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Viscosity and electrical conductivity of concentrated solutions of soluble coffee
Journal of Food Engineering 51 (2002) 93±98
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Viscosity and electrical conductivity of concentrated solutions of soluble coee V. Sobolõk b
y b, V. Tovcigrecko c, M. Delgado a, K. Allaf , R. Zitn
a,*
a
a LMTAI, University of La Rochelle, Av. Michel Crepeau, La Rochelle 17042, France Institute of Process Engineering, Faculty of Mechanical Engineering, Czech Technical University, Technick a 4, 16000 Prague 6, Czech Republic c Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojov a 135, 165 02 Prague 6, Czech Republic
Received 14 October 2000; accepted 29 January 2001
Abstract Viscosity of concentrated aqueous solutions (x 0:5±0:8) of soluble coee was measured in the temperature range 25±95°C. After some time of the shear application in the viscometer and passing a temperature of 95°C, the rheological behaviour was found to be Newtonian. The viscosity was correlated by a ®ve parameter function of coee mass fraction and temperature. Speci®c electrical conductivity of coee solutions in tap water (x 0±0:8) was measured in the temperature range 25±72°C. A seven parameter model based on the assumption that the solution is composed of a partially dissociated species and water describes very well the measured data. A modi®ed Casteel±Amis model equation has been identi®ed for comparison. The conductivity dependence on mass fraction exhibits maxima, which are shifted towards higher concentrations the higher is the temperature. Viscosity, refractivity index, density and thermal conductivity of aqueous coee solutions (x 0±0:5) are reviewed. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Coee extract; Soluble coee; Viscosity; Flow behaviour; Electrical conductivity; Physical properties
1. Introduction Coee is composed of more than 700 components. Purine alkaloids (caeine etc.), minerals, bases, chlorogenic acids, lipids, aliphatic acids and carbohydrates (arabinose, sucrose etc.) and amino acids (tryptophan) are some of them (Garattini, 1993). Data on physical properties of aqueous solutions of soluble coee are scarce although the world production is very important and the coee extracts enjoy an extensive consumer market. The manufacturers guard the con®dentiality of processing. We have found only one paper (Weisser, 1972) which deals with the viscosity and other physical properties of aqueous coee solutions. In this paper, viscosity, surface tension, thermal conductivity, index of refraction and freezing curves were measured in solutions with coee mass fractions in the range 0±0.5. Dierent mixtures were examined of several coee types prepared either by freeze drying (Vox Mocca, Vox Robusta) or by spray drying (Nescafe Gold, Maxwell Exquisit). As this paper is written in *
Corresponding author. Tel.: +33-5-4645-8780; fax: +33-5-46458616. E-mail address: [email protected] (V. Sobolõk).
Czech, the most important results are summarised in the following paragraphs. The dependence of the refractivity index on the coee mass fraction x was expressed by the relation: 2 2 n20 D 1:333 0:1728x 8:93 10 x :
1
At x 0:5, the refractivity indexes of the coee and sucrose are about 1.44 and 1.42, respectively. It is dicult to measure the refractivity index of more concentrated coee solutions because the dark brown colour hinders in scale observation. The density was calculated from the density of water qW and the true density of the solid coee qC : 1 x 1 x ; q x; T qC qW
2
where qW 1000 0:036 T 0:004 T 2 and qC 1654 1:79 T 0:0063 T 2 . The dierence in the densities of the coee and sucrose is about 1% at x 0:5. The ¯ow curves were measured by a Haake rotational viscometer. The rheological behaviour was characterised as slightly pseudoplastic and thixotropic. The values of the limiting viscosity l1 are also given, i.e., the values which did not change with increasing shear rate. The viscosity increased non recoverably when the solution
0260-8774/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 0 4 2 - 5
94
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98 Notation a, b, c parameters in Eqs. (8) and (9) k number of model parameters refraction index (yellow Na light at 20°C) n20 D N number of data pji parameters in Eq. (11) R correlation coecient, q P PN j xj ; Tj 2 = Nj1 jj j2 R 1 j1 jj T temperature (°C) x, y parameters of modi®ed Casteel±Amis model, Eq. (10), ()) c shear rate (s 1 ) j speci®c electrical conductivity (S m 1 )
was stored for a longer time. This fact was explained by swelling of high molecular substances which are present in the coee. Weisser (1972) did not ®nd any important dierence in viscosity between dierent types of coee prepared either by spray drying or by freeze drying. Due to the presence of surface active substances, the surface tension of coee solutions was found to be lower than that one of water. For x > 0:1, the surface tension was equal to 0.042 N m 1 at 20°C and 0.037 N m 1 at 40°C. The thermal conductivity of coee solutions was found to be the same as the conductivity of sucrose solutions. It was described by the relation: k 10
3
565:1 1:8T
0:0058T 2 1
0:54x:
3
