Contemporary Engineering Sciences, Vol. 11, 2018, no. 21, 1013 - 1024

HIKARI Ltd, www.m-hikari.com

https://doi.org/10.12988/ces.2018.8386

Steady and Shear Dynamic Rheological

Properties of Squash (Cucurbita moschata) Pulp

Somaris E. Quintana1, Diana Machacon1, R. M. Marsiglia2,

Edilbert Torregroza2 and Luis A. García-Zapateiro1

1 Faculty of Engineering, Food Engineering Program, Group of Investigation in

Engineering of Complex Fluids and Food Rheology (IFCRA)

University of Cartagena, Cartagena, Colombia

2 Social Sciences and Education Faculty

University of Cartagena, Cartagena, Colombia

Copyright © 2018 Somaris E. Quintana at al. This article is distributed under the Creative

Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any

medium, provided the original work is properly cited.

Abstract

Squash (Cucurbita moschata) is being progressively utilized for the manufacture of

different products and the design of different processing methods requires

information about its rheological properties of the pulp. The present work has

evaluated the rheological properties of the pulp as function of temperature (20 – 100

°C). The rheological properties of natural pulp were evaluated as a function of the

temperature. The product flow behavior is well described by the Carreau-Yasuda

model (R2 > 0.9712). The product has shown a weak gel behavior, with storage

modulus higher than loss modulus in the evaluated frequency range. The Cox-Merz

rule was found to not be applicable to the pulp. The results obtained are potentially

useful for future studies on the new products, for the extraction of microcomponents

with technological functionality and process design.

Keywords: Squash (Cucurbita moschata), rheology, Carreau-Yasuda models,

Arrhenius equation, viscoelasticity

Introduction

Squash is an annual herbaceous plant belonging to the family Cucurbitaceae; it is

widely cultivated and has been used as food since ancient times. It is an economically important and diverse crop species of vegetable in the genus Cucurbita.

1014 Somaris E. Quintana at al.

It is grown commercially in fields as well as domestic gardens and is native to the

Americas. Cucurbita sp. crops have of great incidence and importance in the

Bolívar Department (Colombia), where this vegetable presents an essential product

for inhabitants’ food safety [1].

There is evidence that shows it was introduced to Europe in the 16th century [2].

Due to the increasing acceptance and commercialization of the products derived

from fruits and vegetables, more extensive scientific information about the

characteristics of this fruit is required. For this reason, the study of the rheological

behavior of the pulp of this fruit is of interest, to aid the characterization and use in

the development of new products [3], [4]. Traditionally, fruit pulp can be used as

raw material in the food industry to obtain various products, such as nectars, jams,

ice creams and other products that can also be sold directly to consumers. The

rheological characteristics of a complex fluid are one of the essential criteria in the

development of products in the food industry, in terms of quality control, as well as

in the understanding and characterization of textural attributes.

The rheological behavior of fruit juices and pulps is associated to the levels of

soluble solids in suspension and as a function of the form, size and concentrations

of the suspended particles and the structure of the system. Fruits pulps are generally

characterized as non-Newtonian fluids as a result of complex interactions among

their component. Different models have been used to describe the rheological

behavior of fruit pulp. One of the most widely used mathematical models is the

power law of Ostwald de Waele [5], which has been used to describe the rheological

behavior of mango pulp (Mangífera indicates L-Keitt) [6], guava pulp (Psidium

guajava), soursop pulp (Annona muricata), zapote pulp (Calocarpum sapota Merr)

and medlar pulp (Achras sapota) [7]. For the case of cranberry purée, the Sisko

model has been used [8]. Casson's model has also been applied to a wide range of

food products such as fruit purées and tomato concentrates [9], non-Newtonian

behavior was also observed in the borojó pulp (Borojoa patinoi Cuatrec) [3].The

literature on the rheology of fruit derivatives has established that temperature,

soluble solids concentration, pectin content, and insoluble solids content are the

main factors responsible for the rheological behavior[10]–[12]. The rheological

properties of different foods usually have significant importance to their processing,

transport and storage [13]. Numerous research studies in food rheology have

confirmed the variety of flow behaviors found in food systems. Non-Newtonian

fluids exhibit a flow behavior that depends on the shear rate and, generally, time

because of structural changes [13].The purposes of this study were to determine the

rheological properties of the pulps of squash (Cucurbita moschata), as a function

of the temperature.

