Results and discussion
Design of experiments interpretation.
The mathematical model generated for each response Y was a quadratic model with first-order interactions, designed according to the following equation:
i and X
j represent the levels of the factors; a
0 is the intercept representing the mean of the measured response data; a
i and a
ii and a
jj, and a
ij correspond to the coefficients of first-order terms, the coefficients of second-order quadratic terms, and the coefficient
of second-order interaction terms, respectively. The coefficient corresponding to a factor or interaction shows its importance
to the studied response. The symbol e represents pure error.
To simplify the design-of-experiments interpretation, the coefficients of second-order quadratic terms are not presented.
Results are expressed according to the following equation:
For the multilevel categoric factor C presenting three levels, the software calculated two coefficients, C(1) and C(2), corresponding
to the difference between the high level and the average, and the difference between the low level and the average, respectively.
The coefficient values were expressed in coded units to compare each one's relative effects to those of the others. Analysis
of variance was performed to determine the significance of the model. A term that had a probability value lower than 0.05
was considered a significant effect. A probability value greater than 0.10 was regarded as insignificant. Table I summarizes
the p values for the coefficients of factors for the different responses tested. Graphical analyses of responses were performed
to determine the most important factors for a response by comparison with the other factors. Figure 4 shows the effects of
factors and interactions on the responses. The red bars correspond to the factors that influenced the response. When an interaction
between water quantity and extrusion system is underlined, the mean response value according to the extrusion system is shown
according to three water-quantity values (i.e., minimum, medium, and maximum).
Table I: Significant effects for the main factors and interactions for various responses Yx.
The pellet-morphology study showed great differences between the three extrusion systems. At the lowest water quantity (i.e.,
22.5%), pellets created after radial extrusion presented a wide size distribution with many small particles, compared with
pellets created after axial extrusion, which presented a majority of rods. Only dome extrusion provided pellets of the correct
specifications. The pellets' morphology is linked to extrudate characteristics and the spheronization step. At low water quantities,
radial extrudates were not densified enough and broke during the spheronization step, in contrast with axial extrudates, which
were well densified but did not have enough plasticity to deform during the spheronization step. An increase in the water
quantity improved the morphology of all pellets excepted those produced by the dome system.
The following equations obtained for pellet size, pellet dispersion, and usable yield, in which significant terms are shown
in bold type, are represented in Figure 4: