Response Surface Methodology in Rheological Characterization of Papaya Puree

Abstract

The individual and interactive effects of temperature (5–65°C), total soluble solids (TSS) (10–30°Brix), pH (3–7), and α-amylase concentration [(0.25–1.25)kg 100 kg⁻¹ puree] on rheological characteristics of papaya (Carcia papaya L.) puree were studied by the application of the response surface methodology (RSM) using a computer controlled rotational viscometer. Papaya puree exhibited pseudoplasticity with yield stress and flow following Herschel-Bulkley model. A quadratic model developed for rheological parameters met all the criteria of good fit and provided information for characterizing the effect of different variables. It was observed that temperature, TSS and pH individually and in combination affected consistency index (P<0.05) while flow behavior index was significantly influenced by all four factors (P<0.05). The temperature and enzyme concentration considerably affected apparent viscosity.

Keywords:

• Papaya puree
• Rheolofcgy
• Total soluble solids
• Enzyme concentration
• Temperature
• pH

Introduction

Knowledge of the rheological properties of food products is essential for the product development, design and evaluation of the process equipment such as pumps, piping, heat exchangers, evaporators, sterilizers, and mixers. Rheological measurements have also been considered as an analytical tool to provide fundamental insights on the structural organization of food. Numerous studies have been conducted on the rheological properties of fruit and vegetable products.1 2 3 4 5 6 7 Various factors affecting the rheological behavior of fruit purees and concentrates include temperature,8 9 10 total soluble solids (TSS)/concentration,1 11 12 13 particle size,14 15 addition of enzyme,2 16 and pH.17 It has been reported that fruit purees behave as non-Newtonian fluid as a result of complex interactions among soluble sugars, pectic substances, and suspended solids9 and therefore rheological parameters of various fruit purees are needed for research and engineering applications as design and optimization of processing units.

Various rheological models have been used to represent the flow behavior of pureed foods. The power law model is one most commonly used to describe the flow of food products without yield stress, while Casson and Herschel-Bulkley models have been employed for foods with definite yield stress. Concentrated fruit pulps exhibit flow properties, which depend on time as well as shear rate. Fruit juices are mostly Newtonian in nature and commonly represented by power law model (flow behavior index=1.0). Fruit juice concentrates and purees with higher total soluble solids have been well described by Herschel-Bulkley model.16 18 19 20

Papaya (Carcia papaya L.) is an important fleshy fruit of the tropics and is an excellent source of vitamin A and C. The fruit has attracted attention of the food processors and some processes for preservation of fruits have been reported.21 22 Papaya is processed into various forms after the extraction of pulp. Puree is one of the important intermediate papaya products, which is thermally processed and stored for the manufacture of beverage, ice-cream, jam, jelly, among other products.6

The response surface methodology (RSM) is a statistical method with an empirical modeling technique23 used to find the optimum condition of a process response variable. The technique deals with the process which is not well understood or it is too complicated to allow the best model to be formulated from theory. It evaluates the existing relation between a group of controlled experimental factors and the observed results of one or more selected variables.24 The central composite rotatable design (CCRD) has the advantage to predict responses based on selected experimental data wherein all factors are varied within a chosen range. Numerous applications of the RSM technique in food processing and research are available in the literature.

The objective of this work was, therefore, to evaluate the suitability of the RSM to study the effects of temperature (5–65°C), TSS (10–30°Brix), pH (3∼7), and α-amylase concentration [(0.25–1.25) kg  kg⁻¹ of solids] on rheological characteristics of papaya puree.