Intensi®cation of soluble coee production requires the treatment of more concentrated solutions. The present paper focuses on the properties which are important for ohmic heating and treatment of highly concentrated coee solutions, i.e., viscosity and electric conductivity. The coee studied was a freeze dried mixture of 65% coee arabica (Colombia) and 35% coee robusta (Brazil), sold under the name ``Cafe ®ltre'' by Carrefour (France). 2. Flow behaviour The dependencies of shear stress on shear rate were measured in a Rheotest II controlled rate viscometer. More details about basic rheological concepts can be found in the book of Bird, Armstrong, and Hassager (1987). Two dierent geometry were used consisting of one external cup with a diameter of 40 mm and two internal cylinders, S1 and S2 with diameters 39.2 and 37.6 mm and a length of 72 mm. The temperature of the external cup and hence of the sample was controlled by a water circulator. Solutions with coee mass fractions x 0:5±0:8 in tap water were examined in a temperature range of 25±95°C. The samples with lower concentrations, x < 0:75, were prepared in a glass beaker
j x; T j jij k l l1 q x xc r s
statistically smoothed estimate of j S m 1 mean value speci®c electrical conductivity S m 1 parameters in Eq. (9) thermal conductivity W m 1 °C 1 viscosity (Pa s) limiting viscosity (Pa s) density kg m 3 coee mass fraction (kg dry coee/ kg solution) critical coee mass fraction in Eqs. (8) and (9) (kg dry coee/ kg solution) standard deviation of j S m 1 , q PN j xj ; Tj 2 = N k r j1 jj shear stress (Pa)
whereas the more concentrated samples were mixed directly in the viscometer cup. The preparation was similar in both cases. The dry coee was poured into water with a temperature of 25°C. The sample was then agitated with a glass bar and heated to 70°C. The stainless steel viscometer cup was preheated to 60°C before it was ®lled with a prepared sample. The cup was then pressed onto the measuring cylinder. A thin plastic disc covered the sample surface to minimize water evaporation. By means of the external cup, the sample was then cooled to the lowest temperature at which the viscosity measurements started. The torque was measured at rotational rates going from the minimum to the maximum one and reverse. The temperature was then increased to the next one and measurements were done at increasing and then decreasing shear rate. After reaching the maximum temperature of 95°C, the measurements were repeated at decreasing temperature steps. The measurements on one sample took about 4 h. The ¯ow curves measured immediately after the sample preparation, i.e., in the series with increasing temperature, exhibited slightly pseudoplastic behaviour with the ¯ow index of about 0.9 and a higher apparent viscosity than the curves measured some time later after passing the maximum temperature of 95°C. The latter curves exhibited Newtonian behaviour. An example of primary data is shown in Fig. 1. This dierence in ¯ow behaviour can be explained by the presence either of larger molecules or of solid particles during the ®rst phase. The concentrated solution of coee extract needs a higher temperature (90±95°C) or a longer exposition to shear rate to become homogeneous or to destroy the large molecules. The data presented in this paper correspond to the viscosity measured in the second phase after passing 95°C. We suppose that the rheological behaviour in this phase correspond to the behaviour of the coee solution after its extraction from granulized roasted coee particles which is carried out at temperatures as high as 180°C (Masters, 1976). The measurements were done until the maximum shear rates attainable in the viscometer. The shear rate
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 1. Flow curves of coee solutions, x 0:7, at 40°C measurements immediately after sample preparation, measurements after 2 h after passing 95°C.
was limited either by the maximum rotational rate or by the maximum torque, which can be achieved in the viscometer. For x 0:5, this limit was the maximum shear rate generated by the largest cylinder S1 (smallest gap). The value of the shear rate in this case is equal to 1574 s 1 . For the solutions with higher viscosity, x > 0:5, the limiting factor was the maximum torque and the smaller cylinder S2 (larger gap) had to be used. For this geometry, the maximal shear rates were lower than 455 s 1 . The viscosity dependence on the absolute temperature and concentration is shown in Fig. 2. For x in the range of 0.5±0.8, the viscosity was ®tted by the relation l exp 1:141
22:42x
973:1
17:78x2
Fig. 3. Dependence of viscosity on temperature and concentration for coee solutions with low concentration [2] x: d ± 0, ± 0.1, ± 0.2, N ± 0.3, ± 0.4, M ± 0.5.
measured by Weisser (1972) for x 0:5 is shown by the open diamond symbols. It does not exhibit great deviations from our measurements. For 60°C, we obtained a value of 0.019 Pa s whereas Weisser (1972) indicates a value of 0.024 Pa s. This quite good agreement con®rms the conclusion that the viscosity is almost independent of the coee type and its treatment. With the aim of extending the range of viscosity dependence also to low concentrations, (x from 0 to 0.5), the results of Weisser (1972) are shown in Fig. 3. The best ®t of these data is by the relationship l exp 12:96
9:43x 8:12x2
1789 4382x= T 273:15:
2
17923x = T 273:15:
95
5
4
The maximum error of viscosity evaluation using this relation was estimated to be less then 15%. The viscosity
3. Speci®c electrical conductivity 3.1. Model design
Fig. 2. Dependence of viscosity on temperature and concentration for concentrated coee solutions x: d ± 0.5, ± 0.6, ± 0.66, N ± 0.7, ± 0.74, M ± 0.8, } ± data (Weisser, 1972) for x 0:5.
