viscoelasticity of a simulated polymer and comparison with chickpea flour doughs

VISCOELASTICITY OF A SIMULATED POLYMER ANDCOMPARISON WITH CHICKPEA FLOUR DOUGHS

NIDHI YADAV1, B.S. ROOPA2 and SUVENDU BHATTACHARYA2,3

1Sant Longowal Institute of Engineering and TechnologyLongowal, Punjab

India

2Food Engineering DepartmentCentral Food Technological Research Institute

Mysore 570020India

Accepted for Publication October 26, 2005

ABSTRACT

An integrated approach consisting of compression and stress relaxationis performed with a simulated model system of poly dimethyl siloxane (PDMS),a viscoelastic polymer material when the compressive strain, height of sampleand crosshead speed were varied. The parameters derived are the forces at theend of compression and relaxation, energy for compression and the extent ofelasticity of the sample based on the ratios of forces as well as the proposedenergy values. The results were verified with food doughs undergoing largedeformations that show a nonlinear behavior. The proposed extent of elasticitybased on the ratios of energy stored and compression can be used as an indexfor the characterization of viscoelasticity. A nonlinear three-parameter modelhad also been proposed to predict the stress decay characteristics as a functionof time, which was found suitable for the PDMS system, and was better thanthe two-parameter Peleg model as judged by lower variance values (0.0006–0.018 and 0.002–0.048, respectively). Further, an actual system of fooddoughs in the form of chickpea (Cicer arietinum L.) flour dough was used toverify the proposed model and viscoelastic index at different moisture contents(27–39%) subjected to compressive strains of 25–75%. The nonlinear relax-ation characteristics of the food dough are sensitive to moisture content aswell as to strain level.

3 Corresponding author. TEL: 0821-2514874; FAX: 0821-2517233; EMAIL: [email protected]

Journal of Food Process Engineering 29 (2006) 234–252. All Rights Reserved.© 2006, The Author(s)Journal compilation © 2006, Blackwell Publishing

234

mailto:[email protected]

INTRODUCTION

An understanding of the rheological behavior of food doughs is importantfor several applications including flattening, sheeting, rolling, mixing and fortransporting and transferring purposes. In addition, it also affects the attributesof the finished products in which the inedible dough is subjected to severalprocessing steps such as extrusion forming, baking, frying, etc, and a combi-nation of these processes. It is thus desirable that the doughs are characterizedthrough experimental values or indices obtained by specific methods to deter-mine their rheological behavior (Bhattacharya et al. 1999).

The characterization of dough can be achieved by several approaches ofwhich empirical and fundamental methods are popular apart from nonoralsensory assessments. The use of fundamental methods such as creep andoscillation techniques are common, although they need sophisticated instru-mentation and a detailed postexperimental analytical procedure, but thesevalues may not be directly related to the attributes of the finished products. Onthe other hand, empirical testing like using an amylograph and a farinographis a routine technique used for the characterization of wheat-based doughs, butmay not be suitable for nonwheat-based doughs because of the lack of gluten.Further, this equipment cannot differentiate minor changes in raw material andadditives. The application of stress relaxation is possibly the most acceptedmethod to determine the behavior of doughs because of the simplicity of itsoperation and the requirement of a rather simple texture-measuring instru-ment. Stress relaxation can be performed in two distinct ways: (1) within linearviscoelastic limit employing a small strain, and (2) the large deformation test.The former method forms the part of a fundamental test, while the latter is anempirical test that can be correlated well with sensory and other qualityattributes of the finished product. A number of studies have been performed onlarge deformation stress relaxation studies of doughs, such as for blackgram(Bhattacharya and Narasimha 1997), wheat (Safari-Ardi and Phan-Thien1998) and corn (Bhattacharya et al. 2003).