Materials and Methods

Preparation of Puree

Papayas of Solo variety were procured from a departmental store of Montreal city; washed thoroughly and exposed to flowing steam for 2 min to coagulate the latex in the peel and inactivates the enzymes in the peel.21 The skin was removed using a stainless steel knife. The fruit was cut into two pieces and the seeds were separated. The pulping was done in a laboratory size food processor (Osterizer, Sunbeam Corporation Ltd., Canada) and passed through a paddle finisher fitted with a sieve of 100 mesh (D'errioo, Canada) to remove fiber leading to puree of uniform consistency. The obtained puree was stored in a sterile glass container at 0°C before use. Total soluble solids and pH of papaya puree were 10.2°Brix and 5.11, respectively. The average proximate composition25 of papaya puree were: 89.05% moisture, 0.31% protein (N×6.25), 0.22% fat, 0.32% ash, and 0.94% crude fiber; the starch content was 1.96%.

Experimental Design

Response surface methodology was selected to investigate the main effect of the process variables on rheological characteristics of papaya puree. The experimental design adopted was a modified configuration of Box's central composite design (CCD) for four variables at five levels each (Table 1). The four independent variables or factors (temperature, TSS, pH, and α-amylase concentration) were selected to optimize responses consistency index (Y1), flow behavior index (Y2), and apparent viscosity (Y3). The complete design included 31 experiments with seven replications of the center point (Table 2), and was rotatable as described by Draper26 and Chen and Ramaswamy.27

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

Sample Preparation

As per the design described above, the samples were prepared by addition of required amount of sugar, citric acid, sodium hydroxide, and α-amylase respectively. The samples were incubated for 6 hours at 37°C to obtain maximum enzyme activity. Sugar was procured from a departmental store while citric acid, sodium hydroxide, and fungal crude α-amylase enzyme (Type X-A; EC 3.2.1.1; Lot 61H0531 from Aspergillus oryzae) were purchased from Sigma Chemicals Company (St. Louis, MO). Total soluble solids (°Brix) and pH were determined using a Refractrometer (Atago, Japan) at 20°C and a pH meter with glass electrode (Accumet, USA).

Rheological Measurement

A rotational viscometer (Haake Model RV20; Haake Mess-Technik, Karlsrulhe, Germany), equipped with an M-05 OSC measuring head and MV1 rotor (o.d. 20.04 mm and height 60 mm) in a concentric cylindrical cup (i.d. 21 mm) assembly interfaced to a microcomputer for control and data acquisition was used for rheological measurement. The sample compartment was maintained at a constant temperature using a water bath/circulator (Haake, Model FK-2).

For each test, the filled sample cup and spindle were temperature equilibrated for about 15 min and the samples were subjected to three-cycle shear changes from 0 to 300 s⁻¹ in 5 min, steady shear at 300 s⁻¹ in 5 min followed by back to 0 s⁻¹ in next 5 min. The rheograms were evaluated by the software (Haake RV20 version 2.3) using the Herschel-Bulkley model [Eq. (1)]. Yield stress values were obtained directly from the software as well as verified from Casson model [Eq. (2)]. The apparent viscosity was computed as the ratio of shear stress to shear rate (τ/γ) at the mid shear rate of 150 s⁻¹.

where τ is the shear stress (Pa), τ ₀ is the yield stress, γ is the shear rate (s⁻¹), K is the consistency index (Pa s ⁿ ), and n is the flow behavior index (dimensionless), K ₀ and K _c are Casson yield stress and Casson constant, respectively. Yield stress was calculated from the relationship K ₀ ²=τ ₀.

Polynomial Equations and Statistical Analysis

A quadratic polynomial regression model was assumed for predicting individual Y variables. The model proposed for each response of Y is:

Where b ₀ is a constant and b _i , b _ii , and b _ij are regression coefficients of the model and X _i and X _j are the independent variables in coded values.

The regression analysis, analysis of variance (ANOVA), canonical analysis, and analysis of ridge maximum of data were carried out using the RSREG procedure of the SAS statistical package28 to fit second order polynomial equations for all response variables. Response surfaces were made by the fitted quadratic polynomial equation obtained from RSREG analysis, holding the independent variables with the least effect on the response at a constant value, and changing the other two variables. Conformity experiments were done to validate the equation, using the combination of independent variables, which were not included in the original experimental design and within the experimental region. Lack-of-fit tests were performed on the fitted models. Coefficients for the linear, quadratic, and interaction terms of each model were calculated and tested from zero. The criteria for eliminating a variable from the full regression equation was based on R ² values, standard error (SE) estimate and significance F-test and the derived P values. Three dimensional response surface plots were generated by using Sigma plot software (Sigma Plot 2000; SPSS Inc.) to illustrate the main and interactive effects of the independent variables.

