Density, viscosity and coefficient of thermal expansion

Journal of Food Engineering 71 (2005) 143–149 www.elsevier.com/locate/jfoodeng

Density, viscosity and coefficient of thermal expansion of clear grape juice at different soluble solid concentrations and temperatures C.A. Zuritz a,*, E. Munõz Puntes b, H.H. Mathey a,z, E.H. Pe´rez a, A. Gascoń a, L.A. Rubio b, C.A. Carullo b, R.E. Chernikoff b, M.S. Cabeza b b

a Facultad de Ciencias Agrarias, UNCuyo, Alte. Brown 500, (5505) Chacras de Coria, Mendoza, Argentina Facultad de Ciencias Aplicadas a la Industria, UNCuyo, Av. San Martıń 358, San Rafael, Mendoza 5600, Argentina

Received 12 July 2004; accepted 24 October 2004 Available online 10 December 2004

Abstract The effect of temperature and soluble solids concentration on density, coefficient of thermal expansion and viscosity of clear grape juices from Mendoza, Argentina, collected during 1999 and 2001, was studied. The juice was obtained from different sections of a commercial evaporator at concentrations ranging from 22.9–70.6 Brix. The properties were measured between 20 C and 80 C, in 10 C increments. It was also characterized in terms of extract, reducing sugars and refractive index at 20 C. The density was correlated as a function of absolute temperature and degrees Brix. The coefficient of thermal expansion was computed from its thermodynamic definition at constant pressure. The juices showed a Newtonian flow behavior within the range of variables studied. The effect of temperature was very well correlated with the Arrhenius equation (r2 > 0.992). The values of activation energy (Ea) increased with solid concentration from 16.3 to 52.0 kJ/mol. An equation to predict the viscosity in terms of temperature and soluble solids concentration was derived. Published predictive equations are statistically different from the equations derived here. 2004 Elsevier Ltd. All rights reserved. Keywords: Density; Coefficient of thermal expansion; Viscosity; Rheology; Grape juice

1. Introduction Concentrated clear grape juices are extensively used in the enological industry. Their use as constituents of juices, jellies, marmalades, jams, colas, beverages, etc., generates a consumer market with an increasing demand because they are natural products with an industrial versatility that allows them to compete with other fruit juices. Argentina is one of the principal producers and exporters of concentrated clear grape juices in the world. * Corresponding author. Tel.: +54 2627 430673; fax: +54 2627 421947. E-mail address: [email protected] (E.M. Puntes). z Deceased.

0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.10.026

They are produced mainly in the provinces of Mendoza and San Juan (Argentine Republic) from the virgin grape juice and in the most part from sulfited grape juices. The province of MendozaÕs legislation establishes that a portion of the grapes must be used for making concentrated clear grape juices. This product has reached a high level of penetration in the export market and constitutes an important and growing productive alternative. An adequate manufacturing process, a correct design of the concentrate plants and an appropriate evaluation of their performance will facilitate optimization of the concentrated juices quality parameters. The plant efficiency is obtained from knowledge of the physics properties of the raw material and products. These

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C.A. Zuritz et al. / Journal of Food Engineering 71 (2005) 143–149