Material and methods

Plant material

Squashes (Cucurbita moschata) with a similar maturity and weight were cultivated

Steady and shear dynamic rheological properties 1015

at Bolivar department (Colombia). The fruits were washed and peeled. The pulp

was crushed by mechanical shear, using a KitchenAid food processor for 2 minutes

in order to obtain a homogeneous natural pulp. The samples were vacuum packed

in small plastic bags and stored at -4ºC until further analysis.

Rheological characterization Rheological characterization of natural pulp was carried out in a controlled-stress

rheometer (Modular Advanced Rheometer System MARS 60, HAAKE, Thermo-

Scientific, Germany). Small-amplitude oscillatory shear (SAOS) tests were

performed inside the linear viscoelastic region, using plate-plate geometries (35 mm

diameter and 1 mm gap), in a frequency range of 10−2 – 102 rad/s. Stress sweep

tests, at frequencies from 0.01 Pa to 1000 Pa at 1 Hz, were previously performed

on each sample to determine the linear viscoelasticity regime.

Steady-state viscous flow tests, in the range 0.001 to 1000 s-1, were performed using

serrated plate–plate geometry (35 mm diameter, 1 mm gap and relative roughness

0.4) to prevent slip effects. At least two replicates of each test were performed on

fresh samples. Rheological tests were always carried out at different temperatures

within the range of 20 to 100 ºC. The temperature was fixed at 25 ºC (using a Peltier

system) and each sample was equilibrated at 600 seconds before the rheological

test, to ensure the same recent thermal and mechanical history for each sample.

Results and discussion Due to the importance of the viscosity and viscoelastic properties of squash pulps,

a rheological study was carried out. The rheological parameters were evaluated at

different temperatures: 20, 40, 60, 80 and 100 ºC. Figure 1 shows the flow curve

behavior of pulps.

Figure 1. Apparent viscosity of squash (Cucurbita moschata) pulps at different

temperatures (20, 40, 60, 80 and 100ºC) adjusting to Carreau-Yasuda models.

10-3

10-2

10-1

100

101

103

104

105

106

Appare

nt vis

cosity (

) / P

a·s

Shear rate () / s-1

20ºC

40ºC

60ºC

80ºC

100ºC

Model of Carreau

.

1016 Somaris E. Quintana at al.

The curves exhibited non-Newtonian behavior. A Newtonian plateau region was

observed at low shear rates (with constant viscosity), followed by a decrease of

viscosity, a shear thinning region and infinite shear rate viscosity at higher shear

rates. Similar results were obtained in mango pulp (Mangifera indica L-Keitt) [6],

nispero (Achras sapota), zapote (Colacarpum sapota Merr) [7], papaya pulp

(Carica papaya) [4] and other fruit pulps [14]. Among the models used to describe

the rheological behavior of the pulp, the Carreau equation [15] (1) provided the best

statistical parameters to fit the experimental data, obtaining a minimum correlation

coefficient R2 > 0.9712.

𝜂 = 𝜂∞ + (𝜂𝑜 − 𝜂∞)[1 + (𝜆𝑐�̇�)𝑎]n−1

𝑎 (1)

This equation represents the fluid viscosity (𝜂) as a function of shear rate (�̇�),

where 𝜂∞ is the infinite shear rate viscosity, 𝜂𝑜is the zero shear rate viscosity, 𝜆𝑐 is

the Carreau time constant, 𝑎 is the transition control factor and n is the behavior

index of the power law. Fitting parameters are shown in Table 1. The results

indicated that all of the squash pulp samples exhibit shear-thinning behaviors at

temperatures applied (flow index < 1) [16]. The rheological properties of fruit pulps

depend on the variety and maturation state of the fruit, the concentration of soluble

solids, the form, size and concentration of the suspended particles in the final

product and other parameters, such as variations in temperature during processing

[17]. The index (n) decreased as pulp temperature increased, characterizing more

concentrated pulps as having a more pronounced pseudo-plastic character.

According to Rao, 2007, this behavior can be explained by clusters in the pulp being

modified and breaking down due to increases in the shear rate. Quintana et al.,

2016 showed that results had a high dependence on the thermic treatment applied

to the pulps before the rheological analyses were carried out. Carbohydrates rotate

and interact with the fluid and can attain subsequent alignment if their concentration

is very high [20].

Table 1. The parameters of the Carreau model Steady shear rheology parameters

of squash (Cucurbita moschata) pulps.

