlation of the Yield number to the Stokes number defined earlier is not straight forward but, assuming that the shear rate is Γ = U0 /a and that the yield strength τ0, of a green granule is a function of the binder viscosity only (the assumption is that the granule is a highly concentrated suspension of small particles), one can define an upper limit for the Stokes number from Eq. (28) beyond which no agglomerates can survive. Slightly before this critical condition is reached, elongated agglomerates form which appear to be in equilibrium at steady state. What was not found, surprisingly enough, is the existence of stable spherical agglomerates at lower binder viscosities as was the case in the fluid bed experiment described above. This seems to suggest that a fluidized bed is far from being homogeneous and the rolling motion of granules entrained by bubbles allows the formation of stable, spherical sizes from larger granules which were broken apart previously. Simple, constant shear in the Couette granulator, on the other hand, causes stable, spherical or elongated (deformed) granules to form depending on their overall yield strength and subsequent breakup if the shear rate is increased or the viscosity (yield strength) is decreased below a certain value.