Density and viscosity of Malus ¯oribunda juice as a function ofconcentration and temperature

E. Cepeda a,*, M.C. Villar�an b

a Department of Ingenier�õa Qu�õmica, Facultad de Farmacia, Universidad del Pa�õs Vasco, Apartado 450, Paseo de la Universidad 7, 01006

Vitoria-Gasteiz, Spainb Fundaci�on LEIA C.D.T., c/ Leonardo da Vinci 11, 01510 Mi~nano, Alava, Spain

Received 22 December 1998; accepted 6 April 1999

Abstract

Density for cloudy and depectinised juice of Malus ¯oribunda was determined in a concentration range from 17 to 70 °Brix at

25°C. Density values were similar to the ones of common apple and were linearly correlated with soluble solids concentration. The

in¯uence of temperature and concentration on the rheological behaviour of depectinised juice of Malus ¯oribunda has been studied

in a temperature range from 10°C to 60°C, and concentrations between 40 and 70 °Brix. The depectinised juice has Newtonian

behaviour and viscosity variation with temperature following the Arrhenius±Guzman equation, with activation energy values be-

tween 26.6 and 64.8 kJ gmolÿ1. A relationship between viscosity, temperature and soluble solids concentration has been pro-

posed. Ó 1999 Elsevier Science Ltd. All rights reserved.

1. Introduction

Malus ¯oribunda is a small crab apple used in orna-mentation and for pollination in big plantations. Thefruit production can be converted to juice or employedto make jelly (Vaughan & Geissler, 1997). The concen-trated juice is obtained from fruit in a process consistingof the following steps: (a) fruit is washed, mashed andpressed and a juice with 11±12 °Brix is obtained, (b)juice is clari®ed and depectinised, (c) juice is vacuumconcentrated, with aroma recovery at the beginning,until a soluble solids of 70 °Brix is obtained. In theprocess, there is a variation of concentration and tem-perature. The temperature interval ranges between 60°C(in the evaporator) and 5°C (temperature of storage).

Data of density and viscosity are necessary to design andevaluate food-processing equipment such as evapora-tors, pumps, ®lters and mixers. In addition, density andviscosity are quality indices (Alvarado & Romero,1989).

Fruit juices are commonly treated as sugar-contain-ing solutions. The o�cial table of density values forsucrose at 20°C was published by Plato (1900) and is stillcommonly in use (Nagy, Chen & Shaw, 1993) in calcu-lation of density for mechanisation of fruit juice indus-trial applications. For more exact calculation, it isadvantageous to use speci®c equations. For juice ofcommon apple (Malus domestica), Aguado and Ibarz(1988) and Constenla, Lozano and Crapiste (1989)proposed equations that related the density with solublesolids concentration (°Brix) and temperature. Alvaradoand Romero (1989) proposed an expression of density asa function of concentration and temperature for fruitjuices including apple. For juice of Malus ¯oribunda, thedetermination of density at various concentrations isnecessary for quality control purposes, and for com-parison with the results of juice of common apple.

The fruit juices present Newtonian behaviour whenpulp content is low, soluble solids content is lower than30 °Brix, or if the juices have been depectinised (Costell,1997, Saravacos, 1970). Temperature in¯uence on vis-cosity has been found to be related to soluble solids

Journal of Food Engineering 41 (1999) 103±107

www.elsevier.com/locate/jfoodeng

Notation

a, b, c Constants of Eq. (3)

C Concentration in soluble solids (°Brix)

Ea Activation energy (J gmolÿ1)

T Absolute temperature (K)

g Absolute viscosity (Pa s)

q Density (g cmÿ3)

* Corresponding author. Tel.: +34-945-01-3031; fax: +34-945-13-

0756; e-mail: iqpcelee@vf.ehu.es

0260-8774/99/$ - see front matter Ó 1999 Elsevier Science Ltd. All rights reserved.

PII: S 0 2 6 0 - 8 7 7 4 ( 9 9 ) 0 0 0 7 7 - 1

content, and experimental data for ®xed concentrationscan be related to the temperature using the Arrhenius±Guzman equation. The rheological behaviour of juicesof Malus ¯oribunda has been studied for cloudy andclari®ed juices (Cepeda, Villar�an & Ibarz, 1998), and noreferences has been found for clari®ed and depectinisedjuice. There are previous references on rheological be-haviour of depectinised juice of common apple, andSaravacos (1970), Rao, Cooley and Vitali (1984), Ibarz,Vicente and Graell (1987) and Schwartz and Costell(1989) found Newtonian behaviour, although there is alot of data dispersion.