properties are fundamental parameters that are used in the designing and calculations on all the equipment used and also in the control process. The rheological behavior influences directly the heat transfer coefficient (Pilati et al., 1998; Rubio et al., 1998) and therefore its knowledge is essential together with the influence of temperature on its value. The juices (concentrate and intermediate products) physical properties, such as density, viscosity, boiling point elevation, specific heat and coefficient of thermal expansion, are affected by their solid content and their temperature. For this reason, it is necessary to know the physical properties values, as a function of the temperature and the solids content, during the manufacture process, not just to obtain an excellent quality, but also to develop a data base, that is essential for optimizing the installation design and the transformation process itself. The principal solids constituents of clear grape juices are sugars (mostly glucose and fructose) and its concentration affects directly the density, viscosity and refraction index. Tables were developed to related reducing sugar contents, refractometric values and density of pure solutions, at 20 C, for concentrate ranges from 0% to 85% w/w and sucrose solutions for concentrations form 0% to 70% and a temperature range from 0 to 100 C (AOAC, 1995). Barbieri and Rossi (1980) worked with white concentrated clear grape juice in a falling film multiple effect evaporator. They obtained 18.2, 27.3, 38.6, 48.6 and 64.6 Brix samples. They measured density, viscosity and boiling point elevation as a function of soluble solids concentration and temperature. They presented the results in plots with predictive equations for the properties studied. Di Leo (1988) published density, refraction index and viscosity data for a rectified concentrated grape juice and an aqueous solution of a 1:1 glucose/levulose mixture, for a soluble solids concentrate range from 60 to 71% (in increments of 0.1%) and 20 C. The author determinated the density in undiluted and 2.5-fold diluted samples (100 g of clear grape juice in 250 ml of solution at 20 C), finding different results between both determinations. He recommended measuring density without dilution. Pandolfi, Romano, and Cerdań (1991) studied physical and chemical characteristics of grape juices produced in Mendoza and San Juan provinces, Argentina. They determined density at 20 C in sulfited grape juices of 20–22 Bx and concentrated grape juices of 68–72 Bx. They obtained no information on intermediate concentrations or other temperatures. In general, the clarified juice concentrates have a Newtonian behavior (Ibarz & Ortiz, 1993; Rao, Cooley, & Vitali, 1984; Saénz & Costell, 1986; Saravacos, 1970),

although some authors have found a small pseudoplasticity in the flow of grape concentrates, from the variety Concord (Vitis labrusca) for concentrations above 55 Bx. This has been attributed to the presence of some soluble solids, mostly pectins and tartrates (Moressi & Spinosi, 1984; Saravacos, 1970). However, other authors consider the juice concentrates as Newtonian, even at high soluble solids concentrations of 60–70 Bx (Barbieri & Rossi, 1980; Di Leo, 1988; Rao et al., 1984; Schwartz & Costell, 1986). If we analyze the temperature influence on this productÕs viscosity, it seems that it is directly related with soluble solids concentration; the higher the concentration, the higher is the variation of the viscosity with temperature (Rao et al., 1984; Saravacos, 1970). Schwartz and Costell (1986) determined clear grape juice viscosity at 20, 30, 40 and 50 C, for 30, 40, 50, 60 and 66% soluble solids concentration, but did not published the experimental data. These authors presented the correlation constants values of the Arrhenius equation for temperature, a potential and an exponential model between viscosity and solids concentration for each temperature studied. The physical property that represents density change in a material, due to an increase in its temperature at constant pressure, is called the coefficient of thermal expansion. The importance of this parameter can be seen in the effect that density change in the product can have over heat transfer during the process. There is no published data on the coefficient of the thermal expansion for grape juices and their concentrates. Although many studies have been done to characterize fruit juices properties and their concentrates, to date there have been no studies related physical properties of fruit juices from the region of Mendoza with local varieties like Cereza, Criolla and Moscatel Rosada (Vitis vinifera cv. Cereza, cv. Criolla and cv. Moscatel Rosada). In many cases, the existing information did not cover all the temperature and concentration ranges that are used in the evaporation process, or else cover to pure sugar solutions, or grape juices of other varieties and/ or originating in other geographical zones. For that reason, the objectives of the present work were: (1) Determine density, viscosity and coefficient of thermal expansion of clear grape juices of Mendoza, over the soluble solids concentration and temperature ranges used in their processing and conservation. (2) Determine the flow Activation Energy (apparent) values for each studied concentration. (3) Derive predictive equations for the studied properties of clear grape juices, as functions of soluble solids concentration and temperature.


