Lynne Wong's PhD thesis
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Lynne Wong's PhD thesis

Lynne Wong's PhD thesis Lynne Wong's PhD thesis

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The isotherm parameters of the Hailwood-Horrobin and GAB models were estimated by the non-linear regression procedure of SigmaPlot (SPSS Inc.) for the calculated EMC data of reconstituted R 570 cane stalk, dry leaf and green leaf aged 52 weeks (Tables 5.29 and 5.31) and aged 36 weeks (Tables 5.30 and 5.32). The values of the isotherm parameters, together with the calculated regression criteria: coefficient of determination R 2 , the mean deviation modulus P and the standard error of the estimate E s , for each model and for the reconstituted cane stalk, dry leaf and green leaf aged 52 and 36 weeks are shown in Table 5.33. All R 2 values approach one and the P values are less than 10, except for reconstituted green leaf aged 36 weeks as predicted by the Hailwood-Horrobin model, and the E s values are also low. The good-fit of the Hailwood-Horrobin and GAB models to the calculated EMC values of reconstituted cane and leaves is confirmed by inspection of the isotherm plots (Fig 5.15). 5.7 CONCLUSIONS The EMC of cane components of variety R 570 aged 52 and 36 weeks were determined at 30, 45, 55 and 60 °C for water activities ranging from 0.17 to 0.98. The resulting sorption isotherms exhibit a type II sigmoid pattern. Three models were found to provide a good-fit to the experimental data: the modified GAB, Hailwood-Horrobin and GAB models in this order. However, the modified GAB model did not extend to water activity values greater than 0.95, whereas the other two models covered the whole range of water activities studied. The EMC of sugar cane stalk of variety R 570 aged 36 and 52 weeks was estimated from the dry mass fractions of cane stalk fibre, stalk pith, rind fibre and rind fines, and the respective individual observed EMC values. Similarly, the EMC of dry leaf and green leaf was calculated from the dry mass fractions of fibre and fines and their constituent experimental EMC. The GAB model was found to fit the calculated EMC values of the reconstituted cane stalk, dry leaf and green leaf of R 570 aged 36 and 52 weeks well; similarly for the Hailwood-Horrobin model except for green leaf aged 36 weeks. The models of the sorption characteristics of the sugar cane component parts could now be used to determine a number of thermodynamic parameters that enable the bound water to be characterised. This work is described in Chapter 6. 233

Table 5.33. Parameters of the Hailwood Horrobin and GAB sorption isotherm models, the coefficient of determination R 2 , mean relative deviation modulus P, and the standard error of the estimate E s for reconstituted R 570 of two ages and at various temperatures. Reconstituted Model Parameter 52 weeks 36 weeks R 570 30 o C 45 o C 55 o C 60 o C 30 o C 45 o C 55 o C 60 o C Cane stalk Hailwood Horrobin b 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.02 c 0.18 0.19 0.24 0.31 0.20 0.20 0.27 0.24 d -0.15 -0.18 -0.24 -0.29 -0.17 -0.19 -0.25 -0.22 R 2 0.98 1.00 1.00 0.99 0.99 0.99 0.99 0.99 P 4.397 11.79 3.916 6.224 6.340 4.846 4.616 6.604 E s 1.288 2.228 0.7431 1.243 1.060 0.9785 1.167 0.8600 GAB m o 5.05 4.58 3.55 3.07 4.67 3.75 3.39 3.66 b 25.90 16.67 13.79 40.23 34.06 -300000000 24.38 14.98 c 0.81 0.85 0.90 0.92 0.82 0.88 0.89 0.87 R 2 0.98 1.00 1.00 0.99 0.99 0.99 0.99 0.99 P 4.530 4.349 3.934 6.217 5.988 9.930 4.656 6.407 E s 1.288 0.694 0.737 1.244 1.032 1.170 0.9805 0.8417 Dry leaf Hailwood Horrobin b 0.015 0.008 0.012 -0.015 0.005 0.003 0.009 -0.057 c 0.133 0.230 0.246 0.392 0.205 0.242 0.218 0.628 d -0.111 -0.206 -0.227 -0.356 -0.176 -0.215 -0.194 -0.554 R 2 0.977 0.992 0.973 0.961 0.988 0.978 0.984 0.808 P 6.584 3.922 8.018 11.12 4.638 12.60 8.067 28.32 E s 1.567 1.038 2.082 3.348 1.216 1.875 1.479 8.345 GAB m o 6.424 3.933 3.581 2.846 4.669 4.055 4.094 2.166 b 13.807 -30000000 -10000000 40000000 48.238 96.221 -50000000 8362848 c 0.770 0.874 0.891 0.938 0.839 0.879 0.867 0.960 R 2 0.977 0.992 0.972 0.960 0.988 0.978 0.983 0.804 P 6.707 5.114 5.114 9.505 4.412 12.61 9.801 27.90 E s 1.550 1.073 1.073 3.325 1.165 1.874 1.508 8.425 Green leaf Hailwood Horrobin b 0.018 0.010 0.007 -0.002 0.219 0.243 0.251 0.597 c 0.158 0.227 0.279 0.312 0.004 0.009 0.011 -0.052 d -0.141 -0.208 -0.261 -0.285 -0.188 -0.222 -0.232 -0.532 R 2 0.978 0.996 0.994 0.973 0.986 0.997 0.991 0.870 P 5.844 4.361 5.758 6.633 44.17 45.78 44.41 63.69 E s 1.622 0.8335 1.213 2.471 5.869 6.288 5.976 14.93 GAB m o 4.664 4.095 3.429 3.257 4.419 3.878 3.698 2.218 b -200000000 28.513 45.999 4013274 66.576 33.752 27.781 10000000 c 0.839 0.881 0.915 0.918 0.844 0.888 0.891 0.969 R 2 0.973 0.996 0.994 0.973 0.986 0.997 0.991 2.218 P 11.18 4.443 5.768 5.768 2.882 6.269 5.576 25.22 E s 1.789 0.8266 1.217 1.217 1.263 0.7331 1.217 8.099 Note: m o , b, c and d are constants. 234