Pulses and legumes are important sources of protein in several continentsincluding Asia, Latin America and Africa. They are becoming increasinglypopular in Europe and Northern America (Kampf and Peleg 2002). The mainadvantages of pulses and legumes are their low cost, long shelf life andmoderate protein content. Chickpea (Cicer arietinum L.) or Bengalgram is apopular pulse in several Oriental countries and is conventionally used to makeconcentrated cooked slurry using split pulses (dhal), and for making a numberof dough-based fried and/or confectionery products. The dough-based prod-ucts are low-pressure extrusion-formed strands followed by frying, and con-fectionery products and thin chips that may be either baked or fried prior toconsumption (Bhat and Bhattacharya 2001). Therefore, knowledge on the

235VISCOELASTICITY OF POLYMER AND CHICKPEA DOUGH

rheological behavior of chickpea flour dough is required for process andproduct standardization, and for quality control purposes. Published data onthe rheology of chickpea flour dough are scarce, although a scope exists tostudy the same, particularly the stress-relaxation characteristics. The strainapplied to the dough may also vary widely depending on the application andthe targeted product, but data on this aspect for chickpea flour dough are notavailable.

On many occasions, a simulated material is often employed to study thebehavior of the same instead of the actual food material under testing (Agarwaland Bhattacharya 2005). The advantage of using a simulated material lies in arelatively simpler property and good repeatability such that better understand-ing is possible rather than directly using a complex system like food dough.Poly dimethyl siloxane (PDMS), a polymer, is often used in rubber industries(Aranguren et al. 1992) and may also be used as a model system to simulatea food dough. Hence, the polymer PDMS was tested to ascertain the differentviscoelastic parameters with variations in height, level of strain and crossheadspeeds.

The objectives of the present work were to (1) determine the stress-relaxation behavior of the simulated model system of PDMS with differentgeometries, and chickpea flour dough at different moisture contents and atvarious strain levels; and (2) propose a new model for stress relaxation andexamination of the suitability of the existing model and the proposed one usingboth model systems as well as chickpea flour dough.

THEORY

In stress-relaxation experiments, the test specimen is compressed up to apredetermined level of strain, and later, the strain is kept constant during whichthe viscoelastic material shows a decaying trend of force/stress as a function oftime (Fig. 1). Although the energy values are to be calculated from the force-deformation curve, Fig. 1 has been represented as a force-versus-time curvefor ease in understanding. For a large deformation compression test prior to theinitiation of relaxation testing, the strain level is always at a few folds higherthan its linear viscoelastic range, and, hence, shows a typical nonlinear decaytrend. Nonlinear viscoelasticity is experimentally and theoretically much morecomplex than linear viscoelasticity.

An ideal viscous body cannot maintain any force/stress in the absence ofmotion, and, thus, reaches the lowest datum level. On the contrary, an idealelastic solid is able to attain instantly the force/stress that is equal to the samemagnitude that it possessed at the beginning of the relaxation testing. It isobvious that a viscoelastic material such as food dough will show an interme-diate effect between these two extreme cases.

236 N. YADAV, B.S. ROOPA and S. BHATTACHARYA

The stress relaxes at a definite rate, but not necessarily at a constant rate.This phenomenon is a result of a molecular and structural reorientation, andliquid flow as well. The nonlinear relaxation curve (Eq. 1) is a function of bothtime (t) and applied strain (e).

F f t= ( )e, (1)

At a constant strain, force depends on time alone with usually threezones; the initial portion shows a high slope, whereas the third zone has thelowest slope and appears to approach a residual (or an equilibrium) value (Fe),whereas the second zone is an intermediate of these two zones. Mohsenin(1986) mentioned that the slope of the initial portion of the curve is indepen-dent of the rate of the strain when the sample is compressed to a small strainlevel. The higher the strain, the higher is the resistive force offered by thedough, and thus, the strain decides (Eq. 2) the magnitude of initial force att = 0.

F f0 = ( )e (2)

Time (s)

Force (N)

Compression Relaxation

Energydissipated

Energystored

Energyfor

compression

Ideal liquid

Ideal solid

FIG. 1. NONLINEAR COMPRESSION–RELAXATION DIAGRAM OF A VISCOELASTICBODY


The relaxation curve can be normalized (Eq. 3) using two empiricalconstants, k1 and k2 (Peleg and Normand 1983; Purkayastha and Peleg 1986).

