doi 10.1515/ijfe-2012-0250 International Journal of Food Engineering 2014; 10(3): 437–445 Renata Silva Diniz, Jane Sélia dos Reis Coimbra*, Marcio Arêdes Martins, Michel de Oliveira dos Santos, Mayra Darliane Martins Silva Diniz, Emílio de Souza Santos, Danielle Dias Santánna, Roney Alves da Rocha and Eduardo Basílio de Oliveira Physical Properties of Red Guava (Psidium guajava L.) Pulp as Affected by Soluble Solids Content and Temperature Abstract: Physical properties of fluid and semisolid foods, such as density and rheological behavior, must be carefully taken into account on designing unit operations for the processing of such kind of products. In this work, a rotational rheometer of concentric cylinders was used to evaluate the rheological behavior of red guava pulp (Psidium guajava L.), with different soluble solids content (5, 10, and 15°Brix), at four temperatures (10, 30, 50, and 70°C). Also density data were obtained using pycnometry. Models were fitted to the obtained experimental data, in order to mathematically represent the rheological parameters and the density as functions of temperature and soluble solids content. The rheological behavior of the red guava pulp was adequately described by the Ostwald-de-Waele model, with a pseudoplastic behavior. Models to describe the simultaneous effect of temperature and concentration on the density were also presented. Keywords: non-Newtonian, power law model, pseudoplastic, Arrhenius-type equation, density *Corresponding author: Jane Sélia dos Reis Coimbra, Departamento de Tecnologia de Alimentos (DTA), Universidade Federal de Viçosa (UFV), CEP 36571-000 Viçosa, MG, Brazil, E-mail: jcoimbra@ufv.br Renata Silva Diniz, Departamento de Tecnologia de Alimentos (DTA), Universidade Federal de Viçosa (UFV), CEP 36571-000 Viçosa, MG, Brazil, E-mail: renadiniz14@gmail.com Marcio Arêdes Martins: E-mail: aredes666@gmail.com, Michel de Oliveira dos Santos: E-mail: michel.saints@gmail.com, Mayra Darliane Martins Silva Diniz: E-mail: mayra_darliane@hotmail.com, Emílio de Souza Santos: E-mail: emilio_ss@hotmail.com, Departamento de Engenharia Agrícola (DEA), Universidade Federal de Viçosa (UFV), CEP 36571-000 Viçosa, MG, Brazil Danielle Dias Santánna: E-mail: danielledias@ufv.br, Roney Alves da Rocha: E-mail: roneyalimentos@yahoo.com.br, Eduardo Basílio de Oliveira: E-mail: eduardo.basilio@ufv.br, Departamento de Tecnologia de Alimentos (DTA), Universidade Federal de Viçosa (UFV), CEP 36571-000 Viçosa, MG, Brazil 1 Introduction Guavas (Psidium guajava L.) are fruits of commercial and nutritional values. Guavas are a member of the myrthe family (Myrtaceae) with the following characteristics: (1) 4–12 cm long, round, or oval depending on the species, with a rough outer skin which often presents a bitter taste; (2) high vitamin C content, and reasonable amounts of provitamin A, minerals (Ca, P, and Fe), dietary fiber, and antioxidant compounds (such as lycopene); (3) pleasant aroma, not much sugar (overall) and almost no fat; (4) sensory and bio-functional properties; (5) excellent acceptance for fresh consumption; (6) can be used in large industrial application; and (7) can grow in adverse weather conditions. Additionally, guava flesh contains considerable amounts of pectin, which makes them widely used for the fabrication of purees, pastes, nectars, jams, and jellies. Guava pulp may be sweet or sour, offwhite (known as white guavas) to deep pink (known as red guavas), with seeds variable in number and hardness depending on the species [1–4]. Guava fruits are an important cultivation in tropical and semitropical regions. For a technically and economically optimal processing of fruits, it is necessary to know several of their physical and chemical properties, as well as how such properties behave in function of the conditions to which the material is submitted during its processing [5]. Rheological behavior and density are among the most important of these physical properties, and both are affected by the solids content of the material and the temperature. Density data are needed, for example, to