Relationships between water activity and viscosity of solutions

J. Mazurkiewicza, P. Tomasikb,*, J. Zapotnya

aDepartment of Physics, Mickiewicz Ave., 21, 31 120 Cracow, PolandbDepartment of Chemistry, University of Agriculture, Mickiewicz Ave., 21, 31 120 Cracow, Poland

Received 1 June 2000; received in revised form 10 August 2000; accepted 6 September 2000

Abstract

Water activity, aw, in solutions of NaCl, glycerol, d-glucose, sucrose, and urea was correlated against viscosity, h of these solutions.Relationship is non-linear, which follows the h pa 2w 1 qaw 1 r equation. Generally, these relationships provide control over the wateractivity of solutions at a required viscosity and, vice versa control over viscosity at a given water activity. q 2001 Elsevier Science Ltd. Allrights reserved.

Keywords: Non-linear relationships; Viscosity control; Water availability

1. Introduction

Water is one of the most essential component of food-

stuffs. Its amount therein determines several foodstuffs

properties such, for example, as sensory properties, texture,

stability on storage due to, for instance, enzymatic and non-

enzymatic decomposition (Rockland & Beuchat 1987;

Rockland & Stewart 1981), rheology (Sikora, Mazurkie-

wicz, Tomasik, & Pielichowski, 1999), and phase transfers,

for instance, crystallisation. Amount of water is also a

crucial parameter in foodstuff manufacture and transport.

However, knowledge of the amount of water is expressed

either in moles or molar concentration as expressing as a

molar fraction might be insufcient for controlling the prop-

erties of foodstuffs and processing taking place therein.

Because of hydration and other intermolecular interactions

in the presence of water, not all water molecules present in

the foodstuff will be available for the role they were antici-

pated to play. Such circumstances are usually encountered

in concentrated, (non-ideal solutions) aqueous solutions and

blends. This phenomenon has been explained in the begin-

ning of the twentieth century. It found a practical involve-

ment in form of so-called activity. This term may be

understood as a correction factor to the concentration

expressed in molality, and molar fraction. Depending on

the method used in the determination of the concentration

these correction factors are known as molal and rational

activities, respectively. Obviously, water activity in solu-

tions depends on the molecular structure of solute and its

dissociation (Apelblat & Korin, 1998; Libus, 1996; Pierotti,

Deal, & Derr, 1959; Rudakov & Sergyevskii, 1997; Wang,

Liu, Fan, & Lu, 1994). In multiphase systems a number of

phases is essential (Chou, Sridhar, & Pal, 1998).

In spite of the the appreciation enjoyed for over a century

and the practical application of water activity, such an

approach in food chemistry and technology evokes consid-

erable interest on the level of determination of water activity

coefcients. Among others Chen (1989) reported an abun-

dant collection of water activity coefcients for various

solutes in a wide range of solution concentrations. Recently

(Hills, Manning, & Ridge, 1996), for heterogeneous porous

systems a new theory of water activity was proposed.

Observed activity was calculated as the volume average of

a local, spatially varying activity of water, independently it

resided in the system as bulk, surface, and/or structural

water. This approach might be useful in studying the

water behaviour in foodstuffs.

Rheological behaviour is another important and readily

available property of solutions and suspensions. It is

commonly used for describing foodstuff properties and qual-

ity. Although viscosity has a strong link to the technological

value of solutions and suspensions, and their sensory quality

there are also links to solvation (Mazurkiewicz & Tomasik,

1982), and shape (Batko, Mazurkiewicz, & Tomasik, 1988) of

solutes, state of hydration of ions (Mazurkiewicz, Nowotny-

Rozansa, & Tomasik, 1988) and interpretation of solute

solute interactions in solutions; a method helpful in predicting

the texture of foodstuffs (Mazurkiewicz, Zaleska, & Zapotny,

1993; Mazurkiewicz, Rebilas, & Tomasik, 2000).

Food Hydrocolloids 15 (2001) 4346

0268-005X/01/$ - see front matter q 2001 Elsevier Science Ltd. All rights reserved.

