uniaxial compression and stress relaxation tests on alginate gels

UNIAXIAL COMPRESSION AND STRESS RELAXATION TESTS ON ALGINATE GELS

MARC0 MANCINI, MAURO MORESI' and ROBERTO RANCINI

Istituto di Tecnologie Agroalimentari Universita della Tuscia

Via S. C. de Lellis, I-01 100 Viterbo, Italy

(Manuscript received August 26, 1998; in final fcirm October 29, 1999)

ABSTRACT

The rheological behavior of alginate gels was analyzed using uniaxial compression and stress relaxation tests. The engineering compressive stress (ud- deformation (E J curves were found to be concave upward and independent of the crosshead speed (VJ for V, 2 I20 mm/min. By considering all the stress (ad- time (t) data for t greater than 10 times the average loading period, the viscoelastic response of these gels was described by means of a 3-element Maxwell body characterized by a relaxation time of 300 s. Such gels exhibited an apparent linear viscoelastic solid behavior for E~ 5 8% and a nonlinear one for larger deformations. However, for E, > 32 % their solid viscoelastic behavior tended to a liquid one. Empirical models allowed rhe viscoelastic properties, as well permanent deformation, of these gels to be quantitatively described as functions of the deformation applied and/or loading rate.

INTRODUCTION

According to Peleg (1976) a rheological model should be capable of predicting real material behavior under any force-deformation history. To achieve this goal, the model parameters might be functions of time (t) and stress (a) or strain ( E ) . Provided that the magnitude of u or E is below certain limits, the mechanical properties may depend on time only, thus leading to so-called linear viscoelastic materials. In food materials, linear viscoelasticity is often observed at strains smaller than 1%, although for fresh fruits and processed foods, such as frankfurters, it was found to be as great as 1.5-3 % (Mohsenin and Mittal 1977) or 3.8% (Skinner and Rao 1986), respectively.

' Correspondence address: Prof. M. Moresi, Istituto di Tecnologie Agroalimentari, Universiti della Tuscia, Via S.C. de Lellis, 1-01100 Viterbo, Italy. Phone: +39-(0)761-357 494; FAX: +39- (0)76 1-357 498 ; E-mail: [email protected]

Journal of Texture Studies 30 (1999) 639-657. All Rights Reserved. "Copyright 1999 by Food & Nutrition Press, Inc.. Trumbull, Connecticut. 639

640 M. MANCINI. M. MORES1 and R. RANCINI

To assess viscoelastic behavior of a given material, two basic quasistatic tests, known as stress relaxation and creep, are usually perfonned. The much simpler uniaxial compression test is generally incapable of elucidating the elastic or plastic nature of the material under study. For a complete assessment of its mechanical behavior, several different definitions of stress and strain have to be used, e.g. those defined by Cauchy, Hencky, Green, etc. (Peleg 1985). For instance, if a Maxwell body is subjected to mechanical tests, the related mathematical model can describe its response both to an initial instantaneous deformation and tensile or compressive load. The compressive 0-E curve is always concave downward.

Another important aspect widely discussed in the literature (Doublier et al. 1992) concerns the real capability of rheological models derived from a single mechanical test to explain and predict the material behavior for the tests mentioned before. This problem will be discussed in this paper with reference to alginate gels.

Rheological behavior of alginate gels has been reported using static (Amici el al. 1996; Mitchell and Blanshard 1976; Nussinovitch et al. 1989) and dynamic (Doublier e? al. 1992) tests. With static testing, the results of stress- relaxation allowed the alginate gels to be described as viscoelastic solids using a mechanical model consisting of two Maxwell elements in parallel with one spring (Amici ef al. 1996; Nussinovitch ef al. 1989). However, the results of creep experiments exhibited a liquid-like viscoelastic behavior as described by another mechanical model consisting of one Maxwell element in series with two Kelvin-Voigt elements (Mitchell and Blanshard 1976). These results clearly show that all or the majority of cross-links in alginate gels are not permanent, but move or break when the gels are sheared.

By testing gels at different alginate concentrations (c), their nonnalised relaxation curves were found to exhibit practically the same relaxation-time spectrum, their initial relaxation stress (Gd, increased with c, but no strain limits were given to assure the linear viscoelasticity of the gel samples (Amici ef aI. 1996; Nussinovitch et al. 1989).

