INTRODUCTION

Grapefruit is the largest and one of the most popularcitrus fruit for many people in Mexico. It is widely usedin drinks and commercial juices prepared from grape-fruit concentrated juice. Citrus juices were originallyconcentrated and later frozen to provide a convenientyear-round source for these juices, which were previous-ly seasonal products.The diminished volume and weightof concentrated juices reduced costs associated withpackaging materials, storage space, transportation andrefrigeration compared to those of single strengthjuices. Freeze concentration and reverse osmosis,among other technologies, have been considered as alternatives to thermal evaporation for the prepara-tion of citrus juice concentrates. However, because offavourable economics, thermal evaporation is still the most widely used concentration process in the citrus industry. Freshly squeezed juice is pumped into an

evaporator where most of the water is removed throughvacuum-assisted heating. Commercial evaporators typi-cally have several stages that sequentially heat the juiceto ever-higher temperatures and then rapidly cool it.Knowledge of the boiling point temperature of grape-fruit juice for a wide range of concentrations is of pri-mary importance for the juice industry, as it makes wideuse of evaporation for juice concentration.

A previous work has been conducted on the effect oftemperature and concentration on elevation of boilingpoint of coffee extract (Telis-Romero et al., 2002).Nevertheless, no published data are available on therise in boiling point at different concentrations ofgrapefruit juice, and theoretical equations are of limiteduse due to the complex composition of the material andlack of knowledge of the components that contribute tothe elevation of boiling point. Experimental data on therise in the boiling points of fruit juices at different con-centrations were presented by Ilagantileke et al. (1991),for Thai tangerine juices, by Crapiste and Lozano (1988)and Moresi and Spinosi (1984) for apple juice, byMoresi and Spinosi (1980) for orange juice, and byVarshney and Barhate (1978) for pineapple, mango andlemon juices.

In this work, the rise in boiling point of grapefruitjuice at various concentrations and pressures was meas-ured and compared with data on sucrose solutions,which are often used as models to represent the behav-iour of fluid foods such as fruit juices.

Thermal Evaporation: Representation of Rise in Boiling Pointof Grapefruit Juice

J. Telis-Romero1, D. Cantú-Lozano2, V.R.N. Telis1 and A.L. Gabas3*

1Departamento de Engenharia e Tecnologia de Alimentos, Universidade Estadual Paulista, São José do RioPreto, São Paulo, 15054-000, Brazil

2División de Estudios de Posgrado e Investigación, Maestría en Ciencias en Ingeniería Química, InstitutoTecnologico de Orizaba, Orizaba, Veracruz, 94 320, México

3Departamento de Engenharia de Alimentos, Universidade de São Paulo, Pirassununga,São Paulo, 13635-900, Brazil

The rise in boiling point of grapefruit juice was experimentally measured at soluble solids concentrationsin the range of 9.3–60.6 °Brix and pressures between °6.0 � 103 and 9.0 � 104 Pa. Different approaches torepresent experimental data, including the Dühring’s rule, the Antoine equation and empirical modelsproposed in the literature were tested. In the range of 9.3–29.0 °Brix, the rise in boiling point was nearlyindependent of pressure, varying only with juice concentration. Considerable deviations of this behaviorbegan to occur at concentrations higher than 29.0 °Brix. Experimental data could be best predicted byadjusting an empirical model, which consisted of a single equation that takes into account the dependenceof rise in boiling point on pressure and concentration.

Key Words: evaporation, concentration, vapour pressure, grapefruit juice

Food Sci Tech Int 2007; 13(3):225–229© SAGE Publications 2007Los Angeles, London, New Delhi and SingaporeISSN: 1082-0132DOI: 10.1177/10820132013207079896

*To whom correspondence should be sent (email: gabas@usp.br).Received 29 August 2006; revised 16 October 2006.

MATERIAL AND METHODS

Sample Preparation

Grapefruit (citrus Paradisi) obtained at the local mar-ket (CEASA-SJRP-SP, Brazil) was used throughout thisstudy. The grapefruit juice was prepared by manualextraction and concentrated under vacuum (about1.04 � 104 Pa, abs.) in a rotary evaporator (Fisatom, SãoPaulo, Brazil), resulting in juices with soluble solids con-tents in the range of 9.3–60.6 °Brix. Soluble solids con-centration was measured at 25°C with a refractometer.