This work has the goal of physicochemical charac-terisation of Malus ¯oribunda depectinised juice and thedetermination of e�ect of temperature (5±50°C) andcomposition (45±72 °Brix) on the rheological behaviour.The choosed concentrations correspond to those typi-cally encountered in the evaporation process. This ob-jective includes: (a) the determination of the density ofcloudy and depectinised juice, (b) to model the rheo-logical behaviour, (c) to apply the Arrhenius equation tomodel the e�ect of temperature and (d) the study of thee�ect of soluble solids content on viscosity.

2. Materials and methods

2.1. Samples

The fruits of Malus ¯oribunda were donated by theEstaci�on de Fruticultura de Zalla (Vizcaya). For juiceelaboration a home fruit processor (Moulinex AV6,France) was employed followed by sieving through clothto separate solid particles. The obtained juice of 17 °Brixwas divided into two fractions; one of them was vacuumconcentrated at 30°C until 72 °Brix and frozen, and theother was clari®ed and depectinised (Pectinex, Novo),vacuum concentrated at 30°C until 72 °Brix and frozen.Other soluble solids concentrations were prepared byaddition of liquid collected as distillate in the concen-tration process.

Analysis of pH, acidity and soluble solids was done inaccordance with AOAC (1980). Soluble solids concen-trations were determined in an ABBE-ZEISS refracto-meter at 20°C and expressed as °Brix. Total acidity wasdetermined by potentiometric titration with NaOH 0.1N until pH 8. The pH was measured with a digital pH-meter at 20°C after eliminating CO2. Soluble sugarswere determined by isocratic HPLC (Pye-Unicam PU4010, UK), with a reverse phase amino-bonded silicacolumn (Phenomenex IB-SIL 5 NH2) with a particle sizeof 5 lm and 25 cm of length, using as mobile phaseacetonitrile-water (80:20) at 0.5 ml/min, and a refractiveindex detector (Waters R401).

The relative density was determined in capillary tubepycnometers of 10 ml capacity; the water and juice

weight were recorded in analytical balance with 0.0001 gprecision after stabilisation in a thermostatic bath(�0.1°C).

2.2. Rheological measurements

Rheological measurements were made in a rotaryviscometer, Mettler RM 180 (Mettler-Toledo, Greinfe-see, Switzerland) with attached computer (MettlerSWR27 software). Measure system DIN 53019 wasused. The temperature was maintained constant bysubmerging the cell in a thermostatic bath, controlled bya thermocouple submerged in the sample. The maxi-mum di�erence between the selected temperature andthe sample in each run was 0.3°C when the shear ratewas varied. Rheological measures of shear stress weredone placing each subsample in the measuring cell andallowed to stand for 10 min before measurement. Shearstress was measured in three rheograms zones: a shearramp from 10 to 700 sÿ1 of 600 s, hold at 700 sÿ1 for 100s and a shear ramp from 700 to 10 sÿ1 of 600 s. Theexperiments were done in duplicate.

3. Results and discussion

Physical and chemical characteristics of concentratedjuices of Malus ¯oribunda are shown in Table 1. TheMalus ¯oribunda juice has di�erent compositions of in-dustrial juice (Table 1), and the high soluble solidsconcentration, high pectin content and composition insugars is noticeable (the fructose:glucose proportion istypically 3 in juices of common apple, Lee & Wrolstad,1988).

The densities of cloudy and depectinised juices havebeen determined at 25°C for concentrations ranged from

Table 1

Composition of Malus ¯oribunda juice

Cloudy juice

Acidity (g citric acid /100 ml) 1.2387

Soluble solids (°Brix) 20.68

pH 3.23

Density (g cmÿ3) 1.0740

Sugars (11 Brix) (mg mÿ1) Fructose 50.3

Glucose 37.0

Sucrose 43.1

Pectins (g Galacturonic ac./l) 0.288

Depectinised juice

Acidity (g citric acid/100 ml) 1.4132

Soluble solids (°Brix) 17.6

pH 3.13

Density (g cmÿ3) 1.0630

Sugars (11 Brix) (mg mÿ1) Fructose 49.5

Glucose 38.0

Sucrose 43.0

Pectins (g Galacturonic ac./l) 0.042

104 E. Cepeda, M.C. Villar�an / Journal of Food Engineering 41 (1999) 103±107

18 to 70 °Brix. The data are shown in Table 2. It can beobserved that (a) cloudy and depectinised juices have thesame density for concentrations between 18 and 70 °Brixand (b) density variation with the concentration is lineal.The experimental data have been correlated with Eq. (1)(Fig. 1).

q25 � 0:0054C � 0:9671 �R2 � 0:9949�; �1�where q25 is the density at 25°C and C the concentration(°Brix).