Speci®c electric conductivity of electrolytes jS m 1 depends upon concentration, mutual interactions and mobility of ions. It is known that increasing viscosity decreases conductivity. Nevertheless our attempt to correlate viscosity and conductivity of the coee solutions failed totally. Some theoretical results originated from the Debye±H uckel theory can be applied to weak electrolytes, see Koryta et al. (1976), but for concentrated electrolytes empirical models, e.g., models describing j x by the normal distribution function or models of the form j x a x expb x, are usually preferred (see De Diego, Madariaga, & Chapela, 1997). A new empirical model describing the temperature and concentration dependency of speci®c electrical conductivity is based on the concept, that the coee solution is composed of water having conductivity jW , dissociated coee species with conductivity jc and non
96
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
dissociated species which act as insulators. It is assumed than the amount of dissociated species is proportional to the mass fraction of coee, x, and also to the mass fraction of water, 1 x,
3.2. Experimental results and model identi®cation
This model does not ®t the experimental data properly with a constant exponent m. Therefore, this exponent must be considered as a function of temperature and concentration, m T ; x. The following empirical Eq. (8) will be used for processing data, exhibiting a slight change of trends at a concentration of xc
The speci®c electrical conductivity was measured by the conductivity probe LF 340 TetraCon 325/S which is suitable for highly viscous materials and pastes. The probe is composed of four graphite electrodes and a thermometer embedded in an epoxy casing. The electrodes are ¯ush mounted in an axial groove. The dimensions of the probe and the amount of coee sample follow from Fig. 4. The samples were prepared by mixing the coee extract with cold tap water in a beaker which was then immersed in water heated to 80°C. The sample was then ®lled into a small cylindrical glass cup and the probe was immersed into the sample. The temperature of the cup was controlled by a water circulator. The measurements started at the lowest temperature (25°C) and continued until 72°C. Approximately 50 values of the conductivity were recorded for each concentration at dierent temperatures. The primary data are shown in Fig. 5. For the reason of clarity, only every second point is depicted. The range of measured temperatures can be also deduced from Fig. 5. The simplest approach to modelling is based upon the quadratic approximation of temperature dependence evaluated separately for each measured concentration xi
m a b max x; xc cT :
ji T p0i p1i T p2i T 2 :
xc x 1
xm :
6
Experiments indicate that the conductivity of concentrated coee depends strongly on temperature and therefore we shall assume linear relationship for approximation of jc T , while temperature dependency of jw for tap water will be neglected in view of the facts, that jw is very small and we are interested in concentrated solutions. Combining speci®c electrical conductivity of three components (non dissociated species-insulator, water, and dissociated species) according to a simple model of parallel resistors, we obtain j jc0 jc1 T x 1
m
x jw 1
x:
7
8
For concentrations bellow the critical concentration xc , m is a function of T only. The resulting model is a rather complicated 7-parametric relation j x; T jc0 jc1 T x 1 jw 1
x:
xab
max x;xc cT
9
The proposed model (9) will be compared with the Casteel±Amis equation for j c; T modi®ed by De Diego et al. (1997) by inclusion of temperature. The Diego's model is based on ®tting of maximum conductivity jmax at the corresponding concentration cmax . The following Eq. (10) diers from the original Diego's model only by replacing concentration c with the mass fraction x: x x j x; T jmax 0 jmax 1 T xmax 0 xmax 1 T exp y x xmax 0 xmax 1 T 2 x x 1 : 10 xmax 0 xmax 1 T The modi®ed Casteel±Amis equation has six parameters, jmax 0 ; jmax 1 ; xmax 0 ; xmax 1 , x, y and only two of them, jmax 0 ; jmax 1 , are at linear terms. In view of the fact, that the predicted conductivity equals zero for x 0, the model (10) cannot describe the conductivity of pure water.
11
Identi®cation of the coecients p0i ; p1i ; p2i by linear regression was done with a relative standard deviation smaller than 1.5%. The results are summarised in Table 1 and shown by full lines in Fig. 5. The signi®cance of the coecient of the second power member, p2i , is more important the higher the concentration. Eq. (11) with the parameters given in Table 1 enable us to access the
Fig. 4. Experimental set-up for conductivity measurements (a) front view, (b) cut-away side view 1 ± conductivity probe, 2 ± electrodes, 3 ± cup, 4 ± cap, 5 ± sample. Dimensions are in millimetres.
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 5. Dependence of speci®c electrical conductivity on temperature x: M ± 0, ± 0.02, N ± 0.05, ± 0.1, ± 0.2, d ± 0.3, ± 0.4, ± 0.5, j ± 0.6, } ± 0.7, r ± 0.8. Full lines represent Eq. (11) with parameters from Table 1.