The main aim of this work was to analyze the nonlinear rheological behavior of alginate gels submitted to large deformations by means of empirical models based upon uniaxial compression and stress relaxation tests.

EXPERIMENTAL

Sample Preparation

Sodium alginate [C6H,06Na], from Luminana hyperborea (BDH Ltd., Poole, UK) was used for gel preparations according to the internal setting

TESTS ON ALGINATE GELS 64 1

method (Onspryen 1992), by varying the alginate concentration (c) in the range 0.75-1.5% w/w. The same batch of alginate powder was previously characterized (Clementi et al. 1999) by determining the mannuronic (M=0.37) and guluronic (G=0.63) fractions, the block frequency I(MM =0.29, MG=0.08, and GG=0.55), intrinsic viscosity at 25C in 0.1 M NaCl ([17]=5.9 dl/g). In a previous work (Clementi et al. 1998), the numher- (M,) and weight- (M,) average molecular masses of several weed [Fucu,~ vesicularus (Mackie et al. 1980), Laminaria digifata (Smidsred 1970), L. hyperborea (Mackie ef al. 1980; Martinsen er al. 1991), L. clousfoni (Donnan arid Rose 1950), Macrocystis pyriferu (Martinsen et ul. 1991)] or bacterial [Azotobacter vinelandii (Mackie ef al. 1980)l alginates were correlated to the corresponding intrinsic viscosities [q], thus establishing two different Mark-Houwink relationships, which were used to estimate the M, (=73 m a ) and M, (=28 1 kDa) values of the sodium alginate used. The former allowed its number-average degree of polymerization to be calculated (dp= M,/198= 369).

For a given alginate concentration (c), it is possible to calculate: (1) the moles of sodium alginate (n,,,,,); (2) the equivalents (k,,, = Y2 nNaAlg dp) of calcium ions to be added (to saturate theoretically all the carboxylic groups present in any alginate molecule); (3) the mass of calcium acid phosphate dihydrate (CaHPO, 2H,O) to be added by multiplying q..,, times the molecular mass of the calcium source (i.e. 172.09 Da). The mass of glucono-6-lactone to be added was taken as equal to the mass of the calcium source used. As an example, to prepare 350 g of a gel at c=1.25% w/w, 4.375 g of the above sodium alginate and 1.9 g of the calcium salt were thoroughly dispersed in 341.825 g of demineralised water at ambient temperature under vacuum to minimize entrapment of air bubbles. By adding 1.9 g of glucono-b-lactone under vigorous mixing, pH was reduced, thus liberating the Ca++ ions. The resulting dispersion was quickly poured into a l-dm3 beaker, which was weighed and stored at room temperature for ca. 24 h. Thereafter, the gel mass was drained, gently wiped with filter paper and weighed to estimate the effective alginate concentration ( c d .

Cylindrical specimens were made using a stainless steel cork borer (inside diameter=25 mm and thickness=0.5 mm) and cut to an height of ca. 25 mm with a very sharp cutter.

A few samples were transversally (i.e. parallel to the diameter) cut into 1- mm slices, which were observed using a light stereoscopic microscope mod. WILDMSA (Wildheerbrugg, CH) and photographed using a YASHICA Fx-3 Super 2000 camera and a microscope adapter.

642 M. MANCINI, M. MORES1 and R. U N C I N I

Mechanical Tests

All mechanical tests were performed using an Instron 4301 Universal Testing Machine (UTM, Instron Int. Ltd, High Wycombe, UK) equipped with a 100 N load cell and connected to a PC Olivetti mod. PCS33 via an analogid digital IEEE PCB EXA 504-148 converter (Instron Int. Ltd., Bucks, UK). A specially designed program (Series, XI1 V2,2004 Cyclic Test, Instron Int. Ltd., Bucks, UK) enabled the UTM to be operated from the computer, and its continuous voltage and external displacement readings versus time output to be acquired.

