Chenlo et al., e-rheo.pt, 4 (2004) 1-6
KINEMATIC VISCOSITY OF AQUEOUS SOLUTIONS OF SEVERAL
SUGARS WITH SODIUM CHLORIDE: CORRELATION WITH
CONCENTRATION AND TEMPERATURE
F. Chenlo, R. Moreira, G. Pereira*
Department of Chemical Engineering, University of Santiago de Compostela, Rua Lope Gómez de
Marzoa, 15782 s/n. Santiago de Compostela, (A Coruña), Spain. Phone: 00 34 981 563 100.
e-mail: gepegon@usc.es, eqhenlo@usc.es, eqmoncho@usc.es,
* -Corresponding author
Keywords: Kinematic viscosity, aqueous solutions, empirical model, osmotic dehydration
Nomenclature:
Subscripts:
a...k, correlation parameters defined in eqs. (4) to (8)
F, parameter defined in eq. (4)
m, molality (mol·kg-1)
T, temperature (K)
TR, reduced temperature defined in eq. (3)
ν, kinematic viscosity (m2·s-1)
i = 1, sugars or glycerol; i = 2, sodium chloride; w = water
Abstract: In this paper an equation to model experimental data of kinematic viscosities of aqueous
solutions commonly employed in osmotic dehydration is proposed. The binary and ternary systems are
constituted by water as solvent and by sugars (sucrose, glucose and lactose) and glycerol with or
without sodium chloride as solutes. The range of concentration of all systems studied covers the
typical experimental conditions of interest in this type of processes and temperature varying from 20
to 50 ºC. The parameters of the equation proposed for each system were optimized and the resulting
expression adjusted to experimental data with deviations less than 3.0%.
1-INTRODUCTION
This work is concerned with the reological aspects of aqueous solutions employed in osmotic
dehydration, and particularly, with modelling kinematic viscosities. The operation of
dehydration is a common method for food materials preservation. Important contributions
during the last years have been made to improve the quality and economics of the global
process, particularly, using combined methods where osmotic dehydration constitutes one
step.
Osmotic dehydration consists on the partial removal of water by direct contact of a wet
material with a hypertonic medium, i.e. a high concentrated sugar or salt solution. During
osmotic dehydration there are complex mass transfer phenomena which have been defined as
dewatering-impregnation-soaking of a food material in concentrated solutions [1], [2]. These
processes are commonly studied considering a global resistance to component transport in the
bulk of the body of the food material neglecting the external resistance (this assumption is
difficult to accept for osmotic systems).
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Chenlo et al., e-rheo.pt, 4 (2004) 1-6
For rigorous models the mass transfer resistance in the fluid phase must be taken into account,
and, in this way, the viscosity of the solutions must be known. The choice of osmotic agents
depends on taste, cost, water activity lowering capacity and also viscosity values of the
solutions (these values are high especially when disaccharides are employed).
As the composition of the food material is changing during osmotic process one of the goals
is to control the solids gain that strongly depends on desired final product characteristics and
can also be related with the viscosity of the solution [3].
Additionally, osmotic dehydration is an effective way to reduce overall energy requirements
[4] operating at ambient conditions, but agitation power is necessary and depends directly on
osmotic media viscosity. Working at low temperatures colour and flavour retention are
favoured [5].
Rheological properties of these solutions are function of physicochemical characteristics of
the solutes, composition and temperature of solutions and must be determined experimentally.
In previous papers kinematic viscosity data of binary and ternary aqueous solutions with
several solutes as sodium chloride and sucrose [6], and glucose [7], glycerol [8], and lactose
[9] were experimentally determined and correlated by mean of several single equations.
The aim of this work is to stablish a unique equation for modelling overall experimental data
of kinematic viscosities of the systems above mentioned for both single and two solutes
commonly employed in osmotic dehydration.