primary data with a smaller deviation than the models where the both T and x are variable. Parameters of model (9), jc0; jc1; jw; a; b; c; xc , were identi®ed by non-linear regression (in house program
97
XREGA), minimising the sum of squares of deviations from 542 observation points (Ti ; xi ; ji ), see Table 2. Interpretation and reliability of an empirical model with such a high number of parameters is always questionable, however, the con®dence intervals of all the parameters calculated from the covariance matrix are suciently narrow (see Table 2) and some predicted values can be veri®ed directly: For example jw 0:05 S m 1 corresponds rather well to the electric conductivity of tap water (0.043 S m 1 at 50°C) and xc 0:454 visually ®ts the mass fraction characterising the sudden change of trends at higher temperatures, see Fig. 6. All parameters have the correct sign, and for example the negative sign of the parameter c ensures not only a progressive increase of conductivity with temperature at a constant x, but also an observed mild shift of maxima j x towards higher concentrations with increasing temperature. It seems that the physical relevance of the parameters would allow a slight extrapolation of conductivity to higher temperatures, may be up to 90°C. Exactly the same procedure and primary data were used for the modi®ed Casteel±Amis model (10), and results are presented in Table 2. This model approxi-
Table 1 Coecients of quadratic approximation (11) of speci®c electrical conductivity ji S m 1 , measured within the temperature range 25±72°C i
x
p0i S m 1
p1i S m
1 2 3 4 5 6 7 8 9 10 11
0 0.02 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
1.48E-5 1.33E-1 3.07E-1 4.22E-1 5.88E-1 5.47E-1 4.81E-1 2.73E-1 9.02E-2 1.79E-2 )4.10E-5
7.20E-7 5.25E-3 1.28E-2 1.90E-2 2.87E-2 3.13E-2 2.96E-2 1.92E-2 9.71E-3 1.20E-3 9.39E-7
1
°C 1
p2i S m
1
°C 2
1.70E-10 6.00E-6 1.40E-5 1.90E-5 4.70E-5 7.80E-5 1.21E-4 1.49E-4 1.47E-4 9.20E-5 1.18E-8
Table 2 Parameter values for the model (9) and the modi®ed Castel±Amis model (10) for the speci®c electrical conductivity of coee (minimisation of standard deviation for N 542 observation points, within the range T 2 (25°C, 72°C) and x 2 (0, 0.8)) Parameters of model (9)
Values and con®dent intervals
Parameters of model (10)
Values and con®dent intervals
jc0 S m 1 jc1 S m 1 °C 1 a b c °C 1 jw S m 1 xc
5:833 0:5 0:2439 0:01 1:731 0:11 2:648 0:16 0:0111 0:0012 0:0503 0:0005 0:454 0:01
jmax 0 S m 1 jmax 1 S m 1 °C 1 xmax 0 xmax 1 °C 1 x y
0:3606 0:140 0:04198 0:0028 0:2667 0:020 0:000678 0:00034 0:4055 0:111 9:941 1:06
Basic statistics r S m 1 R
0.0621 0.9975
r S m 1 R
0.0982 0.9936
98
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 6. Speci®c electrical conductivity as function of coee mass fraction and temperature T : ± 30, ± 40, N ± 50, j ± 60, d ± 70°C Small open rectangles stand for temperatures which dier by 1°C and 2°C from the rated temperatures. Full lines represent Eq. (9) with parameters from Table 2.
mates experimental data rather well, describes all trends, and the con®dence intervals of the parameters are acceptable, but nevertheless basic statistics of errors, see r and R in the Table 2, are signi®cantly worse in comparison with the suggested model (9). Adding the term jw 1 x to the model (10) had no signi®cant in¯uence upon the standard deviation (in fact unbiased estimate was slightly higher, r 0:099, because the number of parameters had been increased from six to seven).
4. Conclusions Immediately after preparation of the coee solution, its rheological behaviour was slightly pseudoplastic with a ¯ow index about 0.9. After some time of the shear application in the viscometer and passing a temperature of 95°C, the coee solutions became Newtonian in the range of measured shear rates 10 6 c 6 1574 s 1 . The viscosity dependence on temperature and coee mass fraction was described by a ®ve parameter relation. The estimated error of viscosity measurements was about 15%. It is not bad result when one considers the inherent experimental diculties with handling concentrated coee solutions (swelling, caramelisation, evaporation etc.).
Quite good agreement with the viscosity data measured by Weisser (1972) con®rmed that the coee viscosity does not depend much on the coee type or the method of the coee drying and treatment. The speci®c electrical conductivity was described by a seven parameter model based on the idea that the amount of dissociated coee molecules is proportional to the coee mass fraction and water mass fraction. This model describes the conductivity with a standard deviation of 0.062 which is much lower than the standard deviation of the modi®ed Casteel±Amis model (r 0:098). The speci®c electrical conductivity exhibits maxima at concentrations of about x 0:35. The higher the temperature the greater the shift of the maximum towards higher concentrations. The maximum electric conductivity of coee solution is about 40 times higher than the conductivity of tap water at the same temperature. The viscosity and speci®c electrical conductivity data obtained in this article should assist the design of equipment for the treatment of highly concentrated coee extracts. Acknowledgements This research has been subsidized by ABCAR D.I.C. Process (Engineering Spin-o Company of the University of La Rochelle, France) and the Research project of the Ministry of Education of the Czech Republic J04/ 98:21220008. References Bird, R. B., Armstrong, R. C., & Hassager, O. (1987). Dynamics of polymeric liquids, Vol. 1 Fluid mechanics. New York: Wiley. De Diego, A., Madariaga, J. M., & Chapela, E. (1997). Empirical model of general application to ®t (j; c; T ) experimental data from concentrated aqueous electrolyte solutions. Electrochemica Acta, 42(9), 1449±1456. Garattini, S. (1993). Caeine, coee, and health. New York: Raven Press. Koryta, J., Prochazka, K., Fischer, O., Dvorak, J., Postler, M., Micka, K., Fellner, P., & Jakes, D. (1976). Theory of electrolytes (in Czech), CSAV, No.7. Praha: Academia. Masters, K. (1976). Spray drying. New York: Wiley. Weisser, H. (1972). Measurements of physical properties of solutions of coee extract. Potravinarska chladõcõ technika, 3, 136±138 (in Czech).