Results and Discussion

Rheological Characteristic of Papaya Puree

All test samples of papaya puree characteristically exhibited a yield stress and therefore the shear stress–shear rate data were fitted to the Herschel-Bulkley model rather than the conventional power law model. For all cases, R ² values were greater than 0.94 and SE were less than 0.09. Differences between the yield stress data computed from instrument software and those calculated from Casson model were not significantly different (P>0.05). Yield values are presented in Table 2. Typical rheological flow curve for papaya puree is shown in Fig. 1. Upward and downward curves essentially gave similar results and hence average values of rheological parameters between upward and downward curves were used. The flow behavior index of papaya puree was less than unity and hence the puree represented a pseudoplastic fluid. Pseudoplasticity has similarly been observed for fruit purees by various researchers.16 18 20

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 shows the time dependency rheology curve of papaya puree as a shear stress vs. time relationship at the peak shear rate of 300 s⁻¹. The observed shear stress at a specific shear rate was not sensitive to the time of shear. Therefore, the puree viscosity was considered to be time-independent within range of test conditions employed in the study.

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

Regression Models of Rheological Parameters (Consistency Coefficient, Flow Behavior Index, and Apparent Viscosity)

From a practical standpoint, it will be more relevant to describe the effects of temperature, TSS, pH, and α-amylase concentration by one combined model. In the literature, the Arrhenius model has been most widely used to describe the effects of temperature, while the effect of concentration has been described by either an exponential or a power relationship. Several authors2 11 12 20 29 used the combined effect of temperature and total solids content on consistency index/apparent viscosity to describe the flow behavior of concentrates or pureed fruits and vegetables. However, none of the above studies takes into account the effects of pH and enzyme concentration on the rheological properties of papaya puree. In this study, K, η, and n were expressed as a function of temperature and concentration through a multiple regression analysis.

The effects of treatment variables as linear, quadratic, or interaction coefficients on response variables were obtained by ANOVA (Tables 3 and 4). Significance of the lack-of-fit error term, R ² value, coefficient of variation (CV), and model significance were used to judge adequacy of model fit. The predictive models developed for Y1, Y2, and Y3 of papaya puree were considered adequate because the associated lack of fit was not significant for these cases and they had satisfactory levels of R ², CV, and model significance. It is evident from Table 3 that all linear, quadratic, and interaction terms were significant (P<0.05) for Y1; X1, X4 and quadratic terms of X1, X3 and X4 were significant for Y3 while interaction term was insignificant for Y2. The R ² values were 0.93, 0.85 and 0.81 for Y1, Y2 and Y3, respectively while SE was less than 0.11 for all the cases. The contribution for linear, quadratic, and cross products terms to the model was 0.633, 0.141, and 0.132 for Y1; 0.320, 0.410 and 0.068 for Y2 and 0.323, 0.388 and 0.095 for Y3, respectively.

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

The fitted equations were obtained considering only significant terms to predict Y1 (K), Y2 (n), and Y3 ( η ) values and are shown below:

Effects of Temperature, Total Soluble Solids, and pH on Consistency Index

The model [Eq. (4)] indicated that temperature (X1) had significant effect (P<0.05) on Y1 as it had the largest coefficient followed by TSS (X2) and pH (X3). These observations were also verified from canonical analysis of response surface. Negative coefficients of X1 and X2 indicated linear effect to decrease Y1. However, X3 had positive effect along with quadratic terms (X1² and X2²) and interaction terms (X1X2 and X2X3) that increased Y1. No significant effect (P>0.05) was observed for enzyme concentration (X4) on Y1. It could be due to interference of pH as the α-amylase enzymes were sensitive to pH. The three-dimensional figures (Fig. 3) show that the three independent variables and their interactions of the predictive model for consistency index. These provide geometrical representation of the behavior of K within the experimental design. The minimum consistency was observed with increase in TSS and temperature while lower pH and higher TSS resulted in optimum consistency index.