calculate heat and mass transfer rates, which are the basis of numerous unit operations. Rheology is the science that studies the deformation and flow of solids and fluids under the influence of mechanical forces. Moreover, rheology attempts to define a relationship between the stress acting on a given Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM 438 R. S. Diniz et al.: Physical Properties of Guava Pulp material and the resulting deformation and/or flow that takes place. Rheological behavior and parameters are necessary in designing and controlling operations such as pumping and transport through pipes, among others. The knowledge of rheological behavior of fluids in the production stage can be useful in quality control, as the rheological characteristics are intimately correlated to the texture perception, thus being also important for the sensory quality control of the final products. The microstructure of a product may be correlated to the rheological behavior, allowing the development of new materials [6–8]. Several studies dealing with the rheological characterization of fruits and fruit-derived products can be found in literature, such as for pulps and purees from murta berries [9]; siriguela pulp [10]; passion fruit pulp [11]; mango puree [12]; pineapple juice [13]; mango pulp [14]; jaboticaba pulp [15]; pitaya juice [16]; pummelo juice [17]; blackberry juice [6]; butia pulp [18]; peach and orange juices, and apple and marmelo pulps [28]. Zainal et al. [19] reported a pseudoplastic behavior for pink guava juice with solid soluble contents of 9 and 11°Brix at temperatures of 60, 65, 70, 75, 80, 85, and 90°C. The consistency index (K) decreased with increasing temperature. Oliveira et al. [20] also observed the pseudoplastic behavior for red guava pulp with 5.5°Brix, at temperature of 20, 25, 30, and 35°C. The Ostwald-deWaele model (power law) was suitable to describe the flow behavior in these two literature reports. The aim of our work was to characterize red guava pulp in terms of the rheological behavior and density, at temperature of 10, 30, 50, and 70°C and solid soluble contents of 5.7, 12.1, and 15.8°Brix. The observed data were used to establish mathematical models to describe the changes in density and viscosity as a function of temperature and solid soluble content. 2 Materials and methods 2.1 Raw material obtaining and preparation Five kilograms of red guava (Paluma variety) in physiological maturation stage was obtained at the local marketing of Viçosa city, Minas Gerais, Brazil. The fruits were received, washed in water, cut in small pieces, and then the seeds were separated from the edible parts. The edible parts were crushed in a microprocessor (RI1861, Philips Wallita, Brazil). The obtained pulp was concentrated by lyophilization (LS 3000, Terroni, Brazil) until the solid content attained about 18.0 °Brix. Starting from this pre-processed pulp, other solids concentrations (5.7, 12.1, and 15.8°Brix) were obtained by dilution with double-distilled and deionized water (electrical resistivity equals to 18.2 MΩ cm; Millipore Inc., Milli-Q, Billerica Headquarters, MA). The different pulps were stored in plastic containers at –18.0°C (freezer Pratice 410 Biplex, Consul, Brazil) until their use in the subsequent experiments. All experiments were conducted by using duplicate with two repetitions. 2.2 Solids content and pH measurements The soluble solids content was measured by direct reading using a portable refractometer (RT-60ATC, Instrutherm, Brazil) with the results expressed in °Brix. The fixed solids (minerals) content was quantified by incinerating the samples in an oven (Q318 D24, Quimis, Brazil) at 550°C and weighting the residual. The pH values were determined directly in the samples using a digital pH meter (pH21, Hanna Instruments, Brazil). 2.3 Density measurements Density (ρ; kg=m3 ) was determined by fluid displacement in pycnometer, according to standard AOAC [21]. A 25 mL pycnometer (nominal volume) previously calibrated with distilled water was used. An analytical balance (M-310, Denver Instrument, USA; accuracy of 10–4 g) was used for all weight measurements. Analyses were carried out in triplicate at 10, 30, 50, and 70°C, for each of the studied pulps [(5.7, 12.1 and 15.8)°Brix]. The temperature was controlled using a thermostatic water bath (TE-184, Tecnal, Brazil). 