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Viscosity and electrical conductivity of concentrated solutions of soluble coee V. Sobolõk b
y b, V. Tovcigrecko c, M. Delgado a, K. Allaf , R. Zitn
a,*
a
a LMTAI, University of La Rochelle, Av. Michel Crepeau, La Rochelle 17042, France Institute of Process Engineering, Faculty of Mechanical Engineering, Czech Technical University, Technick a 4, 16000 Prague 6, Czech Republic c Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic, Rozvojov a 135, 165 02 Prague 6, Czech Republic
Received 14 October 2000; accepted 29 January 2001
Abstract Viscosity of concentrated aqueous solutions (x 0:5±0:8) of soluble coee was measured in the temperature range 25±95°C. After some time of the shear application in the viscometer and passing a temperature of 95°C, the rheological behaviour was found to be Newtonian. The viscosity was correlated by a ®ve parameter function of coee mass fraction and temperature. Speci®c electrical conductivity of coee solutions in tap water (x 0±0:8) was measured in the temperature range 25±72°C. A seven parameter model based on the assumption that the solution is composed of a partially dissociated species and water describes very well the measured data. A modi®ed Casteel±Amis model equation has been identi®ed for comparison. The conductivity dependence on mass fraction exhibits maxima, which are shifted towards higher concentrations the higher is the temperature. Viscosity, refractivity index, density and thermal conductivity of aqueous coee solutions (x 0±0:5) are reviewed. Ó 2001 Elsevier Science Ltd. All rights reserved. Keywords: Coee extract; Soluble coee; Viscosity; Flow behaviour; Electrical conductivity; Physical properties
1. Introduction Coee is composed of more than 700 components. Purine alkaloids (caeine etc.), minerals, bases, chlorogenic acids, lipids, aliphatic acids and carbohydrates (arabinose, sucrose etc.) and amino acids (tryptophan) are some of them (Garattini, 1993). Data on physical properties of aqueous solutions of soluble coee are scarce although the world production is very important and the coee extracts enjoy an extensive consumer market. The manufacturers guard the con®dentiality of processing. We have found only one paper (Weisser, 1972) which deals with the viscosity and other physical properties of aqueous coee solutions. In this paper, viscosity, surface tension, thermal conductivity, index of refraction and freezing curves were measured in solutions with coee mass fractions in the range 0±0.5. Dierent mixtures were examined of several coee types prepared either by freeze drying (Vox Mocca, Vox Robusta) or by spray drying (Nescafe Gold, Maxwell Exquisit). As this paper is written in *
Corresponding author. Tel.: +33-5-4645-8780; fax: +33-5-46458616. E-mail address: [email protected] (V. Sobolõk).
Czech, the most important results are summarised in the following paragraphs. The dependence of the refractivity index on the coee mass fraction x was expressed by the relation: 2 2 n20 D 1:333 0:1728x 8:93 10 x :
1
At x 0:5, the refractivity indexes of the coee and sucrose are about 1.44 and 1.42, respectively. It is dicult to measure the refractivity index of more concentrated coee solutions because the dark brown colour hinders in scale observation. The density was calculated from the density of water qW and the true density of the solid coee qC : 1 x 1 x ; q x; T qC qW
2
where qW 1000 0:036 T 0:004 T 2 and qC 1654 1:79 T 0:0063 T 2 . The dierence in the densities of the coee and sucrose is about 1% at x 0:5. The ¯ow curves were measured by a Haake rotational viscometer. The rheological behaviour was characterised as slightly pseudoplastic and thixotropic. The values of the limiting viscosity l1 are also given, i.e., the values which did not change with increasing shear rate. The viscosity increased non recoverably when the solution
0260-8774/01/$ - see front matter Ó 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 2 6 0 - 8 7 7 4 ( 0 1 ) 0 0 0 4 2 - 5
94
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98 Notation a, b, c parameters in Eqs. (8) and (9) k number of model parameters refraction index (yellow Na light at 20°C) n20 D N number of data pji parameters in Eq. (11) R correlation coecient, q P PN j xj ; Tj 2 = Nj1 jj j2 R 1 j1 jj T temperature (°C) x, y parameters of modi®ed Casteel±Amis model, Eq. (10), ()) c shear rate (s 1 ) j speci®c electrical conductivity (S m 1 )
was stored for a longer time. This fact was explained by swelling of high molecular substances which are present in the coee. Weisser (1972) did not ®nd any important dierence in viscosity between dierent types of coee prepared either by spray drying or by freeze drying. Due to the presence of surface active substances, the surface tension of coee solutions was found to be lower than that one of water. For x > 0:1, the surface tension was equal to 0.042 N m 1 at 20°C and 0.037 N m 1 at 40°C. The thermal conductivity of coee solutions was found to be the same as the conductivity of sucrose solutions. It was described by the relation: k 10
3
565:1 1:8T
0:0058T 2 1
0:54x:
3