F t

F F tk k t0

01 2− ( )

= + (3)

The initial decay rate is reflected by the term 1/k1, whereas 1/k2 denotes theasymptotic value of the relaxed portion of F0. The determination of k1 and k2

constants can thus give an indication of the rheological status of the sample.In the present investigation, a three-parameter model has been proposed

(Eq. 4) to predict the force decay during relaxation. The term Fe is the residualforce, and A and a are the two empirical constants. A is equivalent to F0 - Fe

when t is zero. On the other hand, when t is large, F(t) → Fe. The rate ofexponential decay is represented by a.

F t Ae Ft( ) = +−ae (4)

MATERIALS AND METHODS

Materials

Dehusked split pulses of chickpea (C. arietinum) were procured from alocal supermarket. After cleaning, they were ground in a hammer mill (CMC-CM, Cadmach Machinery, Ahmedabad, India) with sieves. The temperature ofthe samples during grinding was kept below 40C. Later, they were sieved usinga 72-mesh British Standard (BS) sieve with a 212-m opening. The proximatecomposition of the chickpea flour (passing through the 72-mesh BS sieve), asdetermined by AOAC (1980), is shown in Table 1. PDMS slabs were procuredfrom the Indian Rubber Manufacturers Research Association (Mysore, India).

Sample Preparation

The chickpea flour dough samples with different moisture contents (27–39%) were prepared using a Hobart mixer (model # N50CE, Hobart Corp.,Troy, OH) operating at the lowest rotational speed for 3 min, and the doughsamples were allowed to rest for 30 min in a sealed condition to avoid moistureloss prior to rheological testing. Dough specimens (35 mm in diameter and20 mm in length) were manually prepared as detailed earlier (Bhattacharyaand Narasimha 1997). In a similar manner, cylindrical samples (35 mm indiameter and 30 mm in length) were punched out of the PDMS slabs. Later,some of the samples were trimmed manually to 20 or 25 mm in length. Threesamples were prepared each time, and the whole process was repeated once.


Stress Relaxation

The cylindrical samples of PDMS and the chickpea flour dough sampleswere compressed using a universal texture-testing machine (Model # TAHDi,Stable Microsystems, Surrey, U.K.). The extent of the applied strain was 25, 50or 75%. The cylindrical samples were compressed by using a flat stainless steelcircular plate with a diameter of 100 mm. The bottom plate had concentriccircle serrations to reduce slip. Lubrication using paraffin oil was done only forchickpea flour dough samples to avoid migration of moisture during testing at25 ± 1C. When the predetermined level of compression was achieved, themovement of the crosshead surface was stopped and the sample was allowedto relax for 300 s; data were collected at the rate of 25 points per second. Asthe dough sample having 27% moisture compressed at 75% strain showedcracks at the edge, the experiment with this sample was discontinued. Thecrosshead speed for the PDMS sample was varied at 0.1, 1 and 10 mm/s, whileit was 1 mm/s for the chickpea flour dough samples. The compression curvewas used to determine the peak force (F0) and energy for compression. Therelaxation curve was used to obtain the Fe and the percent elasticity (Fe/F0 ¥ 100) based on the ratio of the forces. In addition, the ratio of energies forelasticity and compression was calculated to obtain the extent of elasticitybased on energy. The empirical constants (k1 and k2) were obtained by employ-ing the linear regression method using the rheology software supplied byRheometrics (Piscataway, NJ) from the relaxation curve by plotting relaxationtime t against F0t/[F0 - F(t)] according to Eq. (3). The extent of fit to the linewas judged by calculating the variance according to Eq. (5).

Variance m c m= −( )[ ]=∑ y y y

ni

n 2

1

(5)

TABLE 1.PROXIMATE COMPOSITION OF CHICKPEA FLOUR USED

FOR RHEOLOGICAL CHARACTERIZATION

Content Amount

Moisture 11.6 ± 0.2Protein (N ¥ 6.25) 21.1 ± 0.4Fat 4.7 ± 0.1Ash 2.4 ± 0.2Crude fiber 2.9 ± 0.1Carbohydrate (by difference) 57.3 ± 0.5

Values (mean ± SD) are expressed as percent basis of fourdeterminations.