Calculated data from the equation of Constenla et al.(1989) for density of common apple are coincident withexperimental data, but the data predicted with theequation of Aguado and Ibarz (1988) are di�erent(Fig. 1). Calculated data from the Alvarado andRomero (1989) equation, that includes the densities ofjuices of thirty fruits at concentrations between 5 and 30°Brix, are nearly coincident with the experimental datauntil concentrations of 50 °Brix. From these observa-tions it can be deducted that density of Malus juicesdepends mainly on soluble solids concentration and it isdependent neither on the variety nor on the clari®cationprocess.

Clari®ed and depectinised juice of Malus ¯oribundahas Newtonian behaviour in a concentration range from45 to 71.7 °Brix, for temperatures between 10°C and60°C. Values of viscosity are shown in Table 3. Thee�ect of temperature on the viscosity follows the Ar-rhenius±Guzman equation with r2 values greater than0.95. Magnitudes of activation energy for ¯ow (Ea), re-lating the viscosity of the concentrates to temperature,ranged from 26.6 to 64.8 kJ/gmol (Table 4), which are ofthe order of Schwartz and Costell (1989) values forcommon apple of the Granny Smith variety (Fig. 2).Other authors obtained lower values for common apple

juice, as Saravacos (1970) that obtained values between22.3 and 60.0 kJ gmolÿ1 in a interval of 15±75 °Brix, orhigher ones, as Rao et al. (1984) that obtained values of25.1±80.5 kJ gmolÿ1 for concentrations between 45.1and 75 °Brix (McIntosh variety). The experimental datahave been ®tted to a polynomial equation:

Ea � 1:5541C3 ÿ 220:14C2 � 10975C ÿ 163427

r2 � 0:998�2�

in which Ea is the activation energy (J gmolÿ1) and C theconcentration (°Brix).

The comparative analysis of the results found in thiswork and that of other authors with di�erent varieties ofMalus, con®rms that the soluble solids content de®nesthe temperature in¯uence on the rheological behaviourand that the variety of fruit or di�erences in compositionhave no in¯uence on the viscosity of ®nal product forthe same type of juice.

The increase in concentration and the decrease oftemperature increase viscosity. Both variables can becombined in a single logarithmic model for simulationof processes:

lng � a� b1

T

� �� cC �3�

in which a, b and c are constants, C the concentration(°Brix) and T the absolute temperature (K). Similarequations have been derived for the consistency indexand apparent viscosity of orange juice (Vitali & Rao,1984) and for cloudy and clari®ed juices of Malus ¯or-ibunda (Cepeda et al., 1998). Experimental data havebeen ®tted to Eq. (3). From this, the ®nal equation ob-tained was:

g � exp�ÿ53:46� 9458:59�1=T � � 0:29C�: �4�Fig. 3 display the response surface obtained from

Eq. (4). Although the proposed equation shows a

Table 2

Density of Malus ¯oribunda juices at 25°C

°Brix Density (g cmÿ3)

Cloudy

18.3 1.0735

45 1.2077

50 1.2356

55 1.2581

60 1.3026

65 1.3210

70 1.3550

Depectinised

17.6 1.0630

45 1.2167

50 1.2390

55 1.2544

60 1.2879

65 1.3248

70 1.3550

Fig. 1. Density of depectinised or cloudy juice at 25°C.

E. Cepeda, M.C. Villar�an / Journal of Food Engineering 41 (1999) 103±107 105

regression coe�cient of 0.9987 and an explainedvariance of 99.79%, the relative deviations of the re-sults for low viscosities are high (until 70%). This

equation should be used only for preliminary design ofthe equipment.