2-MODELLING
For modelling, first the binary solutions viscosity experimental data was adjusted, νi (m2·s-1),
with salt and sucrose, glucose, glycerol and lactose, separately. In this way, the follow
expression was obtained:
ν i = ν w ⋅ (1+ Fi )
(1)
where i = 1 is a sugar o glycerol and i = 2 is sodium chloride, νw (m2·s-1) is the kinematic
viscosity of water as function temperature given by [4]:
ν w = 0.09607 ⋅10 −6 ⋅ exp
2.90
TR3
(2)
and TR the reduced temperature:
TR =
T
273.1
(3)
where T (K) is the absolute temperature; and Fi is the term that involves the effect of the
concentration mi (molality) of the solute as:
(
Fi = a ⋅ m i ⋅ exp b·m ic
)
(4)
where a, b and c are parameters.
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Chenlo et al., e-rheo.pt, 4 (2004) 1-6
The parameters a and c don’t change appreciably with temperature, and the following simple
mathematical dependence of the parameter b with the temperature was found:
b=
1
d ⋅ TR3 + e
(5)
where d and e are new parameters for optimizing.
The experimental kinematic viscosity data for ternary solutions of several sugars or glycerol
and sodium chloride were adjusted using an equation that involves the previous expressions
for binary systems and an additional term where the inter-action of both solutes is included.
The equation has the following form:
ν1+ 2 = ν w ⋅ [1 + F1 + F2 + f ⋅ m1 ⋅ m 2 ⋅ exp (g1 ⋅ m1 ) ⋅ exp(g 2 ⋅ m 2 )]
(6)
where F1 and F2 are the particullary form of equation (4), and f, g1 and g2 are new parameters.
To obtain the parameters f and g1 and g2 (the last two are practically constant with
temperature and a mean value is used) and f shows a dependence with temperature that can be
modelled as:
(
f = j ⋅ exp k ·TR3
)
(7)
where j and k are new parameters. Taking into account the previous considerations, and
general equation is obtained:
[
(
ν1+ 2 = ν w 1 + F1 + F2 + j · m1 · m 2 · exp(g1 · m1 )· exp(g 2 · m 2 )· exp k·TR3
)]
(8)
Statistical analysis of experimental data and non-linear fittings were carried out using the
program TableCurve 3D . After optimization of the values of parameters, equation (8) allows
to reproduce the experimental kinematic viscosity data of ternary solutions of several sugars,
glycerol and sodium chloride with high accuracy (deviations less than ±3.0%) using the
parameters values shown in Table 1, where subscript 1 refers to sugar or glycerol and subscript
2 to the sodium chloride in all cases.
Table 1 - Parameters of the model for kinematic viscosities of binary and ternary aqueous solutions.
Solute
Sucrose
Glucose
Lactose
Glycerol
Sodium Chloride
a (m-1)
0.762
0.325
0.720
0.125
0.014
Solutes
Sucrose + NaCl
Glucose + NaCl
Lactose + NaCl
Glycerol + NaCl
j (m-2)
0.851
0.261
0.117
0.028
Binary systems
c
1.12
0.89
1.00
0.22
0.20
Ternary systems
k
-2.130
-1.644
-1.000
-0.866
3
d (mc)
2.430
3.730
1.768
2.291
-0.127
e (mc)
-1.001
-1.689
-1.000
-1.000
0.909
g1 (m-1)
0.600
0.241
0.256
0.076
g2 (m-1)
0.073
0.072
0.235
0.136
Chenlo et al., e-rheo.pt, 4 (2004) 1-6
Figures 1, 2 and 3 show, as example and respectively, both experimental (points) and
calculated (solid lines) data with the equation proposed for solutions of lactose, sodium
chloride and lactose + sodium chloride. Figure 4 shows experimental data versus calculated
values of kinematic viscosity for all ternary systems of glucose with sodium chloride at 25 ºC,
as example.
2.0
20
25
30
35
40
45
50 ºC
6
2 -1
υ 10 (m s )
1.6
1.2
0.8
0.4
0
0.1
0.2
0.3
m1 (mol kg -1)
0.4
0.5
Figure 1 - Experimental and calculated values of kinematic viscosity of lactose aqueous solutions at
several temperatures and concentrations.