The reported results are the means of three observations. The wholeexperiment was repeated once.

Analysis of Data

The viscoelastic parameters for the PDMS samples were determined atdifferent lengths of the samples (20, 25 and 30 mm); strain (25, 50 and 75%);and crosshead speeds (0.1, 1 and 10 mm/s). The variables for chickpea flourdough samples were moisture contents (27, 30, 33, 36 and 39%) and strainlevels (25, 50 and 75%). Thus, a total of 42 experimental data points wereobtained for the dough samples considering three repetitions of each combi-nations and failure of test with the 27% moisture–75% strain combination.These variables were related to the different response functions such as F0, Fe,energy for compression, k1, k2 and percent elasticity based on ratio of forcesand energies by a second-order polynomial using the technique of least squaresas mentioned earlier by Bhattacharya and Narasimha (1997). These polyno-mials were used to draw the three-dimensional response surfaces for ease invisualization of the effect of the individual variables on the response functions.The parameters of Eq. (4) were calculated by employing the method of non-linear analysis method as mentioned earlier.

RESULTS AND DISCUSSION

PDMS System

The model PDMS system, during stress relaxation with different samplelengths and crosshead speeds, shows a similar pattern in force decay but withdifferent Fe (Table 2) indicating its viscoelastic behavior. An increase in thelevel of strain increases Fe markedly. The coefficients of the Peleg model (k1

and k2) are sensitive to compressive strain, length of samples and crossheadspeeds (Table 3), which is also true for the coefficients of the developed model(Eq. 4); the level of strain possesses the most dominating effect. The constanta of Eq. (4) increases exponentially with the strain employed. The low vari-ance values (0.0006–0.018) indicate the better suitability of the developedmodel compared to the Peleg model (variance between 0.002 and 0.048) forthe model system of PDMS.

The viscoelastic samples relaxed gradually with an endpoint dependingon the molecular structure of the material being tested. Stress in viscoelasticsolids would decay to an equilibrium or a residual stress, but the residual stressin viscoelastic liquids would be zero (Steffe 1992).


TAB

LE

2.R

HE

OL

OG

ICA

LPA

RA

ME

TE

RS

OF

EQ

.(4)

OB

TAIN

ED

FOR

POLY

DIM

ET

HY

LSI

LO

XA

NE

SAM

PLE

SW

ITH

DIF

FER

EN

TL

EN

GT

HS

AN

DSU

BJE

CT

ED

TO

VA

RY

ING

STR

AIN

SA

ND

CR

OSS

HE

AD

SPE

ED

S

Con

ditio

nof

mea

sure

men

tR

esid

ual

forc

e,F

e

(N)

Con

stan

tA

(N)

Con

stan

ta

(s-1

)V

aria

nce

(-)

Stra

in(%

)C

ross

head

spee

d(m

m/s

)

Sam

ple

heig

ht(m

m)

251

253.

7±

0.0

8.3

±1.

10.

051

±0.

007

0.00

650

125

21.0

±0.

233

.0±

1.9

0.04

8±

0.00

10.

003

751

2522

2.9

±4.

222

1.8

±4.

40.

037

±0.

003

0.00

125

130

5.8

±0.

211

.4±

1.0

0.06

3±

0.00

10.

004

501

3021

.6±

0.5

33.5

±0.

50.

053

±0.

004

0.00

375

130

226.

1±

1.8

239.

0±

10.6

0.05

1±

0.00

30.

002

250.

120

19.4

±0.

120

.0±

0.6

0.02

4±

0.00

10.

0007

500.

120

34.5

±1.

129

.3±

0.5

0.03

5±

0.00

10.

0006

750.

120

425.

1±

44.2

353.

6±

34.2

0.04

7±

0.00

10.

0006

251

206.

7±

0.7

16.5

±1.

30.

053

±0.

001

0.00

650

120

21.8

±0.

726

.8±

1.6

0.07

0±

0.00

30.

005

751

2015

0.1

±5.

422

3.4

±6.

20.

066

±0.

004

0.00

325

1020

10.1

±0.