Intensi®cation of soluble coee production requires the treatment of more concentrated solutions. The present paper focuses on the properties which are important for ohmic heating and treatment of highly concentrated coee solutions, i.e., viscosity and electric conductivity. The coee studied was a freeze dried mixture of 65% coee arabica (Colombia) and 35% coee robusta (Brazil), sold under the name ``Cafe ®ltre'' by Carrefour (France). 2. Flow behaviour The dependencies of shear stress on shear rate were measured in a Rheotest II controlled rate viscometer. More details about basic rheological concepts can be found in the book of Bird, Armstrong, and Hassager (1987). Two dierent geometry were used consisting of one external cup with a diameter of 40 mm and two internal cylinders, S1 and S2 with diameters 39.2 and 37.6 mm and a length of 72 mm. The temperature of the external cup and hence of the sample was controlled by a water circulator. Solutions with coee mass fractions x 0:5±0:8 in tap water were examined in a temperature range of 25±95°C. The samples with lower concentrations, x < 0:75, were prepared in a glass beaker
j x; T j jij k l l1 q x xc r s
statistically smoothed estimate of j S m 1 mean value speci®c electrical conductivity S m 1 parameters in Eq. (9) thermal conductivity W m 1 °C 1 viscosity (Pa s) limiting viscosity (Pa s) density kg m 3 coee mass fraction (kg dry coee/ kg solution) critical coee mass fraction in Eqs. (8) and (9) (kg dry coee/ kg solution) standard deviation of j S m 1 , q PN j xj ; Tj 2 = N k r j1 jj shear stress (Pa)
whereas the more concentrated samples were mixed directly in the viscometer cup. The preparation was similar in both cases. The dry coee was poured into water with a temperature of 25°C. The sample was then agitated with a glass bar and heated to 70°C. The stainless steel viscometer cup was preheated to 60°C before it was ®lled with a prepared sample. The cup was then pressed onto the measuring cylinder. A thin plastic disc covered the sample surface to minimize water evaporation. By means of the external cup, the sample was then cooled to the lowest temperature at which the viscosity measurements started. The torque was measured at rotational rates going from the minimum to the maximum one and reverse. The temperature was then increased to the next one and measurements were done at increasing and then decreasing shear rate. After reaching the maximum temperature of 95°C, the measurements were repeated at decreasing temperature steps. The measurements on one sample took about 4 h. The ¯ow curves measured immediately after the sample preparation, i.e., in the series with increasing temperature, exhibited slightly pseudoplastic behaviour with the ¯ow index of about 0.9 and a higher apparent viscosity than the curves measured some time later after passing the maximum temperature of 95°C. The latter curves exhibited Newtonian behaviour. An example of primary data is shown in Fig. 1. This dierence in ¯ow behaviour can be explained by the presence either of larger molecules or of solid particles during the ®rst phase. The concentrated solution of coee extract needs a higher temperature (90±95°C) or a longer exposition to shear rate to become homogeneous or to destroy the large molecules. The data presented in this paper correspond to the viscosity measured in the second phase after passing 95°C. We suppose that the rheological behaviour in this phase correspond to the behaviour of the coee solution after its extraction from granulized roasted coee particles which is carried out at temperatures as high as 180°C (Masters, 1976). The measurements were done until the maximum shear rates attainable in the viscometer. The shear rate
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 1. Flow curves of coee solutions, x 0:7, at 40°C measurements immediately after sample preparation, measurements after 2 h after passing 95°C.
was limited either by the maximum rotational rate or by the maximum torque, which can be achieved in the viscometer. For x 0:5, this limit was the maximum shear rate generated by the largest cylinder S1 (smallest gap). The value of the shear rate in this case is equal to 1574 s 1 . For the solutions with higher viscosity, x > 0:5, the limiting factor was the maximum torque and the smaller cylinder S2 (larger gap) had to be used. For this geometry, the maximal shear rates were lower than 455 s 1 . The viscosity dependence on the absolute temperature and concentration is shown in Fig. 2. For x in the range of 0.5±0.8, the viscosity was ®tted by the relation l exp 1:141
22:42x
973:1
17:78x2
Fig. 3. Dependence of viscosity on temperature and concentration for coee solutions with low concentration [2] x: d ± 0, ± 0.1, ± 0.2, N ± 0.3, ± 0.4, M ± 0.5.
measured by Weisser (1972) for x 0:5 is shown by the open diamond symbols. It does not exhibit great deviations from our measurements. For 60°C, we obtained a value of 0.019 Pa s whereas Weisser (1972) indicates a value of 0.024 Pa s. This quite good agreement con®rms the conclusion that the viscosity is almost independent of the coee type and its treatment. With the aim of extending the range of viscosity dependence also to low concentrations, (x from 0 to 0.5), the results of Weisser (1972) are shown in Fig. 3. The best ®t of these data is by the relationship l exp 12:96
9:43x 8:12x2
1789 4382x= T 273:15:
2
17923x = T 273:15:
95
5
4
The maximum error of viscosity evaluation using this relation was estimated to be less then 15%. The viscosity
3. Speci®c electrical conductivity 3.1. Model design
Fig. 2. Dependence of viscosity on temperature and concentration for concentrated coee solutions x: d ± 0.5, ± 0.6, ± 0.66, N ± 0.7, ± 0.74, M ± 0.8, } ± data (Weisser, 1972) for x 0:5.