PII: S0268-005X(00)00048-5

www.elsevier.com/locate/foodhyd

* Corresponding author. Tel.: 148-12-633-88-26; fax: 148-12-633-62-45.

E-mail address: rrtomasi@cyf-kr.edu.pl (P. Tomasik).

In this paper correlation between water activity in

aqueous solutions of NaCl, d-glucose, sucrose, glycerol,and urea and viscosity of these solutions are studied.

2. Materials and methods

2.1. Materials

NaCl, glycerol, urea, d-glucose, and sucrose, all of analy-tical grade, were purchased from Sigma Poland. Water was

re-distilled.

2.2. Viscometric measurements

The viscometric measurements were carried out with the

Zimm rotary viscometer (Zimm & Crothers, 1962) modied

in our laboratory (Mazurkiewicz & Tomasik, 1996).

Measurements were carried out at 25 ^ 0:058C: Concentra-tions of particular solutions are reported in Table 1 Particu-

lar runs were continued until subsequent readings reached

constant value. Water activity coefcients were taken from

the research article by Chen (1989). These data are derived

for solutions at 258C.

3. Results and discussion

Relationships between water activity, aw, in solutions of

dissociating solutes known since the middle of this century,

was proved in numerous studies, and was recently looked

upon in terms of statistical mechanics (Ally & Braunstein,

1998). This study pointed that such relationships are valid

for nonelectrolytes such as solutes also. They are nonlinear

in concentration, c, of the solute as shown by Eq. (1). Para-

meters of this equation for particular solutes are given in

Table 2.

J. Mazurkiewicz et al. / Food Hydrocolloids 15 (2001) 434644

Table 1

Water activity (aw) and viscosity (h [cP]) of aqueous solutions of selected solutes

Molality (g mol/kg) Urea Glycerol NaCl Sucrose d-Glucose

aw h Aw h Aw h aw h aw h

0.1 0.998 0.900 0.998 0.899 0.997 0.899 0.998 0.89

0.2 0.996 0.902 0.996 0.907 0.993 0.908 0.996 0.97

0.3 0.995 0.904 0.995 0.930 0.990 0.916 0.994 1.11

0.4 0.993 0.906 0.993 0.954 0.987 0.924 0.993 1.29

0.5 0.991 0.909 0.991 0.977 0.984 0.932 0.991 1.47

0.6 0.989 0.911 0.989 1.001 0.980 0.940 0.989 1.66

0.7 0.988 0.914 0.987 1.027 0.977 0.948 0.987 1.86

0.8 0.986 0.917 0.986 1.055 0.974 0.957 0.985 2.07

0.9 0.984 0.919 0.984 1.084 0.970 0.967 0.983 2.31

1.0 0.983 0.923 0.982 1.100 0.967 0.977 0.981 2.60 0.982 1.58

1.2 0.980 0.929 0.978 1.146 0.960 1.002 0.976 3.49

1.4 0.976 0.936 0.975 1.212 0.953 1.034 0.972 5.09

1.6 0.972 0.944 0.971 1.283 0.946 1.073 0.968 7.90

1.8 0.970 0.952 0.967 1.320 0.939 1.123 0.963 12.53

2.0 0.967 0.960 0.964 1.400 0.932 1.184 0.963 2.65

2.5 0.959 0.984 0.955 1.543 0.913 1.397

3.0 0.952 1.012 0.946 1.765 0.893 1.721 0.943 6.71

3.5 0.945 1.042 0.937 2.023 0.873 2.180

4.0 0.938 1.076 0.928 2.342 0.852 2.801 0.923 16.47

4.5 0.931 1.114 0.919 2.742 0.830 3.611

5.0 0.925 1.155 0.910 3.244 0.903 34.64

5.5 0.918 1.199 0.901 3.946

6.0 0.912 1.246 0.883 63.94

6.5 0.905 1.297

7.0 0.899 1.351 0.863 107.08

7.5 0.893 1.408 0.853 134.69

8.0 0.887 1.469

8.5 0.881 1.533

9.0 0.875 1.601

9.5 0.869 1.672

10.0 0.863 1.746

Table 2

Parameters of Eq. (1) (c0 0:999)

