Water Diffusivity and Color of Cactus Pear Fruits (Opuntia Ficus Indica) Subjected to Osmotic Dehydration

Figures & data

Table 1 Experimental conditions with Fick's and Page's equations, parameters, and their respective r² and RMSE values.

Run	Conc	T	Fick's equation			Page's equation
No.	(° Brix)	(°C)	De (m^2/s)	r^2	RMSE	k(min^−1)	b	r^2	RMSE
1	40	25	4.95×10^−11	0.989	0.0187	0.023	0.562	0.994	0.0125
2	40	40	4.06×10^−11	0.977	0.0214	0.024	0.534	0.983	0.0199
3	40	55	1.06×10^−10	0.987	0.0264	0.029	0.622	0.996	0.0136
4	50	25	7.58×10^−11	0.976	0.0324	0.043	0.511	0.997	0.0107
5	50	40	6.47×10^−11	0.974	0.0292	0.033	0.535	0.994	0.0139
6	50	55	1.45×10^−10	0.928	0.0654	0.087	0.455	0.987	0.0276
7	60	25	1.12×10^−10	0.982	0.0301	0.034	0.596	0.998	0.0109
8	60	40	1.00×10^−10	0.986	0.0256	0.030	0.603	0.996	0.0134
9	60	55	1.63×10^−10	0.976	0.0381	0.032	0.652	0.989	0.0281
10	40	25	7.08×10^−11	0.950	0.0502	0.055	0.453	0.994	0.0148
11	40	40	7.97×10^−11	0.959	0.0464	0.057	0.463	0.998	0.0095
12	40	55	1.28×10^−10	0.980	0.0380	0.030	0.637	0.995	0.0190
13	50	25	7.95×10^−11	0.978	0.0356	0.038	0.536	0.999	0.0076
14	50	40	9.48×10^−11	0.946	0.0613	0.064	0.468	0.997	0.0130
15	50	55	1.98×10^−10	0.993	0.0288	0.019	0.778	0.989	0.0301
16	60	25	8.47×10^−11	0.973	0.0415	0.036	0.553	0.992	0.0181
17	60	40	1.31×10^−10	0.987	0.0306	0.030	0.639	0.996	0.0154
18	60	55	2.95×10^−10	0.998	0.0163	0.017	0.861	0.998	0.0134

Figure 1 Evolution of experimental moisture ratio and predicted moisture ratio (with Fick's Eq.) with drying time for osmotic dehydration performed at several temperatures.

Figure 2 Evolution of experimental moisture ratio and predicted moisture ratio (with Page's Eq.) with drying time for osmotic dehydration performed at several concentrations.

Table 2 Regression coefficients and variance analysis of the quadratic model Eq. (4) to evaluate the effect of temperature and sucrose concentration on the D_e , k and b values (p<0.05). The bold character indicates that the corresponding parameter has a significant effect on the properties evaluated.

Regression coefficients of the quadratic model (Eq. 5)
Response	β0	β1	β2	β3
Water diffusivity (De r)	8.513	4.689	3.426	4.048
p(t)	2.24E-05	2.60E-04	3.27E-03	3.00E-02
Drying constant (k)	0.040	−0.001	−0.003	−0.003
p(t)	1.73E-04	0.825	0.567	0.779
Parameter b	0.540	0.066	0.053	0.061
p(t)	3.21E-10	0.018	0.050	0.174
Analysis of variance
Response	Source	DF	SS	MS	F	p(F)
Water diffusivity (De )	Regression	3	470.22	156.74	13.94	0.000
	Residual	14	157.39	11.24
	Total	17	627.62	36.92
Drying constant (k)	Regression	3	1.76E-04	5.86E-05	0.16	0.922
	Residual	14	5.15E-03	3.68E-04
	Total	17	5.33E-03	3.13E-04
Constant (b)	Regression	3	0.101	3.36E-02	4.63	0.019
	Residual	14	0.102	0.007
	Total	17	0.202	1.19E-02
p(t)= t-Student probability; p(F)= Fisher probability.

Figure 3 Variation of water effective diffusivity (D_e ) with temperature (a) and sugar concentration (b) in cactus pear during osmotic treatment.

Figure 4 Variation of parameter b with temperature (a) and sugar concentration (b) in cactus pear during osmotic treatment.

Figure 5 Variation of drying constant with temperature (a) and sugar concentration (b) in cactus pear during osmotic treatment.

Table 3 Color measurement results in L*a*b* and total color changes (ΔE) for fresh and osmo-pretreated cactus pear.

Sample, Exp.	L*	a*	b*	ΔE
Fresh cactus pear	57.43 ± 4.01	−3.85 ± 0.90	18.86 ± 3.48
1	55.37 ± 0.06	−4.72 ± 0.07	18.88 ± 0.19	2.24
2	48.51 ± 0.09	−5.27 ± 0.15	23.48 ± 0.38	10.15
3	47.22 ± 0.04	−2.36 ± 0.10	15.94 ± 0.26	10.73
4	52.07 ± 0.29	−3.88 ± 0.33	16.39 ± 0.48	5.90
5	53.50 ± 0.14	−3.79 ± 0.05	27.84 ± 0.34	9.80
6	49.03 ± 0.14	−0.29 ± 0.14	17.70 ± 0.43	9.19
7	61.83 ± 0.22	−4.50 ± 0.02	24.91 ± 0.06	7.51
8	42.20 ± 0.11	−0.70 ± 0.13	21.17 ± 0.29	15.72
9	50.31 ± 0.22	−1.08 ± 0.48	18.87 ± 3.33	7.64
10	52.39 ± 0.09	−3.75 ± 0.53	20.84 ± 0.43	5.41
11	43.16 ± 0.31	−2.15 ± 0.26	15.55 ± 0.32	14.75
12	44.42 ± 0.22	−1.89 ± 0.30	18.36 ± 0.73	13.17
13	55.10 ± 0.18	−2.91 ± 0.09	14.57 ± 0.84	4.97
14	49.88 ± 0.13	−1.39 ± 0.18	16.14 ± 0.36	8.39
15	51.10 ± 0.11	−2.41 ± 0.12	17.71 ± 0.10	6.59
16	55.01 ± 0.10	−0.87 ± 0.42	15.87 ± 0.39	4.86
17	51.04 ± 0.09	−2.30 ± 0.07	16.43 ± 0.11	7.01
18	48.13 ± 0.04	−0.94 ± 0.02	17.52 ± 0.07	9.84

Figure 6Effect of the temperature on total color change (ΔE) of osmo-pretreated samples.

Table 4 Regression coefficients and variance analysis of the quadratic model (Eq. 4) to evaluate the effect of temperature and sucrose concentration on the total color change (p<0.05). The bold character indicates that the corresponding parameter has a significant effect on the properties evaluated.

Regression coefficients of the quadratic model (Eq. 5)
Response	β0	β1	β2	β3
Color change (ΔE)	10.97	2.189	−0.323	−3.633
p(t)	9.81E-08	1.39E-02	0.685	0.017
Analysis of variance
Response	Source	DF	SS	MS	F	p(F)
Color change (ΔE)	Regression	3	111.54	37.18	5.11	0.014
	Residual	14	101.88	7.28
	Total	17	213.42	12.56
p(t)= t-Student probability; p(F)= Fisher probability.