During all tests the ends of each specimen were covered with 40-mm filter paper disks to prevent slippage between the gel and the platens. Specimens were submitted to compression tests up to rupture, to compression-decompression tests or to stress relaxation tests for 30 min by applying 5, 6.5, 8, 10, 12, 16, 25 and 32% relative deformations, whereby cross-head speed (V,) was varied in the range 10-480 d m i n . All tests were replicated five times, and mean values and standard deviations calculated. Specimens submitted to compression testing were weighed and measured with a caliper before and after each test, thus allowing their percentage mass and height variations to be estimated.

Data Analysis

Owing to the bonded compression the cross-sectional area of the sample in contact with the platens was practically constant, while the cylindrical sample assumed a barrel shape. Therefore, the instantaneous values of compression force applied F(t) and specimen height H(t) were converted into engineering stress (aE) and engineering ( E ~ ) or Hencky ( E ~ ) strain according to the following definitions:

where A, and H, are the initial cross-sectional area and height of each specimen. During all relaxation tests the instantaneous engineering stress a, was a

function of time and initial strain applied ( E ~ ) . It was converted into the relaxation modulus G(t,e,) defined by:

TESTS ON ALGINATE GELS 643

This material function is defined similarly to the shear modulus G of an elastic solid and, as for G, it ceases to be a function of strain for small values of E ~ . By taking the instantaneous relaxation modulus relative to the initial one, a dimensionless relaxation modulus, G*(t, E ~ ) , was calculated, which is equal to the ratio between the actual F(t) and initial F(0) compression forces, provided that the cross-sectional area of the sample is constant:

The time course of the dimensionless relaxation modulus was associated to the response of a generalized Maxwell body (a spiring in parallel to n Maxwell elements) (Rao 1992b):

n

G *(t,eEo) = A, + c Aiexp(-t/.t.i) 1

(4)

with

n

A, = I - C A , [to fulfill the initial condition: G*(O, eb)= 11 (5) a

El = Ai G(O,E~) for i=O, 1, ..., n ( 6 ) = Ei 7, for i = l , 2, ..., n (7)

where A, represents the generic dimensionless viscoelastic coefficient; G ( O , E ~ ) the initial dimensionless relaxation modulus and E,, the modulus of elasticity of the spring; while Ei, and 7i refer to the i-th Maxwell element and are the modulus of elasticity of the spring, the effective viscosity of the dashpot and the relaxation time, respectively.

By applying a nonlinear regression method, it was impossible to fit all the experimental G*-t data by the same relaxation time spectrum. This was also observed by other authors (Bertola et al. 1991; Masi 1989). Therefore, the time course of the experimentally observed dimensionless relaxation modulus was reconstructed by assigning initially an arbitrary spectrum of relaxation times, as suggested by Nussinovitch et al. (1989):

7, = a x lo3-' min for i=O, I , ..., 5 (8)

where a is an integer index ranging from 1 to 9.

644 M. MANCINI, M. MORES1 and R. RANCINI

By discarding all the Maxwell elements whose contribution to the reconstruction of G*-t relationship was statistically insignificant at the confidence level of 95 % , it was possible to determine the optimal a value by maximizing the coefficient of determination (?) of the following linearized form of J3q. (4):

where n’ is the overall number of statistically significant Maxwell elements.

RESULTS AND DISCUSSION

Compression Test

The observed stress (u)-deformation (E ) relationships were concave upward independently if stress data were plotted versus engineering or true strain values (Fig. 1). When the data were replotted in corrected coordinates (Fig. lb) to account for the large deformations applied, the upward concavity of uE-eT curves remained. For the “engineering” plot, the yield stress (aER) at failure increased from 100 to 244 kPa as c increased from 0.75 to 1.5% w/w, while the corresponding strain (eER = 0.48f0.01) was practically constant (Table 1).

Figure 2 shows the effect of the loading speed (VJ on the engineering stress-strain curves of alginate gels at c= 1.25 % w/w. For crosshead speeds greater than 120 d m i n such an effect can be regarded as statistically insignificant, whereas for V, = 60 d m i n at eE = const the corresponding stress was generally a little smaller than that observed at higher V, values, probably due to concomitant stress relaxation.