Apparatus and Procedure

A schematic diagram of the apparatus used for exper-imental measurement, which is similar to that describedby Moresi and Spinosi (1980), is shown in Figure 1. Itwas made of glass and consisted of a flat bottom flask (F)with three openings. Samples were introduced into theflask by means of tube A and heated by an electricheater provided with a magnetic stirrer (Fisatom, SãoPaulo, Brazil). When the juice reached boiling tempera-ture, a recirculation flow was established between tubesB and C. The liquid–vapour mixture released from theliquid surface flowed up through tube B, thus heatingthe thermocouple installed in the well, which was con-nected to a temperature transmitter (model TT302,SMAR, Sertãozinho, SP, Brazil). Condensed liquid parti-cles were trapped in compartment D and returned toflask F, allowing vapor to enter reflux condenser R.Condensed vapour also returned to flask F through tubeC with valve V controlling the recirculation flow rate tokeep the juice concentration constant.

The condenser was connected to a vacuum pump,allowing pressure to vary in the range of 3.3 � 103 to

6.4 � 104 Pa. Differential pressure transmitters (modelLD-301, SMAR, Sertãozinho, SP, Brazil) were used tomeasure static pressure at two different positions in thevacuum tube. An HP model 75.000-B data logger, anHP-IB interface and a PC running a data acquisitionprogram written in IBASIC monitored temperaturewith an accuracy of 0.6°C and pressure with an accura-cy of 4.3 m Pa.

In each experiment, a 180 mL sample of concentratedjuice was introduced into the boiling vessel. The coolingwater flow passed through the reflux condenser, the vac-uum pump was turned on with a valve regulated to pro-vide a pressure of about 6 � 103 Pa, and the fluid wasmixed and heated slowly.Temperature and pressure werethen continuously recorded, and final values for solutionboiling point and associated pressure were registeredafter readings had been constant for at least 5 min.

The procedure was repeated almost up to atmos-pheric pressure, allowing measurement of boiling pointsat different pressures with the same juice concentration.In order to check juice concentration, heating was peri-odically interrupted, the vessel was cooled down toroom temperature, and a sample of fluid was removedfor measurement of °Brix. When necessary, juice wassubstituted and the run was repeated.

For juices of different concentrations, all of the aboveprocedure was repeated.

RESULTS AND DISCUSSION

Performance of the apparatus was checked usingaqueous solutions of LiCl and NaOH, whose boilingpoints at various concentrations and pressures areknown. Table 1 permits comparison of experimentaldata obtained in this work and data presented by Perryand Chilton (1986), while Figure 2 shows a typical his-togram of data distribution. The agreement betweenexperimental and reported data was good as was thereproducibility of results, since the histogram shows anormal distribution of measurements around the aver-age value. Values of the standard deviation (sd) andstandard error (se) included in Table 1 were calculatedby equations (1) and (2) respectively

(1)

(2)

where xn is the value of each measurement, x̄ the average value, and n the number of measurements.

The typical manner of presenting boiling point dataof fluid foods consists of relating them with the boiling

226 J. TELIS-ROMERO ET AL.

To vacuum pump andpressure transmitter

Cooling water out

Cooling water in

D

V

C

F

A

B

Figure 1. Scheme of the apparatus used for experi-mental measurements.

temperature of water at the same pressure. Dühring’srule (Foust et al., 1960) stated that the temperature atwhich one liquid exerts a given vapour pressure is a lin-ear function of the temperature at which a referenceliquid exerts the identical vapour pressure (Heldmanand Singh, 1981). Therefore, at a constant concentrationthis realtion is as follows:

(3)

where TA and TA0 are respectively the boiling tempera-tures of grapefruit juice and water at the same pressure.Parameters m0 and m1 were determined by linearregression for each grapefruit juice concentrationtogether with the correlation coefficient, r2 (Table 2).

Defining the rise in boiling point, �TB, as

(4)

and substituting it into equation (3), for m1 � 1,�TB � m0, indicating that at this condition the rise inboiling point varies only with juice concentration and isindependent of pressure. Representation of �TB versus

the boiling point of pure water showed that the slope ofequation (3), m1, was practically equal to one for lowerconcentrations, but considerable deviations began tooccur at higher concentrations (Table 2 and Figure 3).This behaviour led to the conclusion that the pressureinfluence should be taken into account in any proposedmethod for predicting boiling points of grapefruit juice.

