Viscosity and electrical conductivity of concentrated solutions of soluble coffee
V.Sobolík 1, V.Tovcigrecko 2, M.Delgado1, R.Žitný 3, K.Allaf 1
1
LMTAI, University of La Rochelle, Av. Michel Crepeau, 17042 La Rochelle, France
e-mail: vsobolik@univ-lr.fr, kallaf @univ-lr.fr
2
Institute of Chemical Process Fundamentals, Academy of Sciences of the Czech Republic,
Rozvojová 135, 16502 Prague 6, e-mail: tovcigrecko@icpf.cas.cz
3
Institute of Process Engineering, Czech Technical University, Faculty of Mechanical
Engineering, Technická 4, 16000 Prague 6, e-mail: zitny@fsid.cvut.cz
Abstract
Viscosity of concentrated solutions ( = 0.5-0.8) of soluble coffee was measured in the
temperature range 25 - 95°C. After homogenisation, the rheological behaviour was found to
be Newtonian. The viscosity was correlated by a five parameter function of concentration and
absolute temperature.
Specific electrical conductivity of coffee solutions in water ( = 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. Modified Casteel-Amis model equation has been identified for comparison.
The conductivity dependence on concentration exhibits maxima which are the more shifted
towards higher concentrations the higher is the temperature.
Introduction
Coffee is composed of more than 700 components. Purine alkaloids (caffeine etc.),
minerals, bases, chlorogenic acids, lipids, aliphatic acids and carbohydrates (arabinose,
sucrose etc.) and amino acids (tryptophan) are some of them [1].
1
The data on physical properties of the aqueous solutions of soluble coffee are scarce
although the world production is very important and the coffee extracts enjoy extensive
consumer market. The manufacturers guard probably the confidentiality of processing. We
have found only one paper [2] which deals with the viscosity of aqueous coffee solutions. In
this paper, the viscosity, surface tension, thermal conductivity, index of refraction and the
freezing curves were measured in the solutions with coffee mass fraction 0-0.5. Different
mixtures were examined of several coffee sorts prepared either by freeze drying (Vox Mocca,
Vox Robusta) or by spray drying (Nescafé Gold, Maxwell Exquisit). As the paper [2] is
written in Czech, the most important results are summarised in the following paragraphs.
The dependence of the refractivity index on the coffee mass fraction  was expressed
by the relation:
nD20  1.333  0.1728   8.93.10 2  2
(1)
At  = 0.5, the refractivity indexes of the coffee and sucrose are about 1.44 and 1.42,
respectively. It is difficult to measure the refractivity index of more concentrated coffee
solutions because the dark brown colour hinders in scale observation.
The density was calculated from the density of water W and the true density of the
solid coffeeC:
1
 1