Speci®c electric conductivity of electrolytes jS m 1 depends upon concentration, mutual interactions and mobility of ions. It is known that increasing viscosity decreases conductivity. Nevertheless our attempt to correlate viscosity and conductivity of the coee solutions failed totally. Some theoretical results originated from the Debye±H uckel theory can be applied to weak electrolytes, see Koryta et al. (1976), but for concentrated electrolytes empirical models, e.g., models describing j x by the normal distribution function or models of the form j x a x expb x, are usually preferred (see De Diego, Madariaga, & Chapela, 1997). A new empirical model describing the temperature and concentration dependency of speci®c electrical conductivity is based on the concept, that the coee solution is composed of water having conductivity jW , dissociated coee species with conductivity jc and non
96
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
dissociated species which act as insulators. It is assumed than the amount of dissociated species is proportional to the mass fraction of coee, x, and also to the mass fraction of water, 1 x,
3.2. Experimental results and model identi®cation
This model does not ®t the experimental data properly with a constant exponent m. Therefore, this exponent must be considered as a function of temperature and concentration, m T ; x. The following empirical Eq. (8) will be used for processing data, exhibiting a slight change of trends at a concentration of xc
The speci®c electrical conductivity was measured by the conductivity probe LF 340 TetraCon 325/S which is suitable for highly viscous materials and pastes. The probe is composed of four graphite electrodes and a thermometer embedded in an epoxy casing. The electrodes are ¯ush mounted in an axial groove. The dimensions of the probe and the amount of coee sample follow from Fig. 4. The samples were prepared by mixing the coee extract with cold tap water in a beaker which was then immersed in water heated to 80°C. The sample was then ®lled into a small cylindrical glass cup and the probe was immersed into the sample. The temperature of the cup was controlled by a water circulator. The measurements started at the lowest temperature (25°C) and continued until 72°C. Approximately 50 values of the conductivity were recorded for each concentration at dierent temperatures. The primary data are shown in Fig. 5. For the reason of clarity, only every second point is depicted. The range of measured temperatures can be also deduced from Fig. 5. The simplest approach to modelling is based upon the quadratic approximation of temperature dependence evaluated separately for each measured concentration xi
m a b max x; xc cT :
ji T p0i p1i T p2i T 2 :
xc x 1
xm :
6
Experiments indicate that the conductivity of concentrated coee depends strongly on temperature and therefore we shall assume linear relationship for approximation of jc T , while temperature dependency of jw for tap water will be neglected in view of the facts, that jw is very small and we are interested in concentrated solutions. Combining speci®c electrical conductivity of three components (non dissociated species-insulator, water, and dissociated species) according to a simple model of parallel resistors, we obtain j jc0 jc1 T x 1
m
x jw 1
x:
7
8
For concentrations bellow the critical concentration xc , m is a function of T only. The resulting model is a rather complicated 7-parametric relation j x; T jc0 jc1 T x 1 jw 1
x:
xab
max x;xc cT
9
The proposed model (9) will be compared with the Casteel±Amis equation for j c; T modi®ed by De Diego et al. (1997) by inclusion of temperature. The Diego's model is based on ®tting of maximum conductivity jmax at the corresponding concentration cmax . The following Eq. (10) diers from the original Diego's model only by replacing concentration c with the mass fraction x: x x j x; T jmax 0 jmax 1 T xmax 0 xmax 1 T exp y x xmax 0 xmax 1 T 2 x x 1 : 10 xmax 0 xmax 1 T The modi®ed Casteel±Amis equation has six parameters, jmax 0 ; jmax 1 ; xmax 0 ; xmax 1 , x, y and only two of them, jmax 0 ; jmax 1 , are at linear terms. In view of the fact, that the predicted conductivity equals zero for x 0, the model (10) cannot describe the conductivity of pure water.
11
Identi®cation of the coecients p0i ; p1i ; p2i by linear regression was done with a relative standard deviation smaller than 1.5%. The results are summarised in Table 1 and shown by full lines in Fig. 5. The signi®cance of the coecient of the second power member, p2i , is more important the higher the concentration. Eq. (11) with the parameters given in Table 1 enable us to access the
Fig. 4. Experimental set-up for conductivity measurements (a) front view, (b) cut-away side view 1 ± conductivity probe, 2 ± electrodes, 3 ± cup, 4 ± cap, 5 ± sample. Dimensions are in millimetres.
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 5. Dependence of speci®c electrical conductivity on temperature x: M ± 0, ± 0.02, N ± 0.05, ± 0.1, ± 0.2, d ± 0.3, ± 0.4, ± 0.5, j ± 0.6, } ± 0.7, r ± 0.8. Full lines represent Eq. (11) with parameters from Table 1.