115

.7±

0.0

0.16

3±

0.01

60.

015

5010

2023

.9±

1.2

25.0

±1.

10.

181

±0.

012

0.01

875

1020

36.4

±1.

699

.2±

2.3

0.20

4±

0.00

70.

011


TAB

LE

3.R

HE

OL

OG

ICA

LPA

RA

ME

TE

RS

OF

TH

EPE

LE

GM

OD

EL

OB

TAIN

ED

FOR

POLY

DIM

ET

HY

LSI

LO

XA

NE

SAM

PLE

SW

ITH

DIF

FER

EN

TL

EN

GT

HS

AN

DSU

BJE

CT

ED

TO

VA

RY

ING

STR

AIN

SA

ND

CR

OSS

HE

AD

SPE

ED

S

Con

ditio

nof

mea

sure

men

tk 1

(s)

k 2(-

)V

aria

nce

(-)

Com

pres

sion

ener

gy(J

)E

xten

tof

elas

ticity

(%)

Stra

in(%

)C

ross

head

spee

d(m

m/s

)

Sam

ple

heig

ht(m

m)

Forc

eE

nerg

y

251

255.

53±

0.19

0.66

±0.

010.

048

±0.

019

0.02

7±

0.00

114

.91

±0.

2819

.01

±0.

2150

125

5.81

±0.

011.

23±

0.01

0.01

3±

0.00

10.

434

±0.

005

19.8

7±

0.62

23.7

5±

0.64

751

257.

13±

0.07

1.33

±0.

010.

018

±0.

006

2.24

7±

0.11

925

.57

±0.

1229

.58

±0.

1425

130

6.78

±1.

221.

23±

0.03

0.02

7±

0.00

60.

054

±0.

011

19.7

4±

1.72

23.8

2±

1.13

501

307.

13±

0.47

1.28

±0.

060.

009

±0.

001

0.44

3±

0.02

423

.15

±0.

2427

.27

±0.

1875

130

6.93

±0.

631.

36±

0.01

0.02

6±

0.01

52.

509

±0.

165

27.4

9±

0.16

31.2

4±

0.34

250.

120

25.1

1±

0.32

1.56

±0.

010.

030

±0.

001

0.05

8±

0.00

437

.75

±0.

4945

.74

±0.

3650

0.1

2018

.36

±0.

131.

69±

0.06

0.03

0±

0.00

90.

287

±0.

003

41.3

6±

0.25

47.5

6±

0.17

750.

120

14.4

8±

0.06

1.75

±0.

060.

023

±0.

004

2.03

2±

0.24

941

.01

±0.

1347

.31

±0.

1025

120

6.42

±0.

071.

17±

0.02

0.02

7±

0.00

40.

093

±0.

012

15.9

6±

0.18

20.4

7±

0.19

501

205.

12±

0.03

1.19

±0.

020.

017

±0.

011

0.49

8±

0.03

017

.46

±0.

2521

.03

±0.

1975

120

5.05

±0.

341.

25±

0.03

0.03

6±

0.00

41.

693

±0.

100

20.9

5±

0.78

24.2

0±

0.85

2510

202.

29±

0.13

1.08

±0.

020.

008

±0.

009

0.29

5±

0.02

18.

36±

0.17

10.5

2±

0.07

5010

202.

01±

0.07

1.10

±0.

030.

013

±0.

001

1.14

4±

0.02

59.

86±

0.20

11.7

2±

0.14

7510

201.

84±

0.15

1.09

±0.

030.

002

±0.

001

0.64

2±

0.05

79.

16±

0.22

10.9

7±

0.12


Food Dough System

Initial and Residual Force. The F0 indicates the force offered by thedough sample at the end of an applied strain. It also denotes the force priorto initiating the stress relaxation. The F0 values were between 2.3 and357.3 N, and were a function of both the moisture content of dough (27–39%) and the applied strain (25–75%). As cracks on the periphery of thecompressed dough were noticed during the compression of the dough havingthe lowest moisture (27%) at the highest strain (75%), data for the same arenot reported.