Among the numerous empirical models proposed in the literature (Masi er al. 1997; Peleg 1997), the power-law model (Peleg and Campanella 1989) was chosen to describe the experimental nonlinear stress-strain relationships shown in Fig. la:

where k is the rigidity constant that represents a measure of stiffness, while n is the degree of concavity, that accounts for the deviation from linearity. For n= 1, Eq. (10) reduces to Hooke’s law and k coincides with the modulus of elasticity; while for n smaller or greater than one, a downward or upward concavity is accounted for.


b)

300

200

bW 100

0

0 0.2 0.4 EE (-1

i L . 1 ..-, .... 1

0.6 0.8

I t 0 0.2 0.4 0.6 0.8

EH (->

FIG. 1. COMPRESSIVE STRESS (@-STRAIN ( E ) RELATIONSHIPS (EXPRESSED AS ENGINEERING, a, AND TRUE, b. STRESS-STRAIN 'VALUES) OF CYLINDRICAL

SPECIMENS (DIAMETER AND HEIGHT EQUAL TO cii. 25 mm) OF ALGINATE GELS

1.50 (-) % wlw AT FOUR NOMINAL CONCENTRATIONS (C): 0.75 (- - -), 1.00 (--), 1.25 (- -),


TABLE 1 .

STRESS (om) AT FAILURE AND EMPIRICAL PARAMETERS (k AND n) OF THE EFFECT OF ALGINATE CONCENTRATION ON THE ENGINEERING STRAIN ( ~ m ) AND