A second manner of presenting boiling point data onaqueous solutions is based on extending the use ofexpressions suitable for describing the temperaturedependence of pure water vapour pressure, as in thecase of the Antoine equation (Perry and Chilton, 1986):

(5)

where P is the pressure in Pa, TA is the boiling temper-ature of grapefruit juice in Kelvin degrees, and A, B andC are empirical constants dependent on concentration.These constants were determined by a nonlinear regres-sion procedure (Table 3). A comparison of experimen-tal vapor pressure data and predictions of equation (5)is displayed in Figure 4. Although the correlation coef-ficient (r2, Table 3), indicated a good correlationbetween the model and experimental data, it was notpossible to establish an explicit dependence of these

Concentration of Grapefruit Juice 227

Table 1. Experimental rises in boiling point of standard solutions.

Concentration �TB (°C) Standard Standard Solutions % (w/w) Experimental Deviation (°C) Error (°C) �TB* (°C)

NaOH 15 6.23 0.141 0.029 6.525 16.95 0.288 0.060 17.335 33.96 0.249 0.052 34.8

LiCl 5 1.19 0.014 0.003 1.210 3.32 0.044 0.009 3.420 10.95 0.061 0.013 11.0

*Data from Perry and Chilton (1986).

Figure 2. Distribution histogram of boiling points ofNaOH used for checking apparatus performance(�expected normal).

Table 2. Parameters of equation (3) for grapefruitjuice at different concentrations.

Concentration (°Brix) m0 (°C) m1 r2

9.3 0.1727 1.0012 0.99819.1 0.4151 1.0029 0.99824.3 0.5775 1.0043 0.99829.0 0.8047 1.0053 0.99833.6 0.9618 1.0082 0.99839.1 1.4065 1.0097 0.99845.5 1.9415 1.0135 0.99950.3 2.4853 1.0170 0.99956.0 3.2649 1.0223 0.99960.6 4.0182 1.0281 0.999

constants as a function of soluble solids content ofgrapefruit juice.A similar model to describe vapor pres-sure dependence on temperature of concentrated applejuices (Moresi and Spinosi, 1984) described the empiri-cal constants as functions of an ‘equivalent sucroseweight fraction’.

Crapiste and Lozano (1988) proposed an alternativeapproach to representing the elevation of boiling pointof aqueous solutions, which consisted of adopting anempirical model that was simultaneously dependent onpressure and soluble solids concentration, given by thefollowing equation:

(6)

where �TB � TA � TA0 is the rise in boiling point in °C, W represents the mass concentration of solublesolids in °Brix, P is the pressure in mbar in order to

permit comparison with other work and the parameters�, �, � and � could be evaluated by nonlinear regression.

In the case of grapefruit juice, fitting equation (6) toexperimental data resulted in a very good agreement,with a high correlation coefficient (r2 � 0.991) and afavourable distribution of residuals (Figure 5). The ade-quacy of equation (6) for predicting the elevation ofboiling point of grapefruit juice can also be checked,using an observed (experimental) versus predicted dataplot (Figure 6).The great majority of data are containedwithin a 10% range of error, with larger deviationsoccurring only for dilute solutions, where values of risein boiling point are nearly zero.

228 J. TELIS-ROMERO ET AL.

Figure 3. Rise in boiling point of grapefruit juice atdifferent soluble solids contents as a function of theboiling point of pure water. Soluble solids (Brix): (�)9.3, (�) 19.1, (�) 24.3, (�) 29.0, (�) 33.6, (�) 39.1,(�) 45.5, (�) 50.3, (�) 56.0, (�) 60.6.

Table 3. Parameters of Antoine equation for grape-fruit juice at different concentrations.