2.4 Rheological measurements Rheological measurements were performed on a rotational rheometer of coaxial cylinders (RN 4.1, Rheotest Mendigen GMBH, Germany) coupled to a thermostatic bath with water recirculation (RE206, Lauda, Germany). Analyses were carried out in triplicate at 10, 30, and 50°C, for each of the studied pulps [(5.7, 12.1, and 15.8)°Brix]. Shear stress values (τ) were recorded for the shear rate ( γ_ ) range of 0–330 s−1. Each test runs for 3 min. Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM R. S. Diniz et al.: Physical Properties of Guava Pulp Three classical rheological models, Ostwald-deWaele (power law; eq. 1), Herschel-Bulkley (eq. 2), and Casson (eq. 3), were fitted to the obtained experimental curves, τ ¼ f( γ_ ) [22]. τ ¼ K γ_ n ; ð1Þ τ ¼ τ 0 þ K γ_ n ; ð2Þ τ 0:5 ¼ τ 0 0:5 þ KC γ_ 0:5 ; ð3Þ where τ ¼ shear stress, γ_ ¼ shear rate, τ0 ¼ threshold stress needed for flow to occur (τ0 ¼ 0 for Newtonian and power law fluids), K ¼ consistence index, Kc ¼ plastic viscosity of Casson, and n ¼ flow index (n > 1: dilatant fluid; n < 1: pseudoplastic fluid; if the fluid is Newtonian, n ¼ 1 and K ; η, the viscosity). The influence of temperature on apparent viscosity of non-Newtonian fluids is usually modeled by an Arrhenius-like equation (eq. 4). The effect of concentration on the apparent viscosity is usually described by a power model (eq. 5) [23]. ηa ðT Þ ¼ ηo exp
Ea RT ηa ðC Þ ¼ K1 C A1  ð4Þ ð5Þ in eqs (4) and (5), ηa is the apparent viscosity (Pa s) at γ_ ¼ 100 s−1; shear rate value usually adopted in studies involving correlations between sensory and rheological properties of food materials; Ea is the activation energy for viscous flow (J/mol); R is the universal gas constant (8.314 J/mol K); T is the absolute temperature (K); C is the concentration of soluble solids (°Brix); η0, K1, and A1 are constants of the equation to be determined for each material in specific ranges of temperatures and concentrations. It is worth to emphasize that although this exponential function fitted to experimental data to describe the decrease of apparent viscosity when increasing the temperature, values of Ea in the present context have not a clear physical meaning. Indeed, Arrhenius-like equations were originally used to explain the temperature dependency of chemical reaction rates and, in such cases, Ea represents the activation energy of reaction [24]. Nevertheless, here Ea values should be interpreted with caution, as they represent simple numerical coefficients enabling an adequate fitting of exponential functions to experimental data on the decrease of apparent viscosity of materials as the temperature rises [23]. 439 The combined effect of temperature and concentration on the apparent viscosity can be described by eqs (6) and (7) [23]. ηa ðC; T Þ ¼ a1 C b1 exp ηa ðC; T Þ ¼ a2 exp

Ea RT  Ea þ b2 C RT  ð6Þ ð7Þ where a1, a2, b1, and b2 are constants to be determined for each fluid, over specific ranges of temperature and concentration. 2.5 Models fitting Models fitting were performed using the Statistical Analysis System (SAS®) 9.0 software. For density data, simple linear models ρ ¼ f(T,C) were adjusted. Concerning the rheological data, the models represented by eqs (1)–(3) were tested for the fluid flow behavior, whereas those represented by eqs (4) and (5) were tested for the variation of the apparent viscosity in function of temperature and concentration, respectively. The adequate fitting of non-linear models in parameters, or linear without the constant term (eqs 1–7), was assessed in terms of the coefficient of determination (R2 ), square root of the average square of the residue (RQMR; eq. 8, estimated by maximum-likelihood), chisquared (χ 2 ; eq. 9), and absolute mean percentage error (AMPE) described by eq. (10) [25–27]. sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi n  2 1X ^i RQMR ¼ Yi Y n i¼1 χ2 ¼ Pn  i¼1 Yi n Y^ i p 2   ^ i  n  Yi Y X 100   AMPE ¼  n i¼1  Yi  ð8Þ ð9Þ ð10Þ In eqs (8)–(10), Yi is the ith experimental score, Y^i is the ith predicted score, n is the number of score pairs, and p is the number of model parameters. The highest values for R2 and the lowest values for RQMR, χ 2 , and AMPE indicate the best fitting for the models. R2 was calculated by the rate between the sum of squares of the model and the sum of total squares. The sum of total squares not Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM 440 R. S. Diniz et al.: Physical Properties of Guava Pulp corrected by the average was used to estimate R2 in the models without the intercept. The adequate fitting of linear regression models with the constant term (β0 ; eq. 11) was assessed in terms of the coefficient of determination (R2 ). 3 Results and discussion Data of pH, soluble solids, and fixed solids for each guava pulp (5.7, 12.1, and 15.8°Brix) are shown in Table 1. Table 1 Averages and standard deviations for values of pH, soluble solids, and ash, measured in five repetitions in red guava pulp (Paluma variety) in maturation stage Soluble solids (°Brix) 5.7  0.1 12.1  0.1 15.8  0.2 pH Ash (%) 4.07  0.04 3.87  0.03 3.90  0.03 0.29  0.04 0.60  0.03 2.02  0.05 3.1 Density results Density data obtained by pycnometry are given in Table 2. Density values decreased with increasing temperature probably due to volumetric expansion of the fluid caused by the reduction in the intermolecular bond strength. On the other hand, the density increased with increasing concentration of the sample. Similar behavior was observed for other fruit-derived materials, such as mango pulp [14], peach and orange juices, and also apple pulp [28]. A linear polynomial model of second degree was adjusted to these density data in order to mathematically describe the variation of density as a function of temperature and solid concentration, within the studied ranges (10.0–70.0)°C and (5.7–15.8)°Brix. The best fitting was obtained with a four-term polynomial model, described by eq. (11), with parameter estimates presented in Table 3. ρðC; T Þ ¼ β0 þ β1 C þ β2 C2 þ β3 T Guedes et al. [29] found a similar model to describe the density of watermelon pulp as a function of temperature and solids concentration. Ramos and Ibarz [28] reported the suitability of polynomial models to describe the density behavior of orange and peach juices, as a function of these two parameters. In addition, such reports demonstrated that the density is Table 2 Averages and standard deviations for values of density (ρ) of red guava pulp (Paluma variety), measured in five repetitions for three contents of soluble solids (°Brix) and four temperatures (°C) Density, kg/m3 C (°Brix) 5.7  0.1 12.1  0.1 15.8  0.2 10.0°C 30.0°C 50.0°C 70.0°C 1,049.88  0.62 1,115.92  1.00 1,129.77  0.56 1,042.15  0.98 1,101.10  1.23 1,112.44  0.81 984.84  1.23 1,070.64  1.45 1,072.94  1.24 962.73  0.76 1,052.75  0.93 1,066.04  1.56 Table 3 Confidence limits, probability values of t-test, and parameter estimates (βi ) of the second degree regressive linear model adjusted to density data (ρ), concentration (°Brix), and temperature (°C) of red guava pulp (Paluma variety) in maturation stage Parameter β0 β1 β2 β3 Estimated value 910.26823 29.57076 −0.91918 −1.18504 ð11Þ Confidence limits, 95% Lower limit Upper limit 822.06103 10.97916 −1.79435 −1.63414 998.47544 48.16237 −0.04400 −0.73594 t-value Pr > |t| 22.71 3.50 −2.31 −5.81 < 0.0001 0.0050 0.0412 0.0001 Note: R2 ¼ 0:9242. Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM R. S. Diniz et al.: Physical Properties of Guava Pulp influenced by temperature in a linear manner and the concentration in a quadratic way. 3.2 Rheology results Three classical rheological models (Ostwald-de-Waele or power law, Herschel-Bulkley, and Casson) were adjusted to the experimental data, and the resulting regression parameters are shown in Table 4. The rheograms were registered for each guava pulp (5.7, 12.1, or 15.8°Brix) at 10.0, 30.0, 50.0, and 70.0°C. For the Ostwald-de-Waele model, the flow behavior index (n) varied from 0.223 to 0.406 at all conditions evaluated. Therefore, n was less than unity which allows the characterization of red guava pulp as pseudoplastic non-Newtonian fluid. It was not possible to identify the models with better adjustment to experimental data using the R2 value as the only criterion for decision. Choice for the best adjustments was made by putting together adequacy indicators (R2 , χ 2 , RQMR, and AMPE) in only one empirical equation (eq. 12). GS ¼ χ2 R2  RQMR  AMPE ð12Þ In eq. (12), GS is a general score attributed to each of the adjusted models. Higher values of GS correspond to better adjustments of the models to experimental data. In Table 4, GS is normalized to a value rate from zero to one hundred. The guava pulp becomes more pseudoplastic with increasing soluble solids concentration because at a given temperature, the consistency coefficient (K) tends to rise and the flow behavior index (n) tends to decrease with increasing concentration. It was also observed that consistency coefficient decreased with increasing temperature. A pseudoplastic behavior for guava juice at the temperature range between 60 and 90°C for 9 and 11°Brix was observed by Zainal et al. [19]. Also Guedes et al. [29], Cabral et al. [13], and Anuradha et al. [12] observed the same behavior for the watermelon pulp, pineapple juice, and mango puree. The Ostwald-de-Waele model was used to determine the consistency coefficient (K). These authors observed an increase in K with the increment of solids concentration and a decrease of K with the temperature increasing. Figure 1 represents the relation between shear stress (τ) and shear rate (_γ) at all the temperatures and all the 441 concentrations studied with red guava pulp. The shear stress value decreased with increase in temperature at a constant shear rate value. Arrhenius-like model (eq. 4) proved satisfactory to describe the temperature effect (10.0–70.0)°C on the apparent viscosity of guava pulp (η). Estimated parameters, η0 and Ea , were obtained from 12 observations and are reported in Table 5, for the different concentrations of soluble solids. Results of R2 > 0.91 indicate that the adjusted models were satisfactory in all concentrations. It is observed that the values of the constant η0 increase with increasing the concentration of soluble solids. On the other hand, the values of Ea decrease when increasing concentration of 5.7–12.1 °Brix; however, they remain closer when the concentration is increased from 12.1 to 15.8°Brix. Many authors observed the suitability of Arrheniuslike equations to describe the reduction on apparent viscosity of fruits products with the increasing in temperature such as: Ah-Hen et al. [9] for pulps and purees from murta berries; Chuah et al. [16] for dragon fruit (pitaya) juice; and Haminiuk et al. [18] for butia pulp. Moraes et al. [11] also found this behavior for passion fruit pulp. The authors noted that higher temperatures increase particle mobility with a consequent decrease in the viscosity of fruit pulp, which consists of solid particles dispersed in a liquid medium. Indeed, the apparent viscosity of fruit purees or pulps depends on the concentration, size, and shape of suspended solids [30]. To estimate the parameters of eq. (5), which relates the effect of concentration on apparent viscosity, the model was fitted to experimental data at all temperatures studied. The parameters of this model were estimated from 12 observations and are presented in Table 6. The combined effect of temperature and concentration on the apparent viscosity of red guava pulp can be expressed in a single equation, as in eqs (6) and (7). The parameters of these equations were estimated from 12 observations and are presented in Table 7, together with confidence limits, coefficient of determination, and probability values of t-test. Due to the high coefficients of determination and small amplitude of confidence limits, the two models can be satisfactorily used [31–32] to describe the variation of viscosity with concentration and temperature simulta- Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM Ostwald-de-Waele 5.7 Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM 12.1 15.8 Herschel-Bulkley 5.7 12.1 15.8 Casson 5.7 12.1 15.8 Model parameters T (°C) K ðPa sn Þ n 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 4.168 3.951 2.166 2.113 28.516 23.166 16.483 15.675 100.200 80.727 84.830 50.971             0.301 0. 