POWER-LAW MODEL (10) OF CALCIUM ALGINATE GELS

~~~~~ ~~~~ ~

0.75 0.80 0.460rt0.009 101f5 2.63f0.02 2.14rt0.06 0.98

1 .oo I .09 0.484+0.004 165f4 2.76f0.04 2.15f0.05 0.97

I .25 1.33 0.484+0.005 193f6 2.89f0.03 2.22f0.08 0.98

1 S O 1.57 0.483f0.009 237k15 2.98+0.01 2.17k0.03 0.99

c = nominal alginate concentration; ceR= effective alginate concentration; k and n = power-

law parameters; ? = coefficient of determination; sER = engineering strain at failure; oER =

engineering stress at failure.

Each value is the mean of five replicate tests.

200

150

100

50

0 0 10 20 30 40 50

EE (%)

FIG. 2. COMPRESSIVE ENGINEERING STRESS (od-STRAIN (E,J RELATIONSHIPS OF CYLINDRICAL SPECIMENS (DIAMETER AND HEIGHT EQUAL TO ca. 25 mm) OF 1.25 % wlw ALGINATE GELS AT FOUR DIFFERENT CROSSHEAD SPEEDS

(VJ: A, 60 mdmin; 0, 120 mm/min: 0. 240 mm/min;o, 480 d m i n


Such an empirical model was chosen since it allowed the experimental uE+ curves to be reconstructed with coefficients of determination (9) greater than 0.97 (Table 1) with the minimum number of unknown parameters.

The degree of concavity (n) was practically constant and equal to:

n = 2.17*0.04 (11)

for all alginate concentrations. The rigidity constant (k) was found to be a power function of the alginate concentration (Fig. 3):

k = (589k1) c'.'~*'.'~ (9 = 0.997) (12)

The above empirical coefficients were estimated by using the least-squares method upon bilogarithmic transformation of the dependent (k) and independent (c) variables.

1000 - . .

0 0.5 1 I .5 2

c (%w/w)

FIG. 3 . EFFECT OF NOMINAL ALGINATE CONCENTRATION (c) ON THE EMPIRICAL PARAMETERS k (0) AND n (0) OF THE POWER-LAW MODEL (10)

The strain hardening compressive behavior exhibited by the alginate gels under study appears to be unaffected by alginate concentration and can be reconstructed by Eq. (10-12). It may be attributed to highly crosslinked polymer systems or to structure densificaticzn (which is typical of compressible cellular materials, such as bread, sponges and solid foams, Peleg 1997).


Figure 4 shows a 25x picture of a typical 1-mm slice, that was transversally cut from a cylindrical sample. Only a few air cells with a mean diameter of 0.14f0.04 mm can be observed, their number being of the order of l . l f 0 . 2 per mm3. Since the overall air volumetric fraction was smaller than 0.2%, the gel tested cannot be regarded as a solid foam.

FIG. 4. PICTURE OF A TYPICAL 1-MM THICK SLICE (TRANSVERSALLY CUT AT MID- HEIGHT) OF A 25-CM HIGH CYLINDRICAL SPECIMEN OF 1 % W/W ALGINATE GEL

Magnification 25 x.

According to rubber elasticity theory strain hardening might result from the compression of chains joining adjacent crosslinks followed by reorientation of chain segments longer than the distance between crosslinks and probably by the movement of whole molecules relative to one another (Mitchell and Blanshard


1976). Therefore, at small strains crosslinks are practically unaltered (Mitchell and Blanshard 1976), but at larger strains they may move or fracture, thus allowing the compacted structure to offer a progressively increasing resistance, that resembles the deformation behavior of an incompressible solid. Moreover, as crosslinks move or break, specimens will exhibit permanent deformations, which are not regained upon release of stress.

Compression-Decompression Testing

Permanent deformation of the specimens was measured by compression tests performed at a constant loading rate of 10 mdmin on 0.75-1.5% w/w alginate gels by varying cE from 5 to 45 % , up to tbe incipient rupture of the specimens. After any trial, each specimen assumed a barrel shape. It was gently wiped with filter paper to remove the water exuded and weighed.

The amount of water squeezed out (AM) increased up to (5.2+0.2)% of the original gel mass (M,) as eE increased up to 45%, while the permanent deformation (AH) increased to (21 k 1)% of the iniitial height (Fig. 5) . In the range of alginate concentrations used and for V, = 10 mm/min, the responses were only functions of the engineering strain applied ( E ~ ) :

EP = 0.027 [exp (4.73 E ~ . ) -11 (9 = 0..98)

?!!! = 0.048 [exp (1.59 -11 (? = 0.94) Mo

These empirical regressions are given by the continuous and broken lines in Fig. 5 .