2.4
20
25
30
35
40
45
50 ºC
10 6(m2 s -1)
2.0
1.6
1.2
0.8
0.4
0
0.1
0.2
0.3
ml (mol kg -1)
0.4
0.5
Figure 2 - Experimental and calculated values of kinematic viscosity of sodium chloride solutions with
m2 = 4.0 molal at different concentrations of lactose (m1) and temperatures.
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Chenlo et al., e-rheo.pt, 4 (2004) 1-6
2.4
1.6
6
2 -1
υ 10 (m s )
2.0
1.2
m1
0.8
0
0.1
0.2
0.3
0.4
0.5
0.4
0
1
2
3
4
-1
m2 (mol kg )
5
6
Figure 3 - Experimental and calculated values of kinematic viscosity of aqueous solutions with different
molality concentrations of sodium chloride (m2) and lactose (m1) at 25 ºC.
12
6
2
-1
υ calc 10 (m s )
10
8
6
4
2
0
0
2
4
6
8
6
2 -1
υ ex p 10 (m s )
10
12
Figure 4 - Experimental data versus calculated values of kinematic viscosity of all aqueous solutions of
glucose + sodium chloride at 25 ºC.
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Chenlo et al., e-rheo.pt, 4 (2004) 1-6
3-CONCLUSIONS
Proposed equations for binary and ternary systems were tested with several solutions of
interest in osmotic dehydration that allow to estimate the kinematic viscosity in the typical
working range as a function of concentration and temperature of solution. Equations for
ternary systems involve the parameters of the corresponding binary systems and with an
additional term are successfully able to fit experimental data (with maximum deviations of
3.0%). In this way, just one equation form can predict the kinematic values of typical osmotic
media.
ACKNOWLEDGEMENTS
The authors acknowledge to the MCYT and the FEDER the partial support with the project
(AGL2002-00255).
REFERENCES
[1] Shi, G; Le Maguer, M. Osmotic dehydration of foods: mass transfer and modeling aspects.
Food Rev. Int., 18 (2002), 305-335.
[2] Rastogi, N.K.; Raghavarao, K.S.M.S. Recent development in osmotic dehydration:
methods to enhance mass transfer. Trends Food Sci. & Technol., 13 (2002), 48-59.
[3] Giraldo, G.; Talens, P.; Fito, P.; Chiralt, A. Influence of sucrose solution concentration on
kinetics and yield during osmotic dehydration of mango. J. Food Eng., 58 (2003), 33 – 43.
[4] Grabowski, S.; Marcotte, M. ; Poirier, M. ; Kudra, T. Drying characteristics of osmotically
pretreated cranberries-energy and quality aspects. Drying Technol., 20 (2002), 1989-2004.
[5] Ponting, J.D. Osmotic dehydration of fruits – Recent modifications and applications. Proc.
Biochem., 8 (1973), 18-23.
[6] Chenlo, F.; Moreira, R.; Pereira, G.; Ampudia, A. Viscosities of aqueous solutions with
sucrose and sodium chloride of interest in osmotic dehydration processes. J.Food Eng., 54
(2002), 347-352.
[7] Moreira, R.; Chenlo, F.; Pereira, G. Viscosities of ternary aqueous solutions with glucose
and sodium chloride employed in osmotic dehydration operation. J. Food Eng., 57 (2003),
173-177.
[8] Chenlo, F.; Moreira, R.; Pereira, G.; Bello, G. Kinematic viscosity and water activity of
aqueous solutions of glycerol and sodium chloride. European Food Res. Tech., (in press).
[9] Chenlo, F.; Moreira, R.; Pereira, G.; Bello, G. An equation for modeling the kinematic
viscosities of binary and ternary solutions with sugars and sodium chloride as a function of
concentration and temperature. Experimental data of solutions with lactose. Int. J. Food Prop.,
(in press).
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