2. Materials and methods 2.1. Samples obtained and characterization The study was done with white clarified and clear grape juices, obtained by mixing local varieties like Cereza (Vitis vinifera cv.Cereza), Criolla (Vitis vinifera cv. Criolla) and Moscatel Rosada (Vitis vinifera cv. Moscatel Rosada), grown in Mendoza (75% of the total; distributed as 50% of Criolla and 50% of Cereza), San Juan (18%; distributed as 70% of Cereza and 30% of Moscatel Rosada) and La Rioja (7%; all Moscatel Rosada). This grape mixture is sulfited (1600 ppm) before concentration, and is representative of grape juice concentrates manufactured in Mendoza, Argentina. Samples are obtained from two different crops corresponding to 1999 and 2001. Before concentration, the grape juices are decolored with activate carbon, clarified with bentonite and filtered (without enzymatic treatment). Later, they are disulfited, pre-concentrated at 40 Bx, cool treated (to extract the tartrate), filtrated and finally concentrated. Samples were taken from the treated sulfited grape juices before concentration and also form different sections from an industrial falling film evaporator, triple effect and one step, with parallel flow circulation (INTECNO D.E.T.E.T–3000), with an evaporative capacity of 3000 kg/h. The extractions were done in triplicate over three consecutive days of manufacture in each season. They were collected in 1-liter bottles, hermetically sealed and thermally treated to prevent fermentation. The bottles were maintained at ambient temperature until the study. The triplicates obtained for each soluble solids concentration (concentrator section) were mixed, to obtain the following final samples for this study: 22.9, 25.5, 31.0, 34.0, 41.0, 45.0, 51.0, 53.4, 60.7, 67.0 and 70.6 Bx. They were characterized for dry matter, reducing sugars and refraction index at 20 C. Reducing sugars and dry matter were determined by Argentinean Official Methods (Viticulture National Institute). Reducing sugars were determined by chemical methods based in the glucose and levulose reaction with alkaline copper sulfate. The reagent used was Fehling-Causse-Bonnans solution. The method used for determine the dry matter involves water evaporation of a 10 ml sample at 100 C in two steps; first in a boiling water bath for 30 min after followed by 60 min evaporation in an oven at atmospheric pressure. Soluble solids and refraction index were measured at 20 C with a Karl Seiz sucrosemeter and a Hilger & Watts Ltd. Refractometer, respectively. Each instrument had a water flow system to achieve precise temperature control.

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Grape juice density and viscosity were measured between 20 and 80 C, in 10 C increments. Density was determined with 100 ml picnometers. To verify possible changes in their volume due to thermal expansion, each picnometer was calibrated with distillate water at 20, 50 and 80 C. Temperature was maintained constant at the different studied values using a Colora Ultra thermostatized bath, supplied with resistors for heating and centrifugal circulation. The samples and heating water temperatures were controlled using previously calibrated mercurial and digital thermometers. Picnometers were filled with the grape juice samples and placed in a bath without their tops until they reached the specified temperature. At that moment the tops were replaced carefully avoiding air occlusion. Picnometers were then quickly weighted in a Sartorius AG balance with 0.0001 g sensitivity. Viscosity measurements were done with a Brookfield rotational viscometer with concentric cylinders, Model LVDV-III + a Digital Rheometer, with a torque of 673.7 dynes/cm and speed of 0.01–250 rpm in varying increment of 0.1 rpm. The instrument control and the data collection were carried out using a PC using RHEOCALC Application Software. Grape juicesÕ viscosities of with 22.9, 25.5, 31.0, 34.0, 41.0, 45.0, 51.0, 53.4, 60.7 Bx were determined with an Ultra Low Adapter, while grape juice samples of 67.0 and 70.6 Bx used a Small Sample Adapter, SC4-18/ 13RT. The sample chambers fit into a flow jacket so that precise temperature control can be achieved when a circulating water bath is used. In this study, a Mgw LAUDA thermostat, Type K2-D, was used with a circulation pump, electrical heating with resistors of 800 W capacity, supplied with a temperature control system (Messgeate-Werk Laudal Tauber, Bestell-Nr. 1,02). The heating fluid was distilled water. Before beginning each measurement (for each combination of temperature–concentration), and once the study temperature was reached, a sample was sheared at maximum speed (250 rpm), for 1 min, to eliminate possible effects of stratification in the chamber. Then, six increasing deformation rates were evaluated. Preliminary studies showed inconsistent results for higher values of rotational speed, depending on the sample and temperature studied. Variations were observed at NRe P 1300. Taking this into account, all measurements were made at NRe < 1300. Reynolds number over the spindle area was calculated using the following equation: N Re ¼

