3 Dynamics of Spray Granulation in Continuously …
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Compared to 1.8 mm particles, the 3 mm particles tend to even transfer rates
faster after a disturbance in the fluidization behavior, for instance due to different
bed heights, for example due to feeding events in only one of the chambers, or
due to bubble formation and movement inside the bed. If, however, the absolute
fluidization velocities are compared, one observes that R has a similar value for both
particle sizes: The ratio of the two minimum fluidization velocities u m f,3.0 /u m f,1.8 is
approximately 1.5. Comparing the absolute value of u/u m f,3.0 = 3 (2.43 m/s) giving
an R value of 2.04 with the corresponding value of 1.8 mm (between u/u m f,1.8 = 4
and 5), the values are similar (R in [1.59, 2.71]). This means that, as long as the
equilibrium has not been obtained and the fluidization conditions are equal, both
particle sizes are re-circulated in the same manner. One has to note, that this does
not mean that in equal times equal numbers are transported across the weir, but only
that the ratio of the directed transport is equal.
3.4.3 Internal Recirculation of Bi-disperse Particle Mixtures at
Over-Flow Weirs
After having studied the trends for the recirculation of mono-disperse particles at
over- and under-flow weirs for different fluidization velocities, the behavior of bidisperse particle mixtures is investigated. For this purpose, experiments with mixtures
of 1.8 and 3.0 mm particles with different mass fractions were performed under otherwise the same conditions. Note that in the following u m f corresponds to the minimum
fluidization velocity of the mixture, calculated from the Sauter mean diameter. In
most experiments, the fluidization velocity corresponds to 4 u m f ; for the 50%/50%mixture results for the overall circulation are also presented for 3 and 5 u/u m f . In
addition to the over-all circulation of particles at the weirs (regardless of size), also
the individual recirculation of the two particle sizes is presented and discussed.
The trends of time-averaged internal recirculation R for the 50%/50%-mixture
are presented in Table 3. One can observe a decrease in the value of R with increasing fluidization velocity. Comparing this trend with the two individual trends for the
monodisperse material, it can be concluded that for large enough fluidization velocities the exchange behavior of the mixture is dominated by the recirculation behavior
of the smaller (1.8 mm) particles.
Fixing the fluidization velocity to 4 u m f and varying the mass fractions of 1.8 and
3.0 mm particles, the results for the over-all recirculation also shown in Table 3 are
obtained: Now an increase in the value of R can be observed, i.e. the transport tends
towards back-mixed flow (resp. equilibrium state). Comparing the results for the
individual recirculation of the 1.8 and 3.0 mm particles, one sees that with increasing
mass fraction of small particles, the recirculation of both particle sizes increases.
Again, one has to note that the minimum fluidization velocity of the mixture does
correspond to neither of the minimum fluidization velocities of the particles, i.e.
individual particles are experiencing higher and lower velocities than four times
their individual minimum fluidization velocities. This may accelerate reaching the
81
Compared to 1.8 mm particles, the 3 mm particles tend to even transfer rates
faster after a disturbance in the fluidization behavior, for instance due to different
bed heights, for example due to feeding events in only one of the chambers, or
due to bubble formation and movement inside the bed. If, however, the absolute
fluidization velocities are compared, one observes that R has a similar value for both
particle sizes: The ratio of the two minimum fluidization velocities u m f,3.0 /u m f,1.8 is
approximately 1.5. Comparing the absolute value of u/u m f,3.0 = 3 (2.43 m/s) giving
an R value of 2.04 with the corresponding value of 1.8 mm (between u/u m f,1.8 = 4
and 5), the values are similar (R in [1.59, 2.71]). This means that, as long as the
equilibrium has not been obtained and the fluidization conditions are equal, both
particle sizes are re-circulated in the same manner. One has to note, that this does
not mean that in equal times equal numbers are transported across the weir, but only
that the ratio of the directed transport is equal.
3.4.3 Internal Recirculation of Bi-disperse Particle Mixtures at
Over-Flow Weirs
After having studied the trends for the recirculation of mono-disperse particles at
over- and under-flow weirs for different fluidization velocities, the behavior of bidisperse particle mixtures is investigated. For this purpose, experiments with mixtures
of 1.8 and 3.0 mm particles with different mass fractions were performed under otherwise the same conditions. Note that in the following u m f corresponds to the minimum
fluidization velocity of the mixture, calculated from the Sauter mean diameter. In
most experiments, the fluidization velocity corresponds to 4 u m f ; for the 50%/50%mixture results for the overall circulation are also presented for 3 and 5 u/u m f . In
addition to the over-all circulation of particles at the weirs (regardless of size), also
the individual recirculation of the two particle sizes is presented and discussed.
The trends of time-averaged internal recirculation R for the 50%/50%-mixture
are presented in Table 3. One can observe a decrease in the value of R with increasing fluidization velocity. Comparing this trend with the two individual trends for the
monodisperse material, it can be concluded that for large enough fluidization velocities the exchange behavior of the mixture is dominated by the recirculation behavior
of the smaller (1.8 mm) particles.
Fixing the fluidization velocity to 4 u m f and varying the mass fractions of 1.8 and
3.0 mm particles, the results for the over-all recirculation also shown in Table 3 are
obtained: Now an increase in the value of R can be observed, i.e. the transport tends
towards back-mixed flow (resp. equilibrium state). Comparing the results for the
individual recirculation of the 1.8 and 3.0 mm particles, one sees that with increasing
mass fraction of small particles, the recirculation of both particle sizes increases.
Again, one has to note that the minimum fluidization velocity of the mixture does
correspond to neither of the minimum fluidization velocities of the particles, i.e.
individual particles are experiencing higher and lower velocities than four times
their individual minimum fluidization velocities. This may accelerate reaching the