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

The consistency index decreased with increase of temperature and TSS. But the extent of increases or decreases of K at different temperatures or TSS were different because of the interaction between independent variables. Decrease in K with an increase of temperature and increase in K with concentration are commonly reported by researchers.1 10 13 In our case the reverse trend was noticed as added sugar increased TSS with decrease in consistency index significantly (P<0.05). The optimum temperature and TSS to get minimum consistency index was calculated from partial derivatives of the quadratic response equation with respect to X1 and X2, setting the derivatives equal to zero. It was found to be 48°C and 26°Brix, respectively. The eigen values obtained from the canonical analysis were 50% positive and 50% negative, thus indicating that the stationary point is a saddle point.

Effects of Temperature, Total Soluble Solids, pH, and Enzyme Concentration on Flow Behavior Index

It is evident from Eq. (5) that Y2 was dependent (P<0.05) on all the four factors or its quadratic terms. However, no interaction term was found to be significant. Canonical analysis revealed that pH (X3) had maximum effect followed by TSS (X2) and enzyme concentration (X3) on Y2. The negative coefficient of pH (X3) and quadratic terms (X1², X2², X3², and X4²) decreased the magnitude of Y2 while TSS (X2) linearly increased. Figure 4 shows the effects of interaction between temperature–TSS, TSS–pH, and temperature–pH on flow behavior index. The figures (4A–D) show that n increased with process temperature, TSS, and addition of enzyme. Low pH values and high TSS increased flow behavior index (Fig. 4B, C). However the variation was not systematic due to interaction of other factors. The optimum TSS and pH for better flow behavior index were found to be 23°Brix and 4.4, respectively. All eigen values obtained for analysis were negative, thus indicating that the stationary point for the response was maximum.

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

Effects of Temperature, pH, and Enzyme Concentration on Apparent Viscosity

Equation 6 shows that temperature (X1) and enzyme concentration (X4) significantly (P<0.05) influenced the Y3. The negative linear coefficients of X1 and X4; quadratic coefficients of X1, X3, and X4 decreased Y2. No significant effect was observed for TSS (X4) or any interaction terms on Y2. The three-dimensional figures (Fig. 5) show that the independent variables of the predictive model for apparent viscosity with its geometrical representation. Temperature and enzyme concentration reduced the magnitude of η. The addition of α-amylase enhanced the liquefaction of papaya puree with temperature. This observation is supported by earlier reports.2 10

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

The data obtained for minimum apparent viscosity were 24.3°C temperature and 0.665% enzyme concentration, respectively. Canonical analysis indicating that the stationary point is a saddle point (75% negative values) and the processing variables were located within the experimental range implying that the analytical techniques could be used to identify their minimal condition.

Conclusions

The RSM was effective to optimise the rheological behavior of papaya puree and three-dimensional figures well represented to identify the effects of temperature, TSS, pH, and enzyme concentration on rheological parameters of papaya puree. Good fit models were developed for consistency index and flow behaviour index. The importance of the process variables on the flow characteristics could be ranked in the following order: the temperature (X1)>total soluble solids (X2)>pH (X3)>α-amylase concentration (X4). The optimum temperature and TSS for consistency index were found to be 48.4°C and 26°Brix respectively while optimum TSS and pH for flow behavior index was 23°Brix and 4.4, respectively. The apparent viscosity was optimised at 0.665% enzyme concentration at 24.3°C. The flow behaviour was described well by Herschael-Bulkley model and papaya puree behaved as a pseudoplastic fluid with yield stress.