q X R2s l

ð1Þ

where: RS = radius of container (m); q = density (kg/ m3); X = 2px/60 (1/s); x = angular velocity of spindle (rpm); l = viscosity (Pa s).

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2.2. Data analyze Measured density values were correlated with absolute temperature (T) and degrees Brix (Bx), using multiple lineal regression with first, second and third degrees polynomials, using the Marquardt–Levenburg method, supplied in the PSI-Plot software of Poly Software International, Ltd. Eq. (2) shows a third degree polynomial: 2

q ¼ a0 þ a1 T þ a2 Bx þ a3 ðT Þ þ a4 ðBxÞ 3

þ a5 ðT Þ þ a6 ðBxÞ

3

2

ð2Þ

The best fit equation was selected based on the results of a Variance Analysis between measured and calculated values, and on their Root Mean Square Error (RMSE), using the criterion that the equation with the least RMSE gives the best correlation. Equations were also compared to the ones published by Barbieri and Rossi (1980). The coefficient of thermal expansion (b) was calculated from the thermodynamic expression, at constant pressure, using the best fitting polynomial to represent density (q). oð1=qÞ 1 oq b¼q ¼ ð3Þ oT q oT P P The rheological behavior of the studied grape juices was described using NewtonÕs equation of constant viscosity: s ¼ l_c

ð4Þ

in which s is the shear stress; l is the Newtonian viscosity and c_ is the shear rate. Choosing the rheological model (in this work, the Newtonian one) and the accessory, RHEOCALC software captured the angular velocity of the spindle (rpm) and torque (% of the scale from 0 to 100) values, and used them to calculate viscosity (mPa s), shear stress (N/m2) and shear rate (s1). Viscosity values (l), for different samples and assayed temperatures, were calculated from shear stress (s) and shear rate (_c) using linear regression, with y-intercept = 0, using the minimal square method incorporated in Microsoft Excel software. Once viscosity values (l) were established at different temperatures, (apparent) flow Activation Energy values for each studied concentration were calculated using the Arrhenius equation: l ¼ l1 expðEa =RT Þ

ð5Þ

where: l = viscosity (mPa s); l1 = constant (mPa s); Ea = activation energy (kcal/mol); R = universal gas constant (1.987 · 103 kcal/mol-K); T = absolute temperature (K). l1 and Ea from Eq. (5) were determined by correlating exponentially viscosity values (l) with the inverse of

absolute temperature (1/T) using the Marquard–Levenburg method, supplied by PSI-Plot of Poly Software International, Ltd. Finally, to derive a predictive equation for clear grape juice viscosity as functions of soluble solids concentration and temperature, l1 and Ea were correlated with soluble solids concentration (Bx) by multiple linear regression, using the same method indicated before for density. The obtained equation was compared to the ones published by Barbieri and Rossi (1980), and by Schwartz and Costell (1986), using a variance analyze between absolutes differences of the measured and calculated values, and of their root mean square error (RMSE). All correlations and statistic analyzes were done for a 95% confidence interval.