Figure 6 shows the effect of crosshead speed (V,) on cp and AMIM, when 1 % w/w alginate gels were compressed up to 45% relative deformations. The longer the loading period the greater the amount of water exuded and the greater the permanent deformation. The continuous and broken lines in Fig. 6 were calculated by using the following empirical regressions:

0.46 __

v, +0.177 (rZ = 0.95)

AMIM, = ~ 0.34 + 0.02 (r* = 0.99) (16) v,

For V, 2120 mm/min and ~ ,=0 .45 , the average liquid seepage and permanent deformation were of the order of 2% and 18% of the original gel mass and height.


n

a W

w

0.24

0.16

0.08

P /

,R __, .I

0.18

0.12 2

0.06

0 0 0.2 0.4 0.6

‘E (-)

FIG. 5 . EFFECT OF THE ENGINEERING STRAIN APPLIED (E& ON THE PERMANENT DEFORMATION STRAIN (ep: OPEN SYMBOLS) AND RELATIVE MASS VARIATION (AMIM,: CLOSED SYMBOLS) OF CYLINDRICAL GELS OF DIFFERENT ALGINATE

CONCENTRATIONS [c: 0.75 (m, 0); 1 (*, 0); 1.25 (0, 0); 1.5 (A, A) % w/w] DURING COMPRESSION-DECOMPRESSION TESTS PERFORMED AT A CROSSHEAD

SPEED (VJ OF 10 mm/min The continuous and broken lines were calculated by using Eq. (13) and (14), reswtively.

0.24

0.18

0.06

0.06

0 100 200 300 400 500

V, (mm/mim)

FIG. 6. EFFECT OF CROSSHEAD SPEED (VJ ON THE PERMANENT DEFORMATION STRAIN (ep: 0) AND RELATIVE MASS VARIATION (AMIM,:.) OF CYLINDRICAL

PERFORMED UP TO A 45 96 ENGINEERING STRAIN The continuous and broken lines were calculated by using Eq. (15) and (16). respectively.

GELS OF 1 % W/W ALGINATE DURING COMPRESSION-DECOMPRESSION TESTS


According to Peleg and Pollak (1982), the strain level and V, affect the gel hydrostatic pressure, which drives liquid migration through the micropores of the gel network.

Stress Relaxation Test

To assess the range of linear viscoelasticity, cylindrical specimens of 1.25 % wiw alginate gels were loaded at a constant deformation rate of 120 mm/min to final strains of 5 3 2 % . The stress relaxation was monitored for 30 min, which is much longer than the time required (0.6-4 s) to deform the specimens. During all tests the dimensionless relaxation modulus G*(t,c,) exhibited an asymptoti- cally decaying trend with a residual value different from or tending to zero depending on the strain imposed (Fig. 7).

By increasing the crosshead speed to apply an initial strain of 32% from 60 to 480 mm/min, the corresponding initial stress, uE(0), increased from 32+2 N for V,=60 mm/min to 36k2 N for all the other V, values tested (120 to 480 mm/min). Despite an eight times increase in V , ~ ~ ( 0 ) increased not more than 14%, while the dimensionless relaxation modulus G* after 30-min stress relaxation testing was not affected at all (Fig. 8): G*=0.26+0.02 for ~,=0.05 and G*=0.04f0.01 for E~ = 0.32.

1

0.8

0.6 h

v h c v

0.4

0.2

0 E,-32%

.,.

0 300 600 900 1.200 1,500 1,800

(s)

FIG. 7. DIMENSIONLESS RELAXATION MODULUS C;*(t,e,) versus TIME (t) OF CYLINDRICAL SPECIMENS OF 1.25% w/w ALGINATE GELS SUBMITTED TO

SEVERAL DEFORMATIONS ( e 3


0 300 600 900 1200 1500 1800

t (9 FIG. 8. DIMENSIONLESS RELAXATION MODULUS G*(t,cm) VERSUS TIME (t) OF

CYLINDRICAL SPECIMENS OF 1.25 48 w/w ALGINATE GELS SUBMITTED TO 5 % AND 32% RELATIVE DEFORMATIONS (cd USING DIFFERENT CROSSHEAD SPEEDS (V):

A, 60 mmhin; 0, 120 mdmin; 0, 480 mm/min

The results in Fig. 7 show that alginate gels cannot be regarded as linear viscoelastic gels if the deformation exceeded 5-8 % . As cE increased from 8 to 32 % , the so-called three-dimensional cross-linked egg-box structure (Sime 1990) was increasingly damaged transforming these nonlinear viscoelastic solids into viscoelastic liquids, in agreement with previous findings by Mitchell and Blanshard ( 1976).

This operating procedure showed no statistically significant improvement in fitting the time course of any experimental dimensionless relaxation modulus by considering more than two Maxwell elements in parallel to an elastic spring element. The two Maxwell elements were characterized by the following relaxation times:

7, = 5 x lo-* min = 3 s; r2 = 5 x loo min = 300 s.

The viscoelastic response of these gels was described by a 5-element Maxwell body and the dimensionless coefficients, Ai, were estimated by the least-squares method (Table 2). The smallest relaxation time (7,) calculated was of the same order of magnitude of the loading times (0.6-4 s) and this contrasts with the general rule that the relaxation curves are valid only for t greater than 5 or 10 times the loading period (Rao 1992a).