The response surface for F0 as a function of moisture content and strainis shown in Fig. 2. An increase in the moisture content decreased the F0 at allstrains, and the rate of decrease was high at large strains such as 75% possi-bility because of the enhanced mobility of water molecules under compressivestrain. On the contrary, F0 increased with strain; a marginal increase occurredat high moisture contents, whereas a marked increase was observed at lowmoisture contents of the dough. The Fe, obtained at the end of the relaxation,showed a similar trend like that of F0 (Fig. 2).

400

300

200

For

ce (

N)

Moisture content (%)Strain (%)

100

050

0

2530

40 25

50

75

35

FIG. 2. RESPONSE CURVE FOR THE INITIAL FORCE (F0) AND RESIDUAL FORCE (Fe) ATDIFFERENT MOISTURE CONTENTS AND STRAIN LEVELS

Top curve: F0; bottom curve: Fe.


k1 and k2 Values. The k1 and k2 values were calculated from the relax-ation curves. The k1 values varied markedly from 1.8 to 4.2, while the k2 valuesshowed a marginal change from 1.04 to 1.15 per second.

The effect of the moisture content of the dough and the applied strain isshown in Fig. 3. The k1 values decreased markedly with an increasing moisturecontent as well as strain. The rate of decrease in k1 was more pronounced athigh strains. The change in k2 values was marginal, although showing adecreasing trend at high strain levels.

Extent of Elasticity. The elasticity of the dough is an important crite-rion for flattening or sheeting/rolling because it affects the thickness of thesample that in turn can dictate the texture of the finished product. The extentof relaxation, calculated as equal to 100(Fe/F0), was a function of both themoisture content and the strain (bottom curve, Fig. 4). Higher values (7.4–13.2%) were associated with 25% strain samples, while low values (5.1–7.1%) were obtained when the strain was at the highest level of 75%. Anincrease in moisture content made the dough more viscous than elastic, and,hence, should have shown lower elasticity values, but such a clear trend wasnot observed. This phenomenon happens because of the magnitudes of the F0

54

32

1

2530

35

Moisture content (%)40 25

50

75

Strain (%)

Rel

axat

ion

para

met

er

FIG. 3. EFFECT OF MOISTURE CONTENT AND LEVEL OF STRAIN ON RELAXATIONPARAMETERS (k1 AND k2)

Top curve: k1; bottom curve: k2.


values that differ widely because of a change in moisture content. Forexample, for a sample with 50% strain and a moisture content of 27%, F0 ismore than 40 times than that for the sample with a moisture content of 39%.On the other hand, the Fe values are only 27 times higher at these twomoisture contents.

In the present study, a curvilinear relationship with moisture wasobserved (Fig. 4), indicating that an increase in moisture content up to about33% made the dough possess some elasticity, but decreased afterward whenthe moisture was further increased. Possibly, a minimum quantity of moistureis required for the development of dough to form weak bonds like hydrogenbond and van der Waals forces. Excess moisture acts as a plasticizer (Levineand Slade 1990) to yield a weak dough.

It may be inferred that the extent of elasticity, conventionally calculatedas the ratio of 100(Fe/F0), is not an appropriate index to judge the rheologicalstatus of doughs. It is desirable that an appropriately defined and reliable indexmay be worked out that can adequately describe the relaxation behavior ofdough.

In an alternative approach, the ratio of the energy stored and input totalenergy was used to calculate the extent of elasticity. This also showed a similar

2016

128

4

2530Moisture content (%)

Strain (%)3540 25

50

75

Ext

ent o

f ela

stic

ity (

%)

FIG. 4. EXTENT OF ELASTICITY AS A FUNCTION OF MOISTURE CONTENT ANDSTRAIN LEVEL

Top curve is based on energy ratios, while bottom curve is based on force ratios.


trend (Fig. 4, top curve), but with higher magnitudes (8.4–16.2%) compared to5.1–13.2% in an earlier case. This means that the elasticity of dough can alsobe calculated as the ratio of the energy levels.