Solute x y

Urea 0.0003 2 0.0163

Glycerol 0.0001 2 0.0187

d-Glucose 2 0.00005 2 0.0195

Sucrose 2 0.0009 2 0.0198

NaCl 2 0.0015 2 0.0310

aw xc2 1 yc 1 c0 1where c is expressed in g/kg and c0 is the activity coefcient

for pure water.

One may see that deviation from linearity [x-term in Eq.

(1)] is the most pronounced for the series of aqueous solu-

tions of NaCl. Deviations from linearity in the case of

organic, non-dissociating solutes under study are almost negli-

gible. Decrease in both terms x and y in Eq. (1) follows the

order of NaCl . sucrose . d-glucose . glycerol . urea.Intuitively this order corresponds with the number of sites of

solute molecules open for interaction with water though not

necessarily via the hydrogen bond formation. In the case of

dissociating NaCl the number of water molecules involved in

hydration of ions should be taken into account. Such relation-

ships linking rational water activity with the hydration number

of saccharides was shown by Rudakov and Sergyevskii

(1997).

Clearly, there is a non-linear relationship between the

water activity, aw, in solutions of the same solutes and visc-

osity, h , of these solutions. Eq. (2) of the same character asEq. (1) is followed.

h pa2w 1 qaw 1 r 2Unlikely as in Eq. (1) where x and y decreased parallely, q

coefcient in Eq. (2) increases as p coefcient decreases. Eq.

(2) can be presented in an alternative exponential form [Eq.

(3)] with the constant h 0 being the viscosity of pure water at258C.

h h0 1 expt 1 uaw 3Parameters of both equations are given in Table 3.

The p and u reect the deviation of h vs aw function fromthe linearity. The p-value for solution of NaCl is low. It

means that with an increase in concentration of the solution

the number of water molecules engaged in the hydration of

ions and solventsolute interactions did not increase signif-

icantly. It might be assumed that as the concentration of

NaCl increased, ions originally separated by an hydration

coat in the diluted solution formed contact ion pairs with

reduced number of molecules involved in the formation of

hydration coat. Low p-value for urea can be rationalised in a

similar way. Urea is known (Szejtli, 1986) for its ability to

associate into cages being the hosts in channel complexes.

Such an association employs polar groups open for hydra-

tion in diluted solutions. Thus, the association increasing

with concentration of solution liberated water molecules

engaged in hydration of urea molecules in diluted solution.

Relatively low p-value for glycerol suggests that in concen-

trated aqueous solution its molecules might be strongly

associated and in a consequence there is a weak hydration

of such associates. Extremely high p-value for sucrose

might be interpreted as strong hydration of sucrose associ-

ates. Indeed, Robinson and Stokes (1963) reported very

strong hydration of sucrose. A similar approach may be

applied for rationalisation of results of the measurements

by Na, Arnold, and Myerson (1995) who estimated water

activity in supersaturated aqueous solutions of two a-aminoacids of zwitterion structure and two dioic acids.

4. Conclusion

The viscositywater activity relationships provide

control over the water activity of solutions at a required

viscosity and, vice versa control over viscosity at a given

water activity.

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Table 3

Parameters of Eqs. (2) and (3)

Solute Eq. (2) Eq. (3)a

p q r R2 b u t R2b

Urea 44.68 2 89.31 45.53 1.000 2 17.34 13.78 0.97

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d-Glucose 11455 2 21999 10561 0.996 2 28.49 29.23 0.99

Sucrose 12592 2 24980 12390 0.988 2 110.42 108.79 0.99

NaCl 146.88 2 284.44 138.62 0.976 2 15.41 13.65 0.99

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J. Mazurkiewicz et al. / Food Hydrocolloids 15 (2001) 434646