4. Conclusions

The concentrated juices of Malus ¯oribunda presentvalues for density similar to juices of common apple.Relative density can be related with soluble solids con-centration by a single parameter equation. Depectinisedjuices showed Newtonian behaviour. The variation ofviscosity with temperature followed the Arrhenius±Guzman equation, and the activation energy has beenrelated with concentration by a polynomial equation.The e�ect of temperature and concentration on viscosity

Table 3

Viscosity of depectinised juice

Viscosity (Pa s)

Temperature Concentration (°Brix)

T (°C) 71.7 65.5 60 55.1 50.1 45.1

5 3.300 0.490 0.140 0.043 0.023 0.015

10 1.743 0.318 0.098 0.032 0.020 0.012

20 0.552 0.150 0.048 0.019 0.012 0.008

25 0.375 0.100 0.035 0.015 0.009 0.006

30 0.220 0.083 0.028 0.012 0.008 0.006

35 ÿ ÿ ÿ ÿ 0.007 0.005

40 0.090 0.042 0.018 0.008 0.006 0.004

50 0.070 0.028 0.013 0.006 0.005 0.003

60 0.030 0.017 0.010 0.005 ÿ ÿ

Fig. 3. Response surface representing the e�ect of temperature and

soluble solids on viscosity.

Fig. 2. Activation energy-concentration plot for depectinised juice of

Malus ¯oribunda.

Table 4

Values for parameters of the Arrhenius±Guzman equation

�g � g0 exp�Ea=RT ��

°Brix g0 (Pa s) Ea (kJ

gmolÿ1)

r2

71.1 2.01382 ´ 10ÿ12 64.8 0.985

65.5 7.49677 ´ 10ÿ10 47.0 0.998

60.0 6.7227 ´ 10ÿ9 38.8 0.988

55.1 2.39093 ´ 10ÿ8 33.3 0.997

50.1 1.04087 ´ 10ÿ7 28.6 0.988

45.1 1.48273 ´ 10ÿ7 26.6 0.993

106 E. Cepeda, M.C. Villar�an / Journal of Food Engineering 41 (1999) 103±107

can be described by a single equation that could beuseful for preliminary equipment design.

Acknowledgements

The authors are indebted to the Basque CountryUniversity for ®nancial support. Project UPV 069.123-EA236/96.

References

Aguado, M. A., & Ibarz, A. (1988). Variaci�on de la densidad de un

zumo de manzana con la temperatura y concentraci�on. Aliment-

aci�on Equipos y Tecnolog�õa, pp. 209±216.

Alvarado, J. D., & Romero, C. H. (1989). Physical properties of fruits I.

density and viscosity of juices as functions of soluble solids content

and temperature. Latin American Applied Research, 19, 15±21.

Cepeda, E., Villar�an, M. C., & Ibarz, A. (1998). Rheological properties

of cloudy and clari®ed juice of Malus ¯oribunda as a function of

concentration and temperature. Journal of Texture Studies, Sub-

mitted.

Constenla, D. T., Lozano, J. E., & Crapiste, G. H. (1989). Thermo-

physical properties of clari®ed apple juice as a function of

concentration and temperature. Journal of Food Science, 54, 663±

668.

Costell, E. (1997). Reolog�õa de derivados de frutas, In Fundamentos de

Reolog�õa. Los materiales viscoel�asticos. I. Edit. U.I.M.P., Valencia.

Ibarz, A., Vicente, M., & Graell, J. (1987). Rheological behaviour of

apple juice and pear juice and their concentrates. Journal of Food

Engineering, 6, 257±267.

Lee, H. S., & Wolrstad, R. E. (1988). Adulteration in apple juices. In S.

Nagy, M. E. Attaway, & M. E. Rhodes, Adulteration of Fruit Juice

Beverages. New York: Marcell-Dekker.

Nagy, S., Chen, C. S., & Shaw, P. E. (1993). Fruit Juice Processing

Technology. Agscience, Auburndale, Florida.

Plato, F. (1900). Kaiserliche normaleichungs konmission wi-

ssenscha®liche abhandlungen, 2, 153.

Rao, M. A., Cooley, H. J., & Vitali, A. A. (1984). Flow properties of

concentrated juices at low temperatures. Food Technology, 38, 113±

119.

Saravacos, G. D. (1970). E�ect of temperature on viscosity of fruit

juices and purees. Journal of Food Science, 35, 122±123.

Schwartz, M., & Costell E. (1989). In¯uencia de la temperatura y la

concentraci�on en la viscosidad de los zumos de manzana y de uva.

Revista de Agroqu�õmica y Technolog�õa de Alimentos, 29, 239-245.

Vaughan, J. G.,& Geissler C. A. (1997). The New Oxford Book of

Plants. Oxford: Oxford University Press.

Vitali, A. A., & Rao, M. J. (1984). Flow concentrated of low-pulp

concentrated orange juice: e�ect of temperature and concentration.

Journal of Food Science, 49, 882±888.

E. Cepeda, M.C. Villar�an / Journal of Food Engineering 41 (1999) 103±107 107