These facts indicate that the chickpea flour dough samples with moisturecontent between 27 and 39% show poor elasticity. The energy input to thedough by means of compression is mostly lost because of flow. Only a smallportion undergoes recovery while another small segment is absorbed by thedough to induce the breakdown of the temporary dough structures composedof weak forces such as hydrogen bond and van der Waals forces, and possiblybecause of the oozing out of water from the hydrated flour particles.

Table 4 shows the coefficients of variance (CVs) in experimental results.High values were observed for F0, Fe, k1 and compression energy, indicatingthat these parameters are less suitable for comparison of samples that aremarginally different. On the other hand, k2 and the extent of elasticity based onenergy ratios had low CV values to make them more suitable than the otherrelaxation parameters. High variation in texture parameter such as crispness(up to about 56%) for fried banana chips has been reported (Jackson et al.1996).

Compression Energy. The compression energy is an indication of theenergy offered by the dough during its compression at different levels of strain(25–75%). The compression energy was a function of moisture content of thechickpea flour dough and the level of strain (Fig. 5). An increase in moisturecontent decreased compression energy at all levels of strain, but the rate ofdecrease was markedly prominent at high levels of strain. On the other hand,compression energy increased with an increase in strain level as expected, butthe rate of increase was marginal at high moisture contents.

Proposed Model. The proposed three-parameter model (Eq. 4) is bettersuited than the Peleg model as the variance values are lower for the former

TABLE 4.COEFFICIENT OF VARIANCE (%) OF EXPERIMENTAL RESULTS

System Initialforce, F0

(N)

Residualforce, Fe

(N)

k1 (s) k2 (-) Compressionenergy (J)

Extent of elasticity (%)

Force Energy

PDMS 0.1–10.1 0.7–10.4 0.3–18.0 0.1–1.0 0.9–13.2 0.3–8.7 0.2–4.7Chickpea

flourdough

0.7–17.5 3.2–10.5 0.9–11.0 0.1–0.8 0.6–12.3 0.4–11.8 0.4–5.9

PDMS, poly dimethyl siloxane.


system (Table 5). Figure 6 shows a comparison of experimental and calculatedresidual force values. Although an overall correlation coefficient of 0.986 wasobtained, a good linear relationship was observed when the values were�10 N. The calculated Fe values were marginally higher in magnitudes com-pared to the experimented ones. The constant A of the proposed equationshowed a similar trend (Fig. 7) like that for F0 (Fig. 2), indicating that thesetwo parameters depict the same index. The constant a (Fig. 8) indicates the

2.0

1.5

1.0

0.5

2530Moisture content (%)

Strain (%)35

40 25

50

75

Ene

rgy

for

com

pres

sion

(J)

FIG. 5. EFFECT OF DIFFERENT MOISTURE CONTENTS AND LEVELS OF STRAIN ONCOMPRESSION ENERGY

TABLE 5.COMPARISON OF THE PELEG AND THE PROPOSED MODELS

Point of comparison Peleg model Our model

Number of model parameters Two ThreeNormalization of data Required Not requiredChance of error because of normalization Present AbsentMethod of calculation Linear regression Nonlinear analysisCalculation procedure Multistep and tedious One step and simpleVariance Higher Lower

PDMS 0.002–0.048 0.0006–0.018Chickpea flour dough 0.0006–0.055 0.0005–0.047

PDMS, poly dimethyl siloxane.


FIG. 6. COMPARISON OF EXPERIMENTAL AND CALCULATED RESIDUAL FORCES

FIG. 7. EFFECT OF DIFFERENT MOISTURE CONTENTS AND LEVELS OF STRAIN ONCONSTANT A OF THE PROPOSED MODEL


rate of force decay during relaxation, and was sensitive particularly at highstrain levels and at low moisture contents.

Interrelationship of Relaxation Parameters. F0 at the beginning of therelaxation was highly correlated (r � 0.97, P � 0.01) to Fe, compressionenergy and the constant A of the proposed equation (Table 6). The extent ofelasticity (based on force and energy ratios) showed a moderate negativerelation with F0. A similar relationship also existed between k1 and a, meaningthat an increase in k1 decreases the a value. The extent of elasticity wasnegatively related to the constants A and a.