3. Results and discussion In Table 1, are presented the refraction index, dry matter and reducing sugars values determined for the initial juice (22.9 Bx). In Table 2, values of density of clear grape juices are shown with different soluble solids concentrations measured at different temperatures. In Table 1 it could be observed that density is strongly affected by soluble solids concentration (the same effect for all the temperature range), while it is very slightly affected by temperature (the same effect for all the concentrations). For example, for concentrations of 22.9 and 70.6 Bx, density decreases respectively 2.94% and 2.69% for a temperature increase from 20 to 80 C; for temperatures of 20 and 80 C, density increases by respectively, 23.79% and 24.11% for a concentration increase from 22.9 a 70.6 Bx. As indicated before, density values shown in Table 2 were correlated with absolute temperature (T) and degrees Brix by multiple linear regression. The regression parameters obtained with 1, 2 and 3 degrees polynomiTable 1 Values of soluble solids, refraction index, extract and reducing sugars of clear grape juice studied Soluble solids (% w/w)

Refractive index at 20 C

Dry matter (% w/w)

Reducing sugars (% w/w)

22.9 25.5 31.0 34.0 41.0 45.0 51.0 53.4 60.7 67.0 70.6

1.3691 1.3732 1.3830 1.3887 1.4017 1.4106 1.4223 1.4278 1.4441 1.4579 1.4671

24.77 26.94 31.19 36.05 44.06 47.84 53.98 58.14 64.72 68.49 76.57

21.60 23.21 27.51 32.86 38.18 41.71 46.77 48.49 57.14 60.62 66.25


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Table 2 Values of density of clear grape juice in (kg/m3) Soluble solids (% w/w)

Temperature (C) 20

30

40

50

60

70

80

22.9 25.5 31.0 34.0 41.0 45.0 51.0 53.4 60.7 67.0 70.6

1097.3 1108.3 1130.0 1150.3 1190.6 1208.4 1240.0 1253.8 1297.2 1337.3 1358.4

1093.2 1102.9 1126.2 1144.4 1185.4 1203.4 1234.5 1248.1 1290.9 1328.8 1351.8

1089.2 1098.9 1121.8 1140.6 1180.5 1197.6 1228.3 1242.2 1284.7 1322.6 1346.3

1084.5 1094.0 1116.6 1135.5 1174.9 1192.5 1222.8 1236.6 1278.8 1315.7 1339.2

1078.5 1088.0 1111.2 1130.3 1169.8 1185.9 1216.8 1230.1 1271.8 1309.0 1332.5

1071.4 1082.7 1105.7 1123.9 1163.3 1180.2 1211.7 1226.2 1268.2 1302.7 1328.3

1065.0 1076.0 1095.7 1117.5 1155.8 1173.8 1203.7 1218.7 1261.8 1295.4 1321.8

Coefficients

First degree polynomial

Second degree polynomial

Third degree polynomial

a0 a1 a2 a3 a4 a5 a6 r2

1.1391 · 10+03 5.7760 · 1001 5.3941 · 10+03 – – – – 0.9976

1.0462 · 10+03 1.9630 · 1001 3.8568 · 10+00 1.1973 · 1003 1.6533 · 1002 – – 0.9993

2.0816 · 10+03 9.4737 · 10+00 3.9796 · 10+00 2.8793 · 1002 1.3724 · 1002 3.0934 · 1005 2.0035 · 1005 0.9993

als were shown in Table 3, with the correspondent determination coefficient (r2). Though r2 are high and close for all the polynomials, ANOVA (analysis of variance) between means of the absolute values of the differences between measured and calculated values for each polynomial (F-critical = 3.90), showed significant differences between the first and second degrees polynomial (F = 32.60) and for first and third degree (F = 32.86) and no significant difference for second and third degrees polynomials (F = 4.7 · 104). RMSE obtained values were 4.17, 2.28 and 2.27 for the 1, 2 and 3 degrees polynomials, respectively. Calculated densities using the Barbieri and Rossi (1980) equation showed a RMSE value = 7.92, and ANOVA between the 2 degree polynomial and this equation had an F = 34.82. These results indicate that the Barbieri and Rossi (1980) equation is not appropriate for predicting Mendoza grape juice densities, measured in this study. The results from ANOVA and RMSE showed that the 2 polynomial is the best to express density as a function of the absolute temperature (T) and soluble solids concentration (Bx), because it has three fewer fitting coefficients than the 3 polynomial. This polynomial was used in Eq. (3) to obtain the coefficient of thermal expansion (b), derived from Eq. (6):