144 0.054 0.071 1.809 0.664 0.486 0.482 2.228 0.762 1.578 1.375 0.406 0.349 0.399 0.384 0.291 0.274 0.314 0.305 0.223 0.228 0.229 0.262             0.014 0.007 0.005 0.006 0.012 0.006 0.006 0.006 0.004 0.002 0.004 0.005 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 3.777 4.028 2.085 1.311 24.042 77.259 29.947 24.636 22.179 82.528 57.757 251.600             2.620 1.744 0.590 0.442 25.136 40.669 13.407 11.207 3.788 17.542 21.404 122.700 0.419 0.346 0.404 0.450 0.312 0.150 0.243 0.251 0.410 0.226 0.272 0.110             0.096 0.056 0.038 0.047 0.129 0.046 0.050 0.052 0.023 0.023 0.044 0.035 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 10.0 30.0 50.0 70.0 Kc ðPa s0:5 Þ τ0 ðPaÞ 0.944 −0.153 0.193 1.964 7.750 −71.785 −21.723 −14.362 131.700 −2.538 40.310 −245.900             6.444 3.418 1.406 1.210 44.813 48.342 19.804 16.757 9.036 24.629 33.851 135.500 10.483 9.035 5.505 5.169 58.761 45.920 35.636 32.799 175.400 143.400 150.600 97.646             0.668 0.396 0.213 0.190 2.780 1.834 1.415 1.379 2.270 3.519 3.588 4.008 0.191 0.139 0.131 0.122 0.269 0.221 0.232 0.218 0.336 0.310 0.320 0.305             0.007 0.005 0.003 0.003 0.013 0.010 0.008 0.009 0.006 0.011 0.011 0.015 Adequacy indicators 2 2 RQMR AMPE GS 0.9993 0.9998 0.9999 0.9998 0.9994 0.9999 0.9999 0.9998 0.9999 0.9999 0.9999 0.9999 0.8554 0.1161 0.0246 0.0391 10.7068 1.2672 0.9309 0.9021 9.5306 1.1505 4.9933 5.0356 0.8651 0.3187 0.1467 0.1849 3.0608 1.0530 0.9025 0.8885 2.8878 1.0034 2.0902 2.0991 1.8667 1.0069 0.7683 1.1770 1.7927 0.9484 0.9815 0.8910 0.7872 0.2447 0.6200 0.9078 0.20 7.44 100.00 32.58 0.00 0.22 0.34 0.39 0.01 0.98 0.04 0.03 0.9880 0.9958 0.9986 0.9972 0.9800 0.9970 0.9968 0.9961 0.9993 0.9992 0.9973 0.9981 0.9198 0.1250 0.0264 0.0365 11.5057 0.8838 0.8761 0.8963 1.6801 1.2380 4.9845 2.2458 0.8645 0.3187 0.1466 0.1722 3.0575 0.8474 0.8437 0.8534 1.1684 1.0029 2.0124 1.3508 1.8831 1.0154 0.7655 0.9782 1.7412 0.7857 0.8820 0.8825 0.2816 0.2430 0.5719 0.5550 0.18 6.83 93.46 44.97 0.00 0.47 0.42 0.41 0.50 0.92 0.05 0.16 0.9990 0.9994 0.9996 0.9996 0.9991 0.9993 0.9994 0.9993 0.9999 0.9997 0.9997 0.9992 1.3249 0.3921 0.1245 0.0997 16.1795 6.8870 4.3758 4.3349 9.8317 23.5922 24.7343 33.0686 1.0767 0.5857 0.3300 0.2953 3.7626 2.4548 1.9567 1.9476 2.9330 4.5435 4.6522 5.3791 2.9228 2.0622 1.8283 1.8255 2.2236 2.1728 2.1690 2.3324 0.8021 1.5887 1.4561 2.4963 0.07 0.58 3.69 5.16 0.00 0.01 0.01 0.01 0.01 0.00 0.00 0.00 R χ R. S. Diniz et al.: Physical Properties of Guava Pulp C (°Brix) 442 Table 4 Average values and standard deviations of estimates of regressive model parameters by Ostwald-de-Waele, Herschel-Bulkley, and Casson, used for the rheological characterization of red guava pulp, Paluma variety, in maturation stage. Adequacy indicators R2 , χ 2 , RQMR, and AMPE describe the quality of model adjustments to experimental data. GS is a general score, obtained from adequacy indicators 443 R. S. Diniz et al.: Physical Properties of Guava Pulp 200 50 40 Shear stress (Pa) Shear stress (Pa) 150 30 20 100 50 10 0 0 0 50 100 150 200 250 300 350 0 50 100 Shear rate (s–1) 150 200 250 300 350 Shear rate (s–1) (b) (a) 400 Shear stress (Pa) 300 200 100 0 0 50 100 150 200 250 300 350 Shear rate (s–1) (c) Figure 1 Rheograms with average values and standard deviations of shear stress (τ, Pa) and shear rate (_γ, s 1 ) of red guava pulp, Paluma variety, in maturation stage, for different concentrations of soluble solids and temperature values: (a) 5.7°Brix, (b) 12.1°Brix, and (c) 15.8° Brix. Temperatures: ●, 10.0°C; H , 30.0°C; and ■, 50.0°C. Lines: Ostwald-de-Waele model Table 5 Averages and standard deviations of estimates of Arrhenius-like model