density of grape juice

7/29/2019 Density of Grape Juice

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Density, viscosity and coefficient of thermal expansion of cleargrape juice at different soluble solid concentrations and temperatures

E. Munoz Puntes a,*, L.A. Rubio a, C.A. Carullo a, R.E. Chernikoff a,C.A. Zuritz b, M.S. Cabeza a

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

Received 12 July 2004; accepted 24 October 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 22.970.6 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 ver-satility 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.

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 Mendozas legislation establishes

that a portion of the grapes must be used for making

concentrated clear grape juices. This product hasreached 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 effi-

ciency is obtained from knowledge of the physics

properties of the raw material and products. These

0260-8774/$ - see front matter 2004 Elsevier Ltd. All rights reserved.

doi:10.1016/j.jfoodeng.2004.10.026

* Corresponding author. Tel.: +54 2627 430673; fax: +54 2627

421947.

E-mail address: [email protected] (E.M. Puntes).

www.elsevier.com/locate/jfoodeng

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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 tem-

perature 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 concen-

tration affects directly the density, viscosity and refrac-

tion index.

Tables were developed to related reducing sugar con-

tents, refractometric values and density of pure solu-

tions, 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 concen-

trated 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, viscosityand boiling point elevation as a function of soluble sol-

ids concentration and temperature. They presented the

results in plots with predictive equations for the proper-

ties 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 mix-

ture, 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 Cerdan (1991) studied physi-

cal 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

2022 Bx and concentrated grape juices of 6872 Bx.

They obtained no information on intermediate concen-

trations or other temperatures.

In general, the clarified juice concentrates have a

Newtonian behavior (Ibarz & Ortiz, 1993; Rao, Cooley,

& Vitali, 1984; Saenz & Costell, 1986; Saravacos, 1970),

although some authors have found a small pseudoplas-

ticity 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 concen-trates as Newtonian, even at high soluble solids concen-

trations of 6070 Bx (Barbieri & Rossi, 1980; Di Leo,

1988; Rao et al., 1984; Schwartz & Costell, 1986).

If we analyze the temperature influence on this prod-

ucts viscosity, it seems that it is directly related with sol-

uble solids concentration; the higher the concentration,

the higher is the variation of the viscosity with tempera-

ture (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 pre-

sented the correlation constants values of the Arrhenius

equation for temperature, a potential and an exponen-

tial 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 character-ize 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 ther-

mal expansion of clear grape juices of Mendoza,

over the soluble solids concentration and tempera-

ture 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 proper-

ties of clear grape juices, as functions of soluble sol-

ids concentration and temperature.

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2.2. Data analyze

Measured density values were correlated with abso-

lute temperature (T) and degrees Brix (Bx), using multi-

ple lineal regression with first, second and third degrees

polynomials, using the MarquardtLevenburg method,

supplied in the PSI-Plot software of Poly Software Inter-national, Ltd. Eq. (2) shows a third degree polynomial:

q a0 a1 T a2 Bx a3 T2

a4 Bx2

a5 T3 a6 Bx

3 2

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 calcu-lated from the thermodynamic expression, at constant

pressure, using the best fitting polynomial to represent

density (q).

b q o1=q

oT

P

1

q

oq

oT

P

3

The rheological behavior of the studied grape juices was

described using Newtons equation of constant viscosity:

s l_c 4

in which s is the shear stress; l is the Newtonian viscos-

ity and_

c is the shear rate.Choosing the rheological model (in this work, the

Newtonian one) and the accessory, RHEOCALC soft-

ware captured the angular velocity of the spindle

(rpm) and torque (% of the scale from 0 to 100) values,

and used them to calculate viscosity (mPas), shear stress

(N/m2) and shear rate (s1). Viscosity values (l), for dif-

ferent samples and assayed temperatures, were calcu-

lated 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 valuesfor each studied concentration were calculated using the

Arrhenius equation:

l l1 expEa=RT 5

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 tem-

perature (K).

l1

and Ea from Eq. (5) were determined by correlat-

ing exponentially viscosity values (l) with the inverse of

absolute temperature (1/T) using the MarquardLeven-

burg 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 concentra-

tion and temperature, l1

and Ea were correlated with

soluble solids concentration (Bx) by multiple linear

regression, using the same method indicated before fordensity. 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 calcu-

lated 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 mea-

sured 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 20to 80 C; for temperatures of 20 and 80 C, density in-

creases by respectively, 23.79% and 24.11% for a con-

centration increase from 22.9 a 70.6 Bx.

As indicated before, density values shown in Table 2

were correlated with absolute temperature (T) and de-

grees Brix by multiple linear regression. The regression

parameters obtained with 1, 2 and 3 degrees polynomi-

Table 1

Values of soluble solids, refraction index, extract and reducing sugars

of clear grape juice studiedSoluble solids

(% w/w)

Refractive index

at 20 C

Dry matter

(% w/w)

Reducing sugars

(% w/w)

22.9 1.3691 24.77 21.60

25.5 1.3732 26.94 23.21

31.0 1.3830 31.19 27.51

34.0 1.3887 36.05 32.86

41.0 1.4017 44.06 38.18

45.0 1.4106 47.84 41.71

51.0 1.4223 53.98 46.77

53.4 1.4278 58.14 48.49

60.7 1.4441 64.72 57.14

67.0 1.4579 68.49 60.62

70.6 1.4671 76.57 66.25


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als were shown in Table 3, with the correspondent deter-

mination 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-criti-

cal = 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 va-

lue = 7.92, and ANOVA between the 2 degree polyno-

mial 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 den-

sities, measured in this study.

