UNIÓN EUROPEA

AL4 - - 9.4 109.1 219.1 365.4 GR4 - - 87.3 187.7 324.5 DS4 14.7 125.7 242.4 395.3 0V4 54.4 137.8 257.6 DU4 19.0 75.2 LD4 18.6

Table 3 .2 4 f ANOVA o f H eyw ood’s surface coefficient (f) fo r ail coat 4 pellet batches showing significant F values.

AL5 GR5 DS5 0V5 DU5 LD5 CY5

SP5 - - - - 126.0 236.2 388.8 AL5 - - 6.7 172.8 298.9 468.2 GR5 - 4.7 162.3 285.1 450.9 DS5 - 131.7 244.0 398.8 0V5 111.6 216.4 363.3 DU5 17.2 72.1 LD5 18.9

Table 3.24g ANOVA o f H eyw ood’s surface coefficient (j) fo r all fin a l coated batches (coat 5), showing significant F values.

Heywood’s surface and volume coefficients can also be combined as a surface to volume ratio (f/k), thus providing a single number with which to describe the shape o f particles. Numerous authors have previously used this ratio to evaluate the shape o f their particles [Rupp 1970, Nystrom 1978].

Using the values Heywood proposed for a spherical object, the ratio f/k for a perfect sphere = 5.996. This figure can be compared to those in table 3.25 which lists the calculated f/k values for all uncoated and coated pellet batches. All the batches produced values indicating them to be less than perfect spheres, with one exception being the batch o f uncoated GR pellets. Looking at the figures overall, for the four more ‘round’ batches o f pellets (SP, AL, GR, and DS), the f/k values o f the uncoated forms are better i.e. more spherical, than their coated forms; the converse is seen for the more elongated batches (OV, DU, LD, and CY), with their uncoated pellets exhibiting lower f/k values than the coated pellets.

Pellet Batch

Ratio ÊTc

Uncoated Coat 1 Coat 2 Coat 3 Coat 4 Coat 5

SP 5.984 5.770 5.853 5.812 5.772 5.847 AL 5.944 5.788 5.800 5.798 5.744 5.818 GR 6.000 5.791 5.834 5.838 5.882 5.825 DS 5.938 5.846 5.835 5.839 5.866 5.799 OV 5.770 5.737 5.764 5.770 5.753 5.833 DU 5.324 5.528 5.538 5.581 5.580 5.572 LD 4.735 5.089 5.028 5.162 5.266 5.042 CY 4.802 5.080 5.259 5.250 5.077 5.260

Table 3.25 Heywood's surface to volume ratio (f/k) fo r ail pellet batches as a function o f coating level.

Additionally, the Heywood coefficients were recalculated using the mean thickness values from the ring gap sizing studies with the mean length and breadth values from image analysis. The results are shown in table 3.26 .

In nearly all cases, the mean thickness measured by ring gap sizing was lower than the equivalent value from the image analysis (see section 3.3.1.2), which meant that the calculated shape coefficients were lower too.

Batch

Heywood’s Shape Coefficients (mean values) Volume coefficient, k

Uncoated Coated (coat 5)

Surface coefficient, f Uncoated Coated (coat 5)

SP 0.462 0.456 2.834 2.774 AL 0.467 0.485 2.845 2.880 GR 0.480 0.482 2.900 2.871 DS 0.452 0.492 2.802 2.892 OV 0.508 0.479 2.896 2.845 DU 0.502 0.454 2.662 2.615 LD 0.538 0.498 2.581 2.571 CY 0.503 0.458 2.402 2.485

Table 3.26 Heywood's shape coefficients fo r uncoated and fin a l coated pellets, calculated using thickness values measured by ring gap sizing and length and breadth values by image analysis.

Finally to summarize the information gained from the different shape measurements i.e. the aspect ratio, the two-dimensional shape factor c r, the three-dimensional shape factor Cc3, and Heywood’s surface and volume coefficients.

The aspect ratio has previously been shown to be less powerful in discriminating between pellet batches than the others [Podzceck and Newton 1995; Podczeck et al 1995], and thus looking at aspect ratio results may be misleading since so many values would be statistically insignificant. Similarly, the eR results for each pellet batch individually i.e. shape as a function o f coat thickness, produced very few significant differences, and the batches GR, DS, OV and CY showed no significant differences between any coating levels. This would indicate that for these batches there was no change in shape, as measured by eR, when uncoated pellets were layered with increasing coat thicknesses. Significant differences were found when ju st the uncoated pellets o f all batches were compared, with only four insignificant combinations. And similarly when comparing all the fully coated batches, there were only three insignificant combinations.

The ec3 shape factor however, only found the GR pellets having no significant differences between any coating levels, whereas the rest o f the pellet batches showed certain trends. In general, the rounded batches (SP, AL and DS) indicated that their uncoated pellets had a better shape than coated pellets, and the elongated batches (OV, DU, LD and CY) showed that the shape improved when the pellets were coated. Comparing the uncoated pellets o f all batches showed that ec3 differed significantly in all cases except for one combination (SPO + GRO). Looking at the fully coated batches in a similar manner showed eight combinations that were statistically insignificant (mainly amongst the rounder batches). Thus the conclusion could be drawn that coating reduced the shape differences between batches.

So, the three-dimensional ec3 was able to distinguish between more batches than the two-dimensional Or when comparing uncoated pellets o f different shapes. However the combinations that the eR could not differentiate between were only amongst the rounded batches, and this was the same when fully coated pellets were compared. The ec3 values for fully coated pellets produced more insignificant combinations than the eR values and this would lead to conflicting conclusions being drawn depending which shape factor was employed. It would perhaps be logical to say that the ec3 is the

preferred measure o f shape since it is more discriminatory than cr in most cases, especially when comparing similar shaped pellets i.e. visually round. It also provides a clearer indication o f the effect o f coating different pellets i.e. for rounded batches the shape worsens when coated, and for elongated pellets the shape improves when coated.

This trend was also clearly shown by Heywood’s ratio o f f/k (surface coefficient / volume coefficient). Heywood’s coefficients are also not as powerful as the ec3 shape factor, and mainly show significant differences amongst the elongated pellets. Additionally, the f and k values present some misleading results due to the apparent unsuitability o f applying Heywood’s equations to pellets so far removed from the ideal spherical shape.

3.3.3 Density:

3.3.3.1 Bulk/tapped density

Pellet Mean Untapped Density ± standard deviation /g/cm^

Mean Bulk Density at 1000 taps ± standard deviation /g/cm^ Batch Uncoated Coated (coat 5) Uncoated Coated (coat 5)

SP 0.879 ±0.012 0.869 ± 0.008 0.899 ± 0.002 0.874 ± 0.002 AL 0.821 ±0.033 0.847 ± 0.006 0.860 ± 0.009 0.844 ± 0.003 GR 0.824 ± 0.023 0.867 ± 0.002 0.866 ± 0.002 0.867 ± 0.002 DS 0.830 ±0.013 0.862 ± 0.002 0.873 ±0.011 0.864 ± 0.005 OV 0.835 ±0.013 0.849 ± 0.003 0.863 ±0.001 0.849 ± 0.003 DU 0.857 ±0.025 0.846 ± 0.000 0.894 ± 0.006 0.846 ± 0.000 LD 0.866 ±0.021 0.842 ±0.017 0.904 ± 0.006 0.847 ±0.011 CY 0.713 ±0.013 0.792 ± 0.003 0.772 ±0.013 0.792 ± 0.003

ALO GRO DSO OVO DUO LDO CYO