a1 þ 2 a3 T b¼ a0 þ a1 T þ a2 Bx þ a3 T 2 þ a4 Bx2

ð6Þ

where: T = absolute temperature (K); Bx = soluble solids (%w/w); a0, a1, a2, a3 and a4 = Table 3 parameters, for the second degree polynomial. In Fig. 1 is shown the viscosity variance with the soluble solids concentration (Bx) for each studied temperature. In Fig. 1, it can be seen that viscosity rises in an exponential manner with increasing concentration, being less pronounced with temperature increasing. Also, the observed values agree with data of Saravacos (1970) and Rao et al. (1984) being related with soluble solids concentration; the higher this is, the higher is the variation of viscosity with temperature. Comparing viscosity data from MCR and SGL, reported by Di Leo (1988) for 60.7, 67.0 and 70.6% solids concentrations, for MCR it was 45.05, 136.00 and 271.13 mPa s, respectively, and for SGL was 45.78, 140.23 and 299.01 mPa s, respectively. It can be seen that they were very similar to the values shown in Table 2: 45.73, 140.68 and 310.61 mPa s.

20 18 16 Viscosity (Pa.s)

Table 3 Fitting parameters for the first, second and third degree polynomials, to predict the variation of density of clear grape juice with absolute temperature and soluble solids concentration

20ºC

14

30ºC

12

40ºC

10

50ºC

8

60ºC 70ºC

6

80ºC

4 2 0

20

30

40

50

60

Concentration (ºBx)

Fig. 1. Variation of viscosity with soluble solids concentration at each temperature.

148


Table 4 Fitting parameters for the Arrhenius equation, l = l1*exp(Ea/RT), to predict the variation of viscosity of clear grape juice with absolute temperature Brix

l1 (mPa s)

Ea/R (K)

Ea (kcal/mol)

Ea (kJ/mol)

Correlation (r2)

22.9 25.5 31.0 34.0 41.0 45.0 51.0 53.4 60.7 67.0 70.6

2.779 · 1003 2.484 · 1003 1.785 · 1003 1.630 · 1003 1.189 · 1003 8.255 · 1004 3.588 · 1004 1.554 · 1004 2.681 · 1005 2.125 · 1006 1.785 · 1007

1964.36 2021.62 2182.07 2250.55 2503.32 2698.74 3097.48 3425.09 4214.79 5295.72 6256.43

3.903 4.017 4.336 4.472 4.974 5.363 6.155 6.806 8.375 10.523 12.432

16.330 16.807 18.142 18.711 20.811 22.439 25.753 28.476 35.041 44.028 52.015

0.9975 0.9953 0.9969 0.9941 0.9957 0.9926 0.9947 0.9918 0.9953 0.9982 0.9987

In Table 4, flow Activation Energy (Ea) values were shown for each studied concentration calculated using the Arrhenius equation, together with the respective fitting parameters and determination coefficients (r2). Activation Energy (Ea) data obtained in this work were very similar to that reported by Schwartz and Costell (1986), for clear grape and apple juices, and to the one presented by Ibarz and Ortiz (1993), for clear peach juices, in the considered ranges of soluble solids concentration and temperatures. To derive a predictive equation for clear grape juice viscosity, as a function of soluble solids concentration and temperature, l1 and (Ea/R) parameters were correlated with soluble solids concentration (Bx). First, data from Table 4 (l1 and Ea/R vs. Bx) was plotted using logarithmic scales on the y-axis, and it was observed that a correlation of the parameters with equations like the ones presented below could be obtained: l1 ¼ expða0 þ a1 Brix þ a2 Brix2 Þ