Doughs are multicomponent systems in which water plays the mostcritical role, often described as a plasticizing effect (Levine and Slade 1990).There is always a competition by the flour constituents for water, and thus, thelevel of moisture decides the extent of dough consistency or viscoelasticitythat is guided by the formation of weak forces, such as hydrogen bond and vander Waals forces.

It can be concluded from the present study that a simulated viscoelasticpolymer like PDMS of varying sizes can be characterized in terms of the extentof elasticity based on energy ratios, and the proposed three-parameter model.This model is better suited compared to the well-known two-parameter model.The results were also verified by a food dough system (chickpea flour dough).

0.3

0.2

0.1

0.0

25

30Moisture content (%) Strain (%)35

40 25

50

75

Con

stan

t a (

s–1)

FIG. 8. CHANGES IN THE CONSTANT a AS A FUNCTION OF MOISTURE CONTENTAND STRAIN


TAB

LE

6.C

OR

RE

LA

TIO

NM

AT

RIX

BE

TW

EE

NT

HE

RE

LA

XA

TIO

NPA

RA

ME

TE

RS

FOR

CH

ICK

PEA

FLO

UR

DO

UG

HS

Initi

alfo

rce,

F0

Res

idua

lfo

rce,

Fe

Rel

axat

ion

para

met

er,

k 1

Rel

axat

ion

para

met

er,

k 2

Ext

ent

ofel

astic

ityba

sed

onfo

rce

ratio

s

Ext

ent

ofel

astic

ityba

sed

onen

ergy

ratio

s

Com

pres

sion

ener

gyC

onst

ant

A

Res

idua

lfo

rce,

Fe

0.98

7**

Rel

axat

ion

para

met

er,k

1-0

.126

NS

-0.0

64N

S

Rel

axat

ion

para

met

er,k

2-0

.431

NS

-0.4

25N

S0.

518*

Ext

ent

ofel

astic

ityba

sed

onfo

rce

ratio

s-0

.734

**-0

.716

**0.

592*

0.65

3**

Ext

ent

ofel

astic

ityba

sed

onen

ergy

ratio

s-0

.650

**-0

.343

NS

0.53

6*0.

143N

S0.

387N

S

Com

pres

sion

ener

gy0.

983*

*0.

978*

*-0

.072

NS

-0.3

88N

S-0

.665

**-0

.584

*C

onst

ant

A0.

971*

*0.

944*

*-0

.137

NS

-0.4

06N

S-0

.703

**-0

.624

**0.

942*

*a

0.33

5NS

0.27

8NS

-0.6

83**

-0.3

84N

S-0

.591

*-0

.642

**0.

264N

S0.

439N

S

*Si

gnifi

cant

atP

�0.

05.

**Si

gnifi

cant

atP

�0.

01.

NS,

nons

igni

fican

tat

P�

0.05

.


The dough samples with moisture contents between 27 and 39% are typicalinelastic doughs with poor elastic property unlike gluten-developed wheatflour doughs such that a product like bread cannot be appropriately made. Butthese doughs appear to be suitable for making products that need masses thatare able to flow such as fried-shaped dough strands or batter-based productsthat need to come out easily when pressed through die restrictions or throughthe wire mesh or pores of a perforated surface. They may also be suitable formaking products wherein more flow characteristics are desirable such as abatter or spray-coated foods.

NOMENCLATURE

A Constant in Eq. (4)F(t) Force at time t (N)Fe Residual force (N)k1, k2 Constants in empirical normalized Eq. (3)1/k1 Initial decay rate (s-1)1/k2 Hypothetical asymptotic level of the relaxed portion of the force

(dimensionless)n Number of data points being fittedPDMS Poly dimethyl siloxanet Time of relaxation (s)yc Calculated y value of fitym Measured y value of dataa Constant in Eq. (4)e Applied strain (dimensionless)

ACKNOWLEDGMENT

We sincerely thank the anonymous referee for the suggestions concerningthe use of a simulated viscoelastic material for stress relaxation testing.

REFERENCES

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viscoelasticity of a simulated polymer and comparison with chickpea flour doughs

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