The results from ANOVA and RMSE showed that

the 2 polynomial is the best to express density as a func-

tion 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):

b a1 2 a3 T

a0 a1 T a2 Bx a3 T2 a4 Bx

2

6

where: T= absolute temperature (K); Bx = soluble sol-ids (%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 sol-

uble solids concentration (Bx) for each studied

temperature.

In Fig. 1, it can be seen that viscosity rises in an expo-

nential 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 varia-

tion of viscosity with temperature.

Comparing viscosity data from MCR and SGL, re-

ported 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 mPas.

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 1097.3 1093.2 1089.2 1084.5 1078.5 1071.4 1065.0

25.5 1108.3 1102.9 1098.9 1094.0 1088.0 1082.7 1076.0

31.0 1130.0 1126.2 1121.8 1116.6 1111.2 1105.7 1095.734.0 1150.3 1144.4 1140.6 1135.5 1130.3 1123.9 1117.5

41.0 1190.6 1185.4 1180.5 1174.9 1169.8 1163.3 1155.8

45.0 1208.4 1203.4 1197.6 1192.5 1185.9 1180.2 1173.8

51.0 1240.0 1234.5 1228.3 1222.8 1216.8 1211.7 1203.7

53.4 1253.8 1248.1 1242.2 1236.6 1230.1 1226.2 1218.7

60.7 1297.2 1290.9 1284.7 1278.8 1271.8 1268.2 1261.8

67.0 1337.3 1328.8 1322.6 1315.7 1309.0 1302.7 1295.4

70.6 1358.4 1351.8 1346.3 1339.2 1332.5 1328.3 1321.8

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

Coefficients First degree

polynomial

Second degree

polynomial

Third degree

polynomial

a0 1.1391 10+03 1.0462 10+03 2.0816 10+03

a1 5.7760 1001 1.9630 1001 9.4737 10+00

a2 5.3941 10+03 3.8568 10+00 3.9796 10+00

a3 1.1973 1003 2.8793 1002

a4 1.6533 1002 1.3724 1002

a5 3.0934 1005

a6 2.0035 1005

r2 0.9976 0.9993 0.9993

0

2

4

6

8

10

12

14

16

18

20

20 30 40 50 60

Concentration (Bx)

Viscosity

(Pa.s

)

20C

30C

40C

50C

60C

70C

80C

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

temperature.

E.M. Puntes et al. / Journal of Food Engineering xxx (2004) xxxxxx 5

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In Table 4, flow Activation Energy (Ea) values were

shown for each studied concentration calculated using

the Arrhenius equation, together with the respective fit-ting parameters and determination coefficients (r2).

Activation Energy (Ea) data obtained in this work

were very similar to that reported by Schwartz and Cos-

tell (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 concen-

tration 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 corre-

lated with soluble solids concentration (Bx).

First, data from Table 4 (l1 and Ea/R vs. Bx) wasplotted 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 expa0 a1 Brix a2 Brix2 7

Ea=R expa0 a1 Brix a2 Brix2 8

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)

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). Viscosityvalues 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 cal-

culated using Eq. (5) and the Barbieri and Rossi (1980)

equation, for all the range ofBx and temperatures (with

F-critical = 3.90), did not show significant differences be-

tween 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 sig-

nificant differences. The ANOVA result (for F-criti-

cal = 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 Cos-tell (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 ob-

tained 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 dilu-

tion of concentrated grape juices.

4. Conclusions

From the results obtained in the present study the fol-

lowing items can be summarized:

1. Clear grape juices density and viscosity from Men-

doza, Argentina, in a range of soluble solids concen-

tration 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.

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

(mPas)

Ea/R

(K)

Ea(kcal/mol)

Ea(kJ/mol)

Correlation

(r2)

22.9 2.779 1003 1964.36 3.903 16.330 0.9975

25.5 2.484 1003 2021.62 4.017 16.807 0.995331.0 1.785 1003 2182.07 4.336 18.142 0.996934.0 1.630 1003 2250.55 4.472 18.711 0.994141.0 1.189 1003 2503.32 4.974 20.811 0.995745.0 8.255 1004 2698.74 5.363 22.439 0.992651.0 3.588 1004 3097.48 6.155 25.753 0.994753.4 1.554 1004 3425.09 6.806 28.476 0.991860.7 2.681 1005 4214.79 8.375 35.041 0.995367.0 2.125 1006 5295.72 10.523 44.028 0.998270.6 1.785 1007 6256.43 12.432 52.015 0.9987

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 l1

(mPas) Ea/R (K)

a0 2.0365 10+00 7.6346 10+00

a1 2.0933 1002 1.0455 1002

a2 4.3614 1004 3.6897 1004

r2 0.9976 0.9993


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3. The thermal expansion coefficient was calculated

using a thermodynamic expression, with constant

pressure, using a second degree polynomial for den-

sity (Eq. (6)).

4. Clear grape juices showed a Newtonian flow behavior.

5. Activation Energy (Ea) values increased with the sol-

uble 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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