parameters used to assess the effect of temperature (T; K) on the apparent viscosity (η) of red guava pulp, Paluma variety, in maturation stage, for the different concentrations of soluble solids C (°Brix) 5.7  0.1 12.1  0.1 15.8  0.2 η0 (Pa s) E a (kJ/mol) R2 2.08  0.01 104.87  0.05 150.00  0.01 11.44 5.31 6.89 0.980 0.910 0.990 Table 6 Averages and standard deviations of estimates of exponential model parameters used to assess the effect of concentration (°Brix) on the apparent viscosity (η) of red guava pulp, Paluma variety, in maturation stage, for the different temperatures T (°C) 10.0 30.0 50.0 70.0 K1 (Pa sA1 ) 3.16 5.04 3.85 2.49     0.00 0.00 0.00 0.00 Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM 2.51 2.26 2.30 2.41     A1 R2 0.24 0.01 0.07 0.02 0.994 0.996 0.999 0.996 444 R. S. Diniz et al.: Physical Properties of Guava Pulp Table 7 Confidence limits, probability values of t-test, and estimates of Arrhenius-like model parameters adjusted to the data of concentration (°Brix), temperature (°C), and apparent viscosity (η) of red guava pulp, Paluma variety, in maturation stage Equation (R2 ) Parameter Estimated value Confidence limits, 95% Lower limit Upper limit t-value Pr > |t| 4 (0.998) a1 b1 Ea 2:56  10 4 2.379537 807.1639 2:02  10 4 2.318737 766.0768 3:10  10 4 2.440337 848.2510 4.75 39.16 19.65 0.0010 <0.0001 <0.0001 5 (0.993) a2 b2 Ea 6:710  10 3 0.211385 811.0146 4:916  10 3 0.202775 739.4470 8:496  10 3 0.219995 882.5822 3.75 24.56 11.33 0.0046 <0.0001 <0.0001 neously and thus can be very useful in engineering calculations. Acknowledgments: The authors wish to acknowledge the CNPq, FAPEMIG, and FINEP for their financial support. 4 Conclusions Nomenclature The red guava pulp behaved as a non-Newtonian pseudoplastic fluid. The model of Ostwald-de-Waele can be used to describe the rheological behavior of the pulp. The Arrhenius-like equation described the effect of temperature for red guava pulp, indicating the decrease trend of apparent viscosity with temperature increasing. Exponential model can be used to evaluate the effect of concentration on apparent viscosity of the pulp. In addition, models that describe the variation of density and viscosity as a function of temperature and concentration found in this study are of importance for process optimization in the food industry. A1 C Ea K K1 Kc N R T Η ηa γ_ Ρ Τ τ0 Constant (eq. 5) Concentration of soluble solids (°Brix; eq. 5) Activation energy of flow (J/mol; eq. 4) Consistency index (Pa sn; n: flow behavior index; eqs 1–3) Constant (eq. 5) Plastic viscosity of Casson (Pa s; eq. 3) Flow behavior index (eqs 1 and 2) Universal gas constant (8.314 J/mol K; eq. 4) Absolute temperature (K; eq. 4) Constant (eq. 4) Apparent viscosity (Pa s; eqs 4 and 5) Shear rate (s−1; eqs 1–3) Density (kg/m3; eq. 9) Shear stress (Pa; eqs 1–3) Threshold stress (Pa; eqs 2 and 3) References 1. Osorio C, Forero DP, Carriazo JG. Characterization and performance assessment of guava (Psidium guajava L.) Microencapsulates obtained by spray drying. Food Res Int 2011;44:1174–81. 2. Restrepo-Sanchez DC, Narvaez-Cuenca CE, Restrepo-Sanchez LP. Extraction of compounds with antioxidant activity in guava (Psidium guajava L.) fruit produced in Velez-Santander, Colombia. Química Nova 2009;32:1517–22. 3. Steinhaus M, Sinuco D, Polster C, Osorio C, Schieberle P. Characterization of the key aroma compounds in pink guava (Psidium guajava L.) by means of aroma re-engineering experiments and omission tests. J Agric Food Chem 2009;57:2882–8. 4. Tangirala S, Sarkar BC, Sharma HK, Kumar N. Modeling and characterization of blended guava pomace and pulse powder based rice extrudates. Int J Food Eng 2012;8:Article 1. DOI:10.1515/1556-3758.2366. 5. Alstolfi-Filho Z, Telis VR, Oliveira EB, Coimbra JS, Telis-Romero J. Rheology and fluid dynamics properties of sugarcane juices. Biochem Eng J 2011;53:260–5. 6. Cabral RA, Orrego-Alzate CE, Gabas AL, Telis-Romero J. Rheological and thermophysical properties of blackberry juice. Ciên Tecnologia Alimentos 2007;27:589–95. DOI:10.1590/S0101-20612007000300025. 