Table 5.33. Parameters of the Hailwood Horrobin and GAB sorption isotherm models, the coefficient of determination R 2 ,<br />

mean relative deviation modulus P, and the standard error of the estimate E s for<br />

reconstituted R 570 of two ages and at various temperatures.<br />

Reconstituted Model Parameter 52 weeks 36 weeks<br />

R 570 30 o C 45 o C 55 o C 60 o C 30 o C 45 o C 55 o C 60 o C<br />

Cane stalk Hailwood Horrobin b 0.01 0.02 0.02 0.01 0.01 0.02 0.01 0.02<br />

c 0.18 0.19 0.24 0.31 0.20 0.20 0.27 0.24<br />

d -0.15 -0.18 -0.24 -0.29 -0.17 -0.19 -0.25 -0.22<br />

R 2 0.98 1.00 1.00 0.99 0.99 0.99 0.99 0.99<br />

P 4.397 11.79 3.916 6.224 6.340 4.846 4.616 6.604<br />

E s 1.288 2.228 0.7431 1.243 1.060 0.9785 1.167 0.8600<br />

GAB m o 5.05 4.58 3.55 3.07 4.67 3.75 3.39 3.66<br />

b 25.90 16.67 13.79 40.23 34.06 -300000000 24.38 14.98<br />

c 0.81 0.85 0.90 0.92 0.82 0.88 0.89 0.87<br />

R 2 0.98 1.00 1.00 0.99 0.99 0.99 0.99 0.99<br />

P 4.530 4.349 3.934 6.217 5.988 9.930 4.656 6.407<br />

E s 1.288 0.694 0.737 1.244 1.032 1.170 0.9805 0.8417<br />

Dry leaf Hailwood Horrobin b 0.015 0.008 0.012 -0.015 0.005 0.003 0.009 -0.057<br />

c 0.133 0.230 0.246 0.392 0.205 0.242 0.218 0.628<br />

d -0.111 -0.206 -0.227 -0.356 -0.176 -0.215 -0.194 -0.554<br />

R 2 0.977 0.992 0.973 0.961 0.988 0.978 0.984 0.808<br />

P 6.584 3.922 8.018 11.12 4.638 12.60 8.067 28.32<br />

E s 1.567 1.038 2.082 3.348 1.216 1.875 1.479 8.345<br />

GAB m o 6.424 3.933 3.581 2.846 4.669 4.055 4.094 2.166<br />

b 13.807 -30000000 -10000000 40000000 48.238 96.221 -50000000 8362848<br />

c 0.770 0.874 0.891 0.938 0.839 0.879 0.867 0.960<br />

R 2 0.977 0.992 0.972 0.960 0.988 0.978 0.983 0.804<br />

P 6.707 5.114 5.114 9.505 4.412 12.61 9.801 27.90<br />

E s 1.550 1.073 1.073 3.325 1.165 1.874 1.508 8.425<br />

Green leaf Hailwood Horrobin b 0.018 0.010 0.007 -0.002 0.219 0.243 0.251 0.597<br />

c 0.158 0.227 0.279 0.312 0.004 0.009 0.011 -0.052<br />

d -0.141 -0.208 -0.261 -0.285 -0.188 -0.222 -0.232 -0.532<br />

R 2 0.978 0.996 0.994 0.973 0.986 0.997 0.991 0.870<br />

P 5.844 4.361 5.758 6.633 44.17 45.78 44.41 63.69<br />

E s 1.622 0.8335 1.213 2.471 5.869 6.288 5.976 14.93<br />

GAB m o 4.664 4.095 3.429 3.257 4.419 3.878 3.698 2.218<br />

b -200000000 28.513 45.999 4013274 66.576 33.752 27.781 10000000<br />

c 0.839 0.881 0.915 0.918 0.844 0.888 0.891 0.969<br />

R 2 0.973 0.996 0.994 0.973 0.986 0.997 0.991 2.218<br />

P 11.18 4.443 5.768 5.768 2.882 6.269 5.576 25.22<br />

E s 1.789 0.8266 1.217 1.217 1.263 0.7331 1.217 8.099<br />

Note: m o , b, c and d are constants.<br />

234

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