 ( , T )  C
W
(2)
where W = 1000 - 0.036- 0.004 2 and C = 1654 - 1.79- 0.0063 2. The difference in
the densities of the coffee and sucrose is about 1% at  = 0.5.
The flow curves were measured by a rotational viscometer Haake. The rheological
behaviour was characterised as slightly pseudoplastic and thixotropic. The values of the
limiting viscosity  are also given, i.e. the values which did not change with increasing shear
rate. The viscosity increased non recoverably when the solution was stored for a longer time.
2
This fact was explained by swelling of high molecular substances which are present in the
coffee. Weisser did not found any important difference in viscosity of different sort of coffee
prepared either by spray drying or by freeze drying.
Due to presence of surface active substances, the surface tension of coffee solutions was
found to be smaller than that one of water. For  > 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 coffee solutions was found to be the same as the
conductivity of sucrose solutions. It was described by the relation:
  103 (5651
.  18
. T  0.0058T 2 )(1  054
. )
(3)
Intensification of soluble coffee 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 coffee solutions, i.e. viscosity and electric conductivity.
The coffee studied was a freeze dried mixture of 65% coffee arabica (Colombia) and 35 %
coffee robusta (Brazil), sold under the mark “Café filtré” by Carrefour (France).
1 Viscosity
The dependencies of shear stress on shear rate [3] were measured in a controlled rate
viscometer Rheotest II, (VEB Prüfgeräte, Medingen, Germany). Two different 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
coffee mass fraction  = 0.5 – 0.8 in tap water were examined in a temperature range of
25 - 95°C. The samples with the lower concentrations,  < 0.75, were prepared in a glass
beaker whereas the more concentrated samples were mixed directly in the viscometer cup.
3
The preparation was similar in both cases. The dry coffee 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 filled with a prepared
sample. The cup was then pressed onto the measuring cylinder. A thin plastic disc covered the
sample surface with the aim to diminish water evaporation. By means of the external cup, the
sample was then cooled to the low temperature at which the viscosity measurements started.
The torque was measured at shear 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 of one
sample took about 4 hours.
The flow curves measured immediately after the sample preparation, i.e. in the series
with increasing temperature, exhibited slightly pseudoplastic behaviour with the flow 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 difference in flow behaviour can be
explained by the presence either of larger molecules or of solid particles during the first
phase. The concentrated solution of coffee 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.
The measurements were done until the maximum shear rates shown in Fig.2. The range
of the shear rate applied in the measurements lies below the corresponding lines. For example
the dotted area represents the range for = 0.8. The shear rate was limited either by the
maximum rotational rate or by the maximum torque, which can be achieved in the viscometer.
4
For = 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,  > 0.5, the limiting factor was the maximum torque and the smaller
cylinder S2 (larger gap) has to be used. For this geometry, the maximum shear rate is equal to
455 s-1 .
The viscosity dependence on the absolute temperature and concentration is shown in
Fig.3. For  (0.5-0.8), the viscosity was fitted by the relation
  exp[1.141  22.42  17.78 2  (973.1  17923 2 ) /(T  273.15)]
(4)
The maximum error of viscosity evaluation using this relation was estimated to be less then
15 %. The viscosity measured by Weisser [2] for = 0.5 is shown by the open diamond
symbols. It does not exhibit great deviations from our measurements. For 60°C, we
determined 0.019 Pa.s whereas Weisser has found 0.024 Pa.s. This quite good agreement
confirms the conclusion of paper [2] that the viscosity is almost independent of the coffee sort
and its treatment.
With the aim to extend the range of viscosity dependence also for low concentrations,
(0-0.5), the results of paper [2] are shown in Fig. 4. The best fit of these data is by the
relation
  exp[ 12.96  9.43  812
.  2  (1789  4382 ) / (T  27315
. )]
(5)
2 Specific electrical conductivity
2.1
Model design
Specific electric conductivity of electrolytes  [S.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 coffee
5
solutions failed totally. Some theoretical results originated from Debye-Hückel theory can be
applied for weak electrolytes [4], but for concentrated electrolytes empirical models, e.g.
normal distribution of () or models of the form ()=a() exp[b()], are usually
preferred [5].
A new empirical model describing the temperature and concentration dependency of
specific electrical conductivity is based on the idea, that the coffee solution is composed of
water having conductivity w [S.m-1], dissociated coffee species with conductivity c and non
dissociated species which is an insulator. It is assumed than the amount of dissociated species
is proportional to the mass fraction of coffee, , and also to the mass fraction of water, 1-,
c   (1   ) m .
(6)
Experiments indicate that the conductivity of concentrated coffee depends strongly on
temperature and therefore we shall assume linear relationship for approximation of c(T),
while temperature dependency of tap water will be neglected in view of the fact, that w is
very small.
Combining specific electrical conductivity of three components (non dissociated species
– insulator, water, and dissociated species) according to a simple model of parallel resistors,
we obtain
  ( c0   c1T ) (1   ) m   w (1   )
(7)
This model is not able to describe the experimental data properly with a constant
exponent m which must be considered as a function of temperature and concentration,
m(T, ). The following quite empirical Eq.(8) will be used for processing data, exhibiting a
slight change of trends at concentration c
m  a  b max( ,c )  cT .
(8)
The resulting model is rather complicated 7-parametric relation
6
  ( c0   c1T ) (1   ) a b max( , ) cT   w (1   )
c
(9)
The proposed model (9) will be compared with the Casteel-Amis equation for  (c, T)
modified by Diego [5] by inclusion of temperature. The Diego's model is based on fitting of
maximum conductivity max at the corresponding concentration cmax . The following Eq.(10)
differs from the original Diego's model only by replacing concentration c with the mass
fraction  :
  ( max 0   max 1T )(