Concentration(°Brix) A B C r2

9.3 23.594 4058.6 �36.90 0.98919.1 23.700 4130.9 �34.28 0.99524.3 23.491 4007.1 �39.05 0.97829.0 23.525 4031.6 �38.27 0.99333.6 22.984 3717.9 �50.33 0.98439.1 24.307 4551.4 �19.10 0.98445.5 24.261 4535.2 �19.98 0.98350.3 23.871 4297.2 �28.97 0.96656.0 24.572 4783.8 �11.61 0.97660.6 23.842 4322.9 �28.70 0.981

Figure 4. Vapour pressure of grapefruit juice at differ-ent soluble solids contents as a function of temperature.Lines correspond to predictions of equation (5). Solublesolids (Brix): (�) 9.3, (�) 19.1, (�) 24.3, (�) 29.0, (�)33.6 (�) 39.1, (�) 45.5, (�) 50.3, (�) 56.0, (�) 60.6.

Figure 5. Distribution of residuals obtained betweenexperimental and predicted [equation (6)] elevation ofboiling point of grapefruit juice.

Numerical values for parameters �, �, � and � (Table 4)were compared with the same constants obtained for cof-fee extract (Telis-Romero et al., 2002) and for apple juiceand sugar solutions obtained (Crapiste and Lozano,1988). A similar order of magnitude was observed forcoffee extract and apple juice. Nevertheless, these valueswere considerably different from those corresponding tosucrose solution, leading to the conclusion that importanterrors could arise from the use of data on sucrose solu-tions to estimate the rise in boiling point of grapefruitjuice, which is a common practical procedure.

It is important to stress that this work was conductedwith grapefruit juice produced at atmospheric pressure.

These are mostly reducing sugars, but there are alsolarge sugar molecules, as well as proteins that alsoundergo hydrolysis under processing conditions (Telis-Romero et al., 2002). The experimental data presentedin this paper consists of a considerable advance againstthe use of data on sucrose solutions.

ACKNOWLEDGEMENT

The authors wish to express their thanks to CNPq forits financial support (Proc. 300539/2003-7).

REFERENCES

Crapiste G.H. and Lozano J.E. (1988). Effect of concentra-tion and pressure on the boiling point rise of apple juiceand related sugar solutions. Journal of Food Science53(3): 865–868 and 895.

Foust A.S., Wenzel L.A., Clump C.W., Maus L. andAndersen L.B. (1960). Principles of Unit Operations.New York: John Wiley & Sons.

Heldman D.R. and Singh R.P. (1981). Food ProcessEngineering, 2nd edn. New York: Van NostrandReinhold.

Ilagantileke S.G., Ruba Jr, A.B. and Joglekar. H.A. (1991).Boiling point rise of concentrated thai tangerine juices.Journal of Food Engineering 15: 235–243.

Moresi M. and Spinosi M. (1980). Engineering factors inthe production of concentrated fruit juices. 1. Fluid phys-ical properties of orange juices. Journal of FoodTechnology 15: 265–276.

Moresi M. and Spinosi M. (1984). Physical properties ofconcentrated apple juices. In: McKenna B.M. (ed.).Engineering and Food,Vol. 1, Engineering Sciences in theFood Industry. Essex: Elsevier Applied SciencePublishers Ltd.

Perry R. and Chilton C. (1986). Manual de EngenhariaQuímica, 5th edn. Rio de Janeiro: Ed. Guanabara Dois.

Telis-Romero J., Cabral R.A.F., Kronka G.Z. and TelisV.R.N. (2002). Elevation on boiling point of coffeeextract. Brazilian Journal of Chemical Engineering19(1): 119–126.

Varshney N.N. and Barhate V.D. (1978). Effect of concen-trations and vacuum on boiling points of fruit juices.Journal of Food Technology 13: 225–233.

Concentration of Grapefruit Juice 229

7

6

5

4

3

(TA

-TA

O) o

bs

(TA-TAO)pred

2

1

00 1 2 3 4 5 6 7

+10%

−10%

Figure 6. Observed (experimental) versus predicted[equation (6)) rise of boiling point of grapefruit juice.

Table 4. Parameters of equation (6) for grapefruitjuice, coffee extract, apple juice and sugar solutions

(pressure was taken in mbar to compare with other works).

Juices � � 102 � � � 102 � r2

Grapefruit juice 0.4164 1.2851 2.227 0.1113 0.998Coffee extract* 0.8474 0.9895 2.570 0.1163 0.997Apple juice** 1.3602 0.7489 3.390 0.1054 0.998Sucrose solutions** 3.0612 0.0942 5.329 0.1356 0.999

*Values from Telis-Romero et al. (2002).**Values from Crapiste and Lozano (1988).