ð7Þ

Ea =R ¼ expða0 þ a1 Brix þ a2 Brix2 Þ

ð8Þ

Fitting parameters of the two equations, with respective determination coefficients (r2), are presented in Table 5. In Table 5, it could be observed that both equations show an excellent fit, represented by r2 values. Eqs. (7)

Table 5 Fitting coefficients for Eqs. (7) and (8), for the parameters l1 and (Ea/ R), as a function of soluble solids concentration of clear grape juice Coefficients a0 a1 a2 r2

l1 (mPa s)

Ea/R (K) +00

2.0365 · 10 2.0933 · 1002 4.3614 · 1004 0.9976

7.6346 · 10+00 1.0455 · 1002 3.6897 · 1004 0.9993

and (8) incorporated into Eq. (5) predict clear grape juice values, in the studied range of Bx and temperature. Viscosity values from Table 2 and calculated values were compared using Eq. (5) and the ones calculated with the equations presented by Barbieri and Rossi (1980), and by Schwartz and Costell (1986). Viscosity values were calculated for all the studied variable range with the equation presented by Barbieri and Rossi (1980). Although Schwartz and Costell (1986) presented two equations: one exponential and the other potential, for 20, 30, 40 and 50 C, only the potential equation could be used to compare with Eq. (5), just because the same parameter values were assigned for 30 and 40 C for the exponential equation, so it gave the same viscosity values for both temperatures. Mean ANOVA of the absolute values of the differences between the measured viscosity and those calculated using Eq. (5) and the Barbieri and Rossi (1980) equation, for all the range of Bx and temperatures (with F-critical = 3.90), did not show significant differences between the two equations (F = 2.05). The RMSE values obtained were 4.59 and 7.85, respectively, indicating the best fit to the experimental data was found by using Eq. (5). The comparison between Eq. (5) and the potential equation presented by Schwartz and Costell (1986), in the temperature range indicated previously, showed significant differences. The ANOVA result (for F-critical = 4.02) was F = 5.03, while the RMSE values were 0.31 and 3.89, respectively. These results indicate that the potential equation presented by Schwartz and Costell (1986) is not appropriate for predicting grape juice viscosities in this work. Lastly, it can be remarked that the results presented here were determinated using grape juices samples obtained during the concentration process in a commercial evaporator, at different concentrations, with a chemical composition more representative of the process, which are different to prepared samples obtained by water dilution of concentrated grape juices.

4. Conclusions From the results obtained in the present study the following items can be summarized: 1. Clear grape juices density and viscosity from Mendoza, Argentina, in a range of soluble solids concentration between 22.9 and 70.6 Bx and temperatures between 20 and 80 C, were measured. 2. Density was correlated as a function of the absolute temperature (T) and degrees Brix (Bx) with a second degree polynomial (r2 = 0.999): q = a0 + a1 * T + a2 * Bx + a3 * (T)2 + a4 * (Bx)2.


3. The thermal expansion coefficient was calculated using a thermodynamic expression, with constant pressure, using a second degree polynomial for density (Eq. (6)). 4. Clear grape juices showed a Newtonian flow behavior. 5. Activation Energy (Ea) values increased with the soluble solids from 3.9 to 12.4 kcal/mol (16.3 to 52.0 kJ/ mol). There are very similar to the ones reported in the literature for clear grape, apple and peach juices. 6. An equation to predict clear grape juices viscosity as a function of the soluble solids concentration and temperature was obtained. It was presented as Eq. (5) together with Eqs. (7) and (8). 7. The Variance (ANOVA) and the Root Mean Square Error (RMSE) indicated that the equations published in the literature were statically different to the ones derived, so they are not appropriate for predicting grape juices density and viscosity in the present study.

Acknowledgement This study was supported by FCAI — UNCuyo (San Rafael, Mendoza, Argentina), Project: Comparative studies in tube evaporators.

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