) x exp[ y (  max 0  max 1T ) 2  x (
 1)] .
max 0  max 1T
max 0  max 1T
(10)
The modified Casteel-Amis equation has 6 parameters, max0, max1, max0, max1, x, y and only
two of them, max0, max1, are linear. In view of the fact, that the predicted conductivity equals
zero for  = 0, the model (10) cannot describe the conductivity of pure water.
2.2
Experimental results and model identification
The specific electrical conductivity was measured by the conductivity probe LF 340
TetraCon 325/S, (Wissenschaftlich-Technische Werkstatten GmbH, Weilheim, Germany)
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 flush mounted
in an axial groove. Dimensions of the probe and the amount of coffee sample follow from
Fig.5. The samples were prepared by mixing the coffee extract with a cold tap water in a
beaker which was then immersed in water heated to 80°C. The homogenous sample was then
filled 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
low temperature (25°C) and continued until 72°C. The range of temperature and
7
concentration is shown in Fig.6. Approximately 50 values of the conductivity were recorded
for each concentration at different temperatures.
The simplest approach of modelling is based upon the quadratic approximation of
temperature dependence evaluated separately for each measured concentration i
i (T) = p0i + p1iT + p2iT2
(11)
Identification of the coefficients p0i, p1i, p2i by linear regression was done with a relative
standard deviation smaller than 1.5%. The results are summarised in Tab.1.
Parameters of model (9), c0, c1, w, a, b, c, c, were identified by nonlinear regression
(in house program XREGA), minimising sum of squares of deviations from 542 observation
points (Ti,  i , i), see Tab.2. Interpretation and reliability of more or less empirical model
with such a high number of parameters is always questionable, however, confidence intervals
of all parameters calculated from covariance matrix are sufficiently narrow (see Tab.2) and
some predicted values can be verified directly: For example w=0.05 S.m-1 corresponds rather
well to the electric conductivity of tap water (~0.043 S.m-1 at 500C) and  c=0.454 visually
fits the mass fraction characterising sudden change of trends at higher temperatures, see Fig.7.
All parameters have 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 , but also an
observed mild shift of maxima () towards higher concentration with increasing
temperature. It seems that physical relevance of parameters would allow a slight extrapolation
of conductivity to higher temperatures, may be up to 900C.
Exactly the same procedure and primary data were used for identification of modified
Casteel-Amis model (10), and results are presented also in the Tab 2. This model
approximates experimental data rather well, describes all trends, confidence intervals of
parameters are acceptable, nevertheless basic statistics of errors are significantly worse in
8
comparison with the suggested model (9). Adding the term w(1-) to the model (10) had no
significant influence upon the standard deviation (in fact unbiased estimate was slightly
higher, =0.099 S.m-1, because the number of parameters had been increased from six to
seven).
3 Conclusions
Immediately after preparation of the coffee solution, its rheological behaviour was
slightly pseudoplastic with a flow index about 0.9. After some time of the shear application in
the viscometer and passing a temperature of 95°C, the coffee solutions became Newtonian in
the range of measured shear rates (10    1574 s-1).
The viscosity dependence on temperature and concentration was described by a five
parameter relation. The estimated error of viscosity measurements was about 15%. It is not
bad result with respect to the inherent experimental difficulties with handling concentrated
coffee solutions (swelling, caramelisation, evaporation etc.).
Quite good agreement with the viscosity data measured by Weisser [2] confirmed that
the coffee viscosity does not depend much on the coffee sort and the way of the coffee drying
and treatment.
The specific electrical conductivity was described by a seven parameter model based on
the idea that the amount of dissociated coffee molecules is proportional to the coffee mass
fraction and water mass fraction. This model describes the conductivity with a standard
deviation of 0.062 [S.m-1] which is much lower than the standard deviation of the modified
Casteel-Amis model (=0.098 S.m-1).
9
The specific electrical conductivity exhibits maxima at concentrations about  = 0.35.
The higher temperature the greater is the shift of the maximum towards higher concentration.
The maximum electric conductivity of coffee solution is about 40 times higher then the
conductivity of tap water at the same temperature.
The viscosity and specific electrical conductivity data obtained in this article render
possible the design of apparatuses for the treatment of highly concentrated coffee extracts.
Acknowledgements:
This research has been subsidized by the Research project of Ministry of Education of the
Czech Republic J04/98:21220008.
References:
1. Caffeine, coffee, and health. (Ed. Silvio Garattini),: Raven Press, New York, 1993.
2. Weisser H.: Measurements of physical properties of solutions of coffee extract (in Czech),
Potravinářská a chladící technika 3, 136-138 (1972).
3. Bird R.B., Armstrong R.C., Hassager O.: Dynamics of polymeric liquids, Volume 1 Fluid
mechanics, John Wiley & Sons, 1987.
4. Koryta J. et al: Theory of electrolytes (in Czech), CSAV, No.7, Academia Praha, 1976.
5. De Diego A., Madariaga J.M., Chapela E.: Empirical model of general application to fit
(, c, T) experimental data from concentrated aqueous electrolyte solutions,
Electrochemica Acta, Vol.42, No.9, pp.1449-1456, (1997)
10
Notation
a, b, c
parameters in Eqs.(8 and 9)
k
number of model parameters
nD20
refraction index (yellow Na light at 20oC)
N
number of data
pji
parameters in Eq.(11)
R
correlation coefficient,
N
N
R  1    i   i , Ti  /   i   
2
i 1
i 1
T
temperature [°C]
x, y
parameters of modified Casteel-Amis model, Eq.(10), [-]

