Response Surface Methodology in Rheological Characterization of Papaya Puree

Figures & data

Table 1 Variables and levels for a rotatable central composite design used in papaya puree rheology experiments

		Coded-variable levels
Variables	Symbol	−2	−1	0	+1	+2
Temperature (°C)	X1	5	20	35	50	65
TSS (°Brix)	X2	10	15	20	25	30
pH	X3	3	4	5	6	7
α-amylase concentration (kg/100 kg puree)	X4	0.25	0.50	0.75	1.0	1.25

Table 2 Central composite rotatable design arrangement and responses

	Independent variable				Response variables
Experiment	X1	X2	X3	X4	τ 0 (Pa)	K (Pa s^n)	n (-)	η (Pa s)
1	−1	−1	−1	−1	16.2	1.13	0.58	0.265
2	−1	−1	−1	+1	13.3	0.86	0.60	0.153
3	−1	−1	+1	−1	24.2	1.02	0.58	0.217
4	−1	−1	+1	+1	22.0	1.07	0.60	0.244
5	−1	+1	−1	−1	23.0	0.41	0.78	0.482
6	−1	+1	−1	+1	18.7	0.37	0.78	0.256
7	−1	+1	+1	−1	21.2	0.76	0.73	0.711
8	−1	+1	+1	+1	21.1	0.98	0.68	0.270
9	+1	−1	−1	−1	22.7	0.45	0.69	0.177
10	+1	−1	−1	+1	13.2	0.39	0.66	0.131
11	+1	−1	+1	−1	14.3	0.70	0.60	0.166
12	+1	−1	+1	+1	10.6	0.38	0.61	0.110
13	+1	+1	−1	−1	19.7	0.26	0.71	0.144
14	+1	+1	−1	+1	16.5	0.17	0.75	0.148
15	+1	+1	+1	−1	10.7	0.60	0.67	0.265
16	+1	+1	+1	+1	21.6	0.59	0.63	0.195
17	−2	0	0	0	21.8	0.98	0.74	0.520
18	+2	0	0	0	12.7	0.56	0.68	0.141
19	0	−2	0	0	36.0	0.81	0.63	0.560
20	0	+2	0	0	6.18	0.38	0.78	0.51
21	0	0	−2	0	9.0	0.24	0.82	0.276
22	0	0	+2	0	13.9	0.59	0.73	0.328
23	0	0	0	−2	11.5	0.46	0.74	0.348
24	0	0	0	+2	6.25	0.30	0.78	0.200
25	0	0	0	0	14.3	0.44	0.81	0.510
26	0	0	0	0	15.2	0.48	0.75	0.590
27	0	0	0	0	8.85	0.33	0.85	0.400
28	0	0	0	0	7.23	0.46	0.82	0.550
29	0	0	0	0	13.1	0.49	0.83	0.450
30	0	0	0	0	12.2	0.55	0.85	0.540
31	0	0	0	0	8.23	0.55	0.77	0.420

Figure 1. Typical shear stress–shear rate curve for papaya puree at selected conditions. Set-1: 20°C, pH 6, 15°Brix, and 0.8% α-amylase concentration; Set-2: 35°C, pH 5, 20°Brix, and 0.6% α-amylase concentration; Set-3: 50°C, pH 6, 15°Brix, and 0.8% α-amylase concentration; Set-4: 20°C, pH 5, 35°Brix, and 1% α-amylase concentration.

Figure 2. Typical time independency of papaya puree at 50°C, pH 4, 15°Brix, and 0.8% α-amylase concentration.

Table 3 Analysis of variance of the second order polynomial model for consistency index, apparent viscosity, and flow behavior index of papaya puree

Response	Source	df	SS	F	P
Consistency coefficient	Linear	4	1.289	27.23	<0.0001
	Quadratic	4	0.287	6.07	0.0036
	Cross product	6	0.269	3.80	0.0152
	Total residual	14	1.846	11.14	<0.0001
	Lack-of-fit	10	0.155
	Pure error	6	0.034	2.75	0.113
	Total error	16	0.189
Flow behavior index	Linear	4	0.069	6.34	0.003
	Quadratic	4	0.088	8.12	0.001
	Cross product	6	0.015	0.90	0.522
	Total residual	14	0.171	4.52	0.003
	Lack-of-fit	10	0.003
	Pure error	6	0.009	2.32	0.157
	Total error	16	0.043
Apparent viscosity	Linear	4	0.277	6.30	0.003
	Quadratic	4	0.334	7.37	0.002
	Cross product	6	0.081	1.23	0.342
	Total residual	14	0.683	4.43	0.003
	Lack-of-fit	10	0.145
	Pure error	6	0.031	2.81	0.110
	Total error	16	0.176

Table 4 Regression coefficients and analysis of variance of the regression models for rheological parameters

			Y1		Y2
Term	b	SE	P	b	SE	P	b	SE	Y3 (P)
Constant	0.471	0.041	0.000	0.811	0.020	0.000	0.494	0.040	0.000
X1	−0.163	0.022	0.000	−0.005	0.011	0.617	−0.084	0.021	0.001
X2	−0.113	0.022	0.000	0.046	0.011	0.000	0.038	0.021	0.100
X3	0.115	0.022	0.000	−0.026	0.011	0.025	0.022	0.021	0.320
X4	−0.035	0.022	0.135	0.002	0.011	0.846	−0.051	0.021	0.031
X1*X1	0.090	0.020	0.000	−0.037	0.010	0.002	−0.060	0.020	0.008
X1*X2	0.079	0.027	0.011	−0.026	0.013	0.066	−0.042	0.026	0.128
X2*X2	0.047	0.020	0.036	−0.039	0.010	0.001	−0.009	0.020	0.656
X1*X3	−0.004	0.027	0.892	−0.009	0.013	0.482	−0.009	0.026	0.724
X2*X3	0.086	0.027	0.006	−0.011	0.013	0.426	−0.024	0.026	0.356
X3*X3	0.002	0.020	0.941	−0.021	0.010	0.046	−0.067	0.020	0.004
X1*X4	−0.028	0.027	0.327	−0.000	0.013	0.962	−0.036	0.026	0.184
X2*X4	0.043	0.027	0.137	−0.004	0.013	0.741	−0.034	0.026	0.211
X3*X4	0.025	0.027	0.371	−0.005	0.013	0.671	−0.010	0.026	0.706
X4*X4	−0.007	0.020	0.727	−0.025	0.010	0.021	−0.074	0.020	0.002

Figure 3. Response surfaces for the effect of temperature, TSS, and pH on consistency index (K) of papaya puree.

Figure 4. Response surfaces for the effect of temperature, TSS, pH, and α-amylase concentration on flow behavior index (n) of papaya puree.

Figure 5. Response surfaces for the effect of temperature, α-amylase concentration, and pH on apparent viscosity (η) of papaya puree.