7. Chen J. Food oral processing – a review. Food Hydrocolloids 2009;23:1–25. 8. Tabilo-Munizaga G, Barbosa-Canovas GV. Rheology for the food industry. J Food Eng 2005;67:147–56. 9. Ah-Hen KS, Vega-Galvez A, Moraga NO, Lemus-Mondaca R. Modelling of rheological behaviour of pulps and purees from fresh and frozen-thawed murta(UGNIMOLINaeTURCZ) berries. Int J Food Eng 2012;8:Article 6. DOI:10.1515/1556-3758.2738. 10. Augusto PE, Cristianini M, Ibarz A. Effect of temperature on dynamic and steady-state shear rheological properties of Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM R. S. Diniz et al.: Physical Properties of Guava Pulp 11. 12. 13. 14. 15. 16. 17. 18. 19. siriguela (Spondias purpurea L.) pulp. J Food Eng 2012;108:283–9. Moraes IC, Fasolin L, Cunha RL, Menegalli FC. Dynamic and steady-shear rheological properties of xanthan and guar gums dispersed in yellow passion fruit pulp (Passifloraedulis f. flavicarpa). Braz J Chem Eng 2011;28:483–94. Anuradha G, Ramaswamy HS, Ahmed J. Effect of soluble solids concentration and temperature on thermo-physical and rheological properties of mango puree. Int J Food Properties 2011;14:1018–36. Cabral RA, Gut JA, Telis VR, Telis-Romero J. Non-Newtonian flow and pressure drop of pineapple juice in a plate heat exchanger. Braz J Chem Eng 2010;27:563–71. Bon J, Vaquiro H, Benedito J, Telis-Romero J. Thermophysical properties of mango pulp (Mangifera indica L. cv. Tommy Atkins). J Food Eng 2010;97:563–8. Sato AC, Cunha RL. Effect of particle size on rheological properties of jaboticaba pulp. J Food Eng 2009;91:566–70. Chuah TG, Ling HL, Chin NL, Choong TS, Fakhru’l-Razi A. Effects of temperatures on rheological behavior of dragon fruit (Hylocereus sp.) juice. Int J Food Eng 2008;4:Article 4. DOI:10.2202/1556-3758.1519. Chuah TG, Keshani S, Chin NL, Lau MC, Chin DS. Rheological properties of diluted pummelo juice as affected by three different concentrations. Int J Food Eng 2008;4:Article 1. DOI:10.2202/1556-3758.1299. Haminiuk CW, Sierakowski MR, Maciel GM, Vidal JR, Branco IG, Masson ML. Rheological properties of butia pulp. Int J Food Eng 2006;2:Article 4. DOI:10.2202/1556-3758.1039. Zainal BS, Abdulrahman R, Ariff AB, Saari BN. Thermophysical properties of pink guava juice at 9 and 11°brix. J Food Process Eng 2001;24:87–100. 445 20. Oliveira RC, Rossi RM, Barros ST. Estudo do efeito da temperatura sobre o comportamento reologico das polpas de gabiroba e goiaba. Acta Sci Technol 2011;33:31–7. 21. Williams S. Official methods of analysis of the association of official analytical chemists, 14th ed. Washington, USA: AOAC Inc., 1990. 22. Steffe JF. Rheological methods in food process engineering, 2nd ed. East Lansing, MI: Freeman Press, 1996. 23. Rao MA. Rheology of fluid and semisolid foods, 2nd ed. Geneva: Springer, 2010. 24. Smith JM, Van Ness HC, Abbott MM. Introduction to chemical engineering thermodynamics, 7th ed. Boston, USA: McGraw Hill Higher Education, 2005. 25. Ferreira LF, Pirozi MR, Ramos AM, Pereira JA. Modelagem matemática da secagem em camada delgada de bagaço de uva fermentado. Pesq. Agropec. Bras. Brasília 2012;47:855–62. 26. Kvalseth TO. Cautionary note about R2. Am Stat 1985;39:279–85. 27. Searle SR. Linear models. New York: John Wiley & Sons, 1971:532p. 28. Ramos AM, Ibarz A. Density of juice and fruit puree as a function of soluble solids content and temperature. J Food Eng 1998;35:57–63. 29. Guedes DB, Ramos AM, Diniz MD. Effect of temperature and concentration on the physical properties of watermelon pulp. Braz J Food Technol 2010;13:279–85. 30. Saravacos GD. Effect of temperature on viscosity of fruit juices and purees. J Food Sci 1970;5:12–125. 31. Lane DM, Scott D, Hebl M, Guerra R, Osherson D, Zimmer H. Online statistics education: an interactive multimedia course of study. Houston, TX; http://onlinestatbook.com/ Online_Statistics_Education.pdf. Accessed: 25 Oct 2013. 32. Ratkowsky DA. Handbook of nonlinear regression models. New York and Basel: Marcel Dekker, 1990:241p. Brought to you by | Universidade Federal de Viçosa UFV Authenticated | 10.248.254.158 Download Date | 9/12/14 4:04 PM