By analyzing the stress-relaxation data collected at times greater than 30 s only, the above rheological model reduced to a 3-element Maxwell body,


characterized by a unique relaxation time of 300 s and an elastic component (A:) responsible for the equilibrium residual stress, which effect is reduced from 43 to 3% as cE increased from 5 to 32% (Table 2:).

TABLE 2. RESULTS OF 30-MIN STRESS RELAXATION TESTS PERFORMED ON ALGINATE GELS

UNDER DIFFERENT INITIAL DEFORMATIONS ( E ~ )

5

6.5

8

10.

12

16

25

32

39k 5 28.3fl.X 27.5f0.6

41k8 28.2k1.4 22k1

46k2 28.6M.9 27f3

57k7 23.8k1.0 26k2

65+ 3 19.8f0.6 30+1

6 0 f 6 12.8+1.2 38k3

Il2?r5 5.4k0.5 52f1

159f 2 0.8f0. I 64.4f0.2

44f2

49.7k0.4

4552

50fl

50f1

49+2

43&1

34.8f0.3

0.97

0.98

0.98

0.99

0.99

0.97

0.93

0.91

27+4 43+2 57i2 0.98

29i6 48*l 52+1 0.98

31*l 46t0 54iO 0.95

33*4 42*1 58*1 0.99

34*2 36*l 64 i l 0.99

35*2 23*l 77*1 0.97

52*2 121tl 88*l 0.93

55*1 3iO 97+0 0.87

Alginate concentration: 1.25% w/w nominal concentration; 1.33f0.04% w/w effective

concentration; G(0) = initial relaxation stress; A,, A, and A, = dimensionless viscoelastic

constants; r2 = coefficient of determination; E~ = initial dehmation.

The sets of parameters [G(O), A;] and [G(O)', A,'] were respectively estimated by

considering stress relaxation data collected for times t 2 0 or 30 s to ignore stress relaxation

during the loading period.


The contini.ious line plotted in Fig. 9 represents the best reconstruction of A,,' against E,,, that was calculated using the following empirical model:

0.46 f 0.02

0.46 exp [ - (10.0+0.9)(~~ - E;)]

for E ~ . , I 6; = 0.08

for E,:" r 6;

(r2 = 0.94) (17) A: =

The elastic component (A,,') was practically constant for relative deformations smaller than a critical value of 8 % , indicating the gels apparently behave as a linear viscoelastic solid, at least on the time-scale examined here. For deformations greater than &El, &' exhibited an exponential decay and tended to such small values as 0.03 for E&= 32%. Under these circumstances, the alginate gels showed a prominently viscoelastic liquid behavior. However, the deformation level did not affect the relaxation times of the elastic component (~,=300 s).

0.6

0.4

0.2

0 0 0. I 0.2 0.3 0.4

E b

FIG. 9. DIMENSIONLESS ELASTIC COMPONENT &' VERSUS APPLIED INITIAL ENGINEERING STRAIN ( E ~ ) OF CYLINDRICAL SPECIMENS OF 1.25 % w/w

ALGINATE GELS AS ESTIMATED (0) BY STRESS RELAXATION DATA AND CALCULATED (-) BY MEANS OF THE EMPIRICAL MODEL (17)

CONCLUSIONS

Although relaxation tests are commonly used to characterize the mechanical properties of food gels, the mechanism involved in the relaxation behavior of


these materials is not well understood. Stress decay was attributed to shifting of cross-linked alginate chains (Mitchell 1980), to {he development of internal hydrostatic pressures causing water exudation thrcugh the network (Peleg and Pollak 1982), or to junction zones breakdown (Pines and Prins 1973). Although all the above mechanisms might contribute to stress relaxation in alginate gels, the compression-decompression tests carried out at different crosshead speeds suggested that the rapid build-up of a hydraulic pressure, registered as a normal stress representing the overall resistance of the gel network to liquid seepage, affects the amount of water exuded and consequently the permanent deformation of the samples.

No mechanical model, consisting of spring and dashpot elements, will in principle be capable of forecasting the phenomena mentioned above and describing the rheological behavior of alginate gel!;. However, the fact that the stress relaxation data were easily fitted using a 3-element Maxwell body allows a series of rheological parameters (A,,’, 7) to be estimated and correlated to the engineering strain applied. In this way, the range of apparent linear viscoelasticity was determined, and also their response to slow or fast uniaxial compression and stress relaxation was empirically modeled for a wide range of deformations. The empirical models here developed might thus be useful for successful product and/or process design.

ACKNOWLEDGMENTS

This research was supported by a special grant (COFIN98) from the Italian Ministry of Research and University.