primary data with a smaller deviation than the models where the both T and x are variable. Parameters of model (9), jc0; jc1; jw; a; b; c; xc , were identi®ed by non-linear regression (in house program
97
XREGA), minimising the sum of squares of deviations from 542 observation points (Ti ; xi ; ji ), see Table 2. Interpretation and reliability of an empirical model with such a high number of parameters is always questionable, however, the con®dence intervals of all the parameters calculated from the covariance matrix are suciently narrow (see Table 2) and some predicted values can be veri®ed directly: For example jw 0:05 S m 1 corresponds rather well to the electric conductivity of tap water (0.043 S m 1 at 50°C) and xc 0:454 visually ®ts the mass fraction characterising the sudden change of trends at higher temperatures, see Fig. 6. All parameters have the correct sign, and for example the negative sign of the parameter c ensures not only a progressive increase of conductivity with temperature at a constant x, but also an observed mild shift of maxima j x towards higher concentrations with increasing temperature. It seems that the physical relevance of the parameters would allow a slight extrapolation of conductivity to higher temperatures, may be up to 90°C. Exactly the same procedure and primary data were used for the modi®ed Casteel±Amis model (10), and results are presented in Table 2. This model approxi-
Table 1 Coecients of quadratic approximation (11) of speci®c electrical conductivity ji S m 1 , measured within the temperature range 25±72°C i
x
p0i S m 1
p1i S m
1 2 3 4 5 6 7 8 9 10 11
0 0.02 0.05 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80
1.48E-5 1.33E-1 3.07E-1 4.22E-1 5.88E-1 5.47E-1 4.81E-1 2.73E-1 9.02E-2 1.79E-2 )4.10E-5
7.20E-7 5.25E-3 1.28E-2 1.90E-2 2.87E-2 3.13E-2 2.96E-2 1.92E-2 9.71E-3 1.20E-3 9.39E-7
1
°C 1
p2i S m
1
°C 2
1.70E-10 6.00E-6 1.40E-5 1.90E-5 4.70E-5 7.80E-5 1.21E-4 1.49E-4 1.47E-4 9.20E-5 1.18E-8
Table 2 Parameter values for the model (9) and the modi®ed Castel±Amis model (10) for the speci®c electrical conductivity of coee (minimisation of standard deviation for N 542 observation points, within the range T 2 (25°C, 72°C) and x 2 (0, 0.8)) Parameters of model (9)
Values and con®dent intervals
Parameters of model (10)
Values and con®dent intervals
jc0 S m 1 jc1 S m 1 °C 1 a b c °C 1 jw S m 1 xc
5:833 0:5 0:2439 0:01 1:731 0:11 2:648 0:16 0:0111 0:0012 0:0503 0:0005 0:454 0:01
jmax 0 S m 1 jmax 1 S m 1 °C 1 xmax 0 xmax 1 °C 1 x y
0:3606 0:140 0:04198 0:0028 0:2667 0:020 0:000678 0:00034 0:4055 0:111 9:941 1:06
Basic statistics r S m 1 R
0.0621 0.9975
r S m 1 R
0.0982 0.9936
98
V. Sobolõk et al. / Journal of Food Engineering 51 (2002) 93±98
Fig. 6. Speci®c electrical conductivity as function of coee mass fraction and temperature T : ± 30, ± 40, N ± 50, j ± 60, d ± 70°C Small open rectangles stand for temperatures which dier by 1°C and 2°C from the rated temperatures. Full lines represent Eq. (9) with parameters from Table 2.
mates experimental data rather well, describes all trends, and the con®dence intervals of the parameters are acceptable, but nevertheless basic statistics of errors, see r and R in the Table 2, are signi®cantly worse in comparison with the suggested model (9). Adding the term jw 1 x to the model (10) had no signi®cant in¯uence upon the standard deviation (in fact unbiased estimate was slightly higher, r 0:099, because the number of parameters had been increased from six to seven).
4. Conclusions Immediately after preparation of the coee solution, its rheological behaviour was slightly pseudoplastic with a ¯ow index about 0.9. After some time of the shear application in the viscometer and passing a temperature of 95°C, the coee solutions became Newtonian in the range of measured shear rates 10 6 c 6 1574 s 1 . The viscosity dependence on temperature and coee mass fraction was described by a ®ve parameter relation. The estimated error of viscosity measurements was about 15%. It is not bad result when one considers the inherent experimental diculties with handling concentrated coee solutions (swelling, caramelisation, evaporation etc.).
Quite good agreement with the viscosity data measured by Weisser (1972) con®rmed that the coee viscosity does not depend much on the coee type or the method of the coee drying and treatment. The speci®c electrical conductivity was described by a seven parameter model based on the idea that the amount of dissociated coee molecules is proportional to the coee mass fraction and water mass fraction. This model describes the conductivity with a standard deviation of 0.062 which is much lower than the standard deviation of the modi®ed Casteel±Amis model (r 0:098). The speci®c electrical conductivity exhibits maxima at concentrations of about x 0:35. The higher the temperature the greater the shift of the maximum towards higher concentrations. The maximum electric conductivity of coee solution is about 40 times higher than the conductivity of tap water at the same temperature. The viscosity and speci®c electrical conductivity data obtained in this article should assist the design of equipment for the treatment of highly concentrated coee extracts. Acknowledgements This research has been subsidized by ABCAR D.I.C. Process (Engineering Spin-o Company of the University of La Rochelle, France) and the Research project of the Ministry of Education of the Czech Republic J04/ 98:21220008. References Bird, R. B., Armstrong, R. C., & Hassager, O. (1987). Dynamics of polymeric liquids, Vol. 1 Fluid mechanics. New York: Wiley. De Diego, A., Madariaga, J. M., & Chapela, E. (1997). Empirical model of general application to ®t (j; c; T ) experimental data from concentrated aqueous electrolyte solutions. Electrochemica Acta, 42(9), 1449±1456. Garattini, S. (1993). Caeine, coee, and health. New York: Raven Press. Koryta, J., Prochazka, K., Fischer, O., Dvorak, J., Postler, M., Micka, K., Fellner, P., & Jakes, D. (1976). Theory of electrolytes (in Czech), CSAV, No.7. Praha: Academia. Masters, K. (1976). Spray drying. New York: Wiley. Weisser, H. (1972). Measurements of physical properties of solutions of coee extract. Potravinarska chladõcõ technika, 3, 136±138 (in Czech).