shear rate [s-1]

specific electrical conductivity [S.m-1]

mean value specific electrical conductivity [S.m-1]
ij
parameters in Eqs.(9)

thermal conductivity [W.m-1.°C-1]

viscosity [Pa.s]

density [kg.m-3]

coffee mass fraction [kg dry coffee/ kg solution]

standard deviation [S.m-1] ,  
N
 
i 1

2
   i , Ti  /( N  k )
2
i
shear stress [Pa]
11
Figure captions
Fig.1 Flow curves of coffee solutions,  = 0.7, at 40°C
measurements immediately after sample preparation
measurements after 2 hours after passing 95°C
Fig.2 Range of measured shear rates
Fig.3 Dependence of viscosity on temperature and concentration for concentrated coffee
solutions
:
- 0.5,
- 0.6,
- 0.66,
- 0.7,
- 0.74,
- 0.8,
- data [2] for = 0.5
Fig.4 Dependence of viscosity on temperature and concentration for coffee solutions with low
concentration [2]
:
- 0,
- 0.1,
- 0.2,
- 0.3,
- 0.4,
- 0.5
Fig.5 Experimental set-up for conductivity measurements
a) front view, b) cut of side view
1 – conductivity probe, 2 – electrodes, 3 – cup, 4 – cap, 5 - sample. Dimensions are in
millimetres.
Fig.6 Range of measured specific electrical conductivity
Fig.7 Specific electrical conductivity as function of mass fraction and temperature
T:
- 30,
- 40,
- 50,
- 60,
- 70°C
Small open rectangles stand for temperatures which differ by 1 and 2°C from the rated
temperatures. Full lines represent Eq.(9).
12
Tab.1 Coefficients of quadratic approximation (11) of specific electrical conductivity
i [S.m-1], measured within the temperature range 25 to 72 °C.
i
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
p0i [S.m-1]
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
p1i [S.m-1.°C-1]
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
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
13
Tab.2 Identifications of the model (9) and the modified Castel-Amis model (10) for the
specific electrical conductivity of coffee (minimisation of standard deviation for N = 542
observation points, within the range T(25°C, 72°C) and  (0, 0.8))
Parameters of
model (9)
c0 [S.m-1]
Values and confident.
Parameters of
intervals
model (10)
5.833 0.5
max0 [S.m-1]
c1 [S.m-1.°C-1]
0.2439 0.01
a
1.731 0.11
2.648 0.16
b
max1 [S.m-1.°C-1]
max0
max1 [°C-1]
Values and
confident. intervals
0.3606 0.140
0.04198 0.0028
0.2667 0.020
0.000678 0.00034
c [°C ]
-0.0111 0.0012
x
0.4055 0.111
w [S.m-1]
c
[S.m-1]
0.0503 0.0005
y
-9.941 1.06
-1
R
0.454 0.01
0.0621
0.9975
[S.m-1]
0.0982
R
0.9936
14
1000
 , Pa
100
10
1
1
10
100
 , s-1
1000
Fig.1 Sobolik et al.
15
10000
 s
 = 0.5
1000
0.6
0.65
100
0.7
0.75
0.8
10
20
40
60
80
T ,C
100
Fig.2 Sobolik et al.
16
1E+2
1E+1
  Pas
1E+0
1E-1
1E-2
1E-3
20
40
60
T, ° C
80
100
Fig.3 Sobolik et al.
17
1E+0
1E-1
  Pas
1E-2
1E-3
1E-4
0
20
40
T, ° C
60
80
Fig.4 Sobolik et al.
18
15.3
1
4
5
3
47
2
30
7
a)
28
7
b)
Fig.5 Sobolik et al.
19
80
60
T,° C
40
20
0
0
Fig. 6
0.2
0.4

0.6
0.8
Sobolik et al.
20
3.5
3
 , S/m
2.5
2
1.5
1
0.5
0
0
0.2
0.4

0.6
0.8
Fig.7 Sobolik et al.
21