REFERENCES

AMICI, D., MANCINI, M. and MORESI, M. 1996. Proprieth viscoelastiche di gel di alginato. In Proceedings of the Yd National Congress on Applied Rheology, San Donato Milanese, Sept. 12-15, 1995, pp. 48-53, RHEOTECH-Eniricerche, Baronissi (SA).

BERTOLA, N.C., BEVILACQUA, A.E. and ZARITZKY, N.E. 1991. Changes in rheological and viscoelastic properties and protein breakdown during the ripening of “Port Salut Argentino” cheese. Int. J . Food Sci. Technol. 26, 467-478.

CLEMENTI, F., CRUDELE, M.A., PARENTE, E., MANCINI, M. and MORESI, M. 1999. Production and characterisation of alginate by Azotobacter vinelandii. J . Sci. Food Agric. 79, 602-610.

656 M. MANCINI, M. MORESI and R. RANCINI

CLEMENTI, F., MANCINI, M. and MORESI, M. 1998. Rheology of alginate from Azotobucter vinelundii in aqueous dispersions. J . Food Eng . 36( 1 ) ,

DONNAN, F.G. and ROSE, R.C. 1950. Osmotic pressure, molecular weight, and viscosity of sodium alginate. Can. J. Res. 28 (Sec. B), 105-113.

DOUBLIER, J.L., LAUNAY, B. and CUVELIER, G. 1992. Viscoelastic properties of food gels. In Viscoelastic Properties of Foods, (M.A. Rao and J.F. Steffe, eds.) pp. 371-434, Elsevier Applied Science, London.

MACKIE, W., NOY, R. and SELLEN, D.B. 1980. Solution properties of sodium alginate. Biopolymers 19, 1839- 1860.

MARTINSEN, A., SKJAK-BRAEK, G., SMIDSROD, O., ZANETTI, F. and POLETTI, S. 1991. Comparison of different methods for determination of molecular weight and molecular weight distribution of alginates. Carbohy- drate Polymers 15, 171-193.

MASI, P. 1989. Characterization of history-dependent stress-relaxation behaviour of cheeses. J. Texture Studies 19, 373-388.

MASI, P., SEPE, M. and CAVELLA, S. 1997. Mathematical modelling of the compressive stress-strain relationship of foods submitted to large deformations. In Engineering & Food at ICEF7. Part 1 (R. Jowitt, ed.) pp. A212- 215, Sheffield Academic Press, Sheffield, UK.

MITCHELL, J.R. 1980. The rheology of gels. J. Texture Studies 11, 315-337. MITCHELL, J.R. and BLANSHARD, J.M.V. 1976. Rheological properties of

alginate gels. J. Texture Studies 7, 219-234. MOHSENIN, N.N. and MITTAL, J.P. 1977. Use of rheological terms and

correlation of compatible measurements in food texture research. J. Texture Studies 8, 395-408.

NUSSINOVITCH, A., PELEG, M. and NORMAND, M.D. 1989. A modified Maxwell and a nonexponential model for characterization of the stress relaxation of agar and alginate gels. J. Food Sci. 54, 1013-1016.

ONSOYEN, E. 1992. Alginates. In Thickening and Gelling Agents for Food, (A. Imeson, ed.) pp. 1-24, Blackie Academic & Professional, London.

PELEG, M. 1976. Considerations of a general rheological model for the mechanical behavior of viscoelastic solid food materials. J. Texture Studies

PELEG, M. 1985. Comparison between various correction factors in the calculation of the creep compliance. J. Texture Studies 16, 119-127.

PELEG, M. 1997. Review: Mechanical properties of dry cellular solid foods. Food Sci. Technol. Intl. 3, 227-240.

PELEG, M. and CAMPANELLA, O.H. 1989. The mechanical sensitivity of soft compressible testing machines. J. Rheology 33, 455-467.

PELEG, M. and POLLAK, M. 1982. The problem of equilibrium conditions in stress relaxation analyses of solid foods. J. Texture Studies 13, 1-11.

51-62.

7, 243-255.

TESTS ON ALGINATE GEILS 651

PINES, E. and PRINS, W. 1973. Structure-property relations of thermoreversi- ble macromolecular hydrogels. Macromolecules 6, 888-895.

RAO, M.A. 1992a. Measurement of viscoelastic properties of fluid and semisolid foods. In Viscoelastic Properties ojFoods, (M.A. Rao and J.F. Steffe, eds.) pp. 207-231, Elsevier Applied !science, London.

RAO, V.N. M. 1992b. Classification, description and measurement of viscoelastic properties of solid foods. In Viscoelastic Properties of Foods, (M.A. Rao and J.F. Steffe, eds.) pp. 3-47, Elsevier Applied Science, London.

SIME, W.J. 1990. Alginates. In Food Gels, (P.Harris, ed.) pp. 53-78, Elsevier Applied Science, London.

SKINNER, G.E. and RAO, V.N.M. 1986. Linear viscoelastic behavior of frankfurters. J. Texture Studies 17, 421-432.

SMIDSRIZID, 0. 1970. Solution properties of alginate. Carbohydrate Res. 13, 359-372.

uniaxial compression and stress relaxation tests on alginate gels

Documents