Temp

ºC

Zero shear

viscosity

(Pa·s)

Infinite

shear

viscosity

(s-1)

Time

constant

Transition

control

factor

Power

index R2

20 626944.47 10.6 152.92 1.288 0.124 0.985

40 387615.87 29.3 156.08 1.358 0.121 0.971

60 364521.31 21.8 188.15 1.303 0.129 0.985

80 294061.87 14.4 166.58 1.291 0.122 0.988

100 357867.38 11.2 116.79 1.257 0.123 0.984

Steady and shear dynamic rheological properties 1017

The effect of temperature on the apparent viscosity of fluids in food (at constant

shear rates) could be explained by the Arrhenius equation [21]–[23], which is

expressed as:

𝜂 = 𝐴𝑒𝑥𝑝 (𝐸𝑎

𝑅𝑇)

(2)

where A is the pre-exponential factor, 𝐸𝑎 is the activation energy (parameters

evaluating thermal dependence in J/mol), R is the gas constant (8.314 J/mol·K) and

T is the absolute temperature (K). The apparent viscosity of samples at 2.0 s-1 can

be taken to be typical values found in a wide range of food processes [13] and they

can be well modelled by the Arrhenius Equation (2), being of the same order of

magnitude (Figure 2); the R2 values were always higher than 0.8864.

Figure 2. Viscosity – temperature and Arrhenius viscosity results squash

(Cucurbita moschata) pulp.

2,6 2,8 3,0 3,2 3,4

0,0

1,0

2,0

3,0

4,0

5,0 Squash (Cucurbita moschata) pulp

Arrhenius equation

ln(

/Pa·s

)

1/T (1/K)

The squash pulp activation energy value (𝐸𝑎 =1229.46 J/mol) was lower than

papaya pulp (10.55 kJ/mol) [4], siriguela pulp (15.08 kJ/mol) [24] and Jabuticaba

pulp (13.00 kJ/mol) [25], indicating a less pronounced effect of temperature on its

viscosity. Thus, the internal structure of squash pulp is less affected by temperature

than those of other products. The activation energy is necessary for the movement

of the molecules when the temperature in the liquid increases, they slight more

easily due to the higher activation energy at high temperatures. In this case, an

increase in temperature causes a decrease in the viscosity of the liquid phase,

increasing the movement of the suspended particles and causing a decrease in the

viscosity of the pulp [26].

1018 Somaris E. Quintana at al.

3.3. Viscoelastic properties

To achieve reliable results, the linear viscoelastic region of all samples was

identified by stress sweep experiments. In this region, both the storage modulus

(G’) and loss modulus (G’’) are strain independent at a constant angular frequency.

Furthermore, G’ was higher than G’’, indicating that the pulps present more elastic

than viscous behavior. Frequency sweep was performed within the linear,

viscoelastic region. The mechanical spectra obtained from frequency sweep tests

for pulps at different temperatures are shown in Figure 3.

Figure 3. The storage modulus (G′) and modulus (G′′) as a function of frequency

for squash (Cucurbita moschata) pulps at different temperatures (20, 40, 60, 80

and 100ºC)

100

101

102

104

105

Sto

rag

e m

od

ulu

s (

G') /

Pa

Lo

ss m

od

ulu

s (

G'')

/ P

a

Frecuency () / rad·s-1

G' G''

20ºC 20ºC

40ºC 40ºC

60ºC 60ºC

80ºC 80ºC

100ºC 100ºC

The storage modulus (G’) is higher than the loss modulus (G’’) within the range of

oscillation frequencies studied and this indicates that the pulp has more dominant

elastic properties than viscosity properties. Thus, the product can be classified as a

weak gel [18]. Similar behavior has been reported for other food products, such as

jabuticaba pulp [25], acai pulp [27] and umbu pulp [28]. An increase in G’ and G’’

in relation to temperature was observed, although no dependence on the G’ and G’’

values was observed with increased temperatures. Complex viscosity (η*)

comprises the elastic and viscous properties of squash pulp under zero flow

conditions, as shown in Figure 4 and it is found to be very high at low angular

frequency.

Steady and shear dynamic rheological properties 1019

Figure 4. Complex viscosity versus angular frequency for squash (Cucurbita

moschata) pulps at different temperatures (20, 40, 60, 80 and 100ºC).

100

101

102

103

104

105

Co

mp

lex v

isco

sity (

*) /

Pa

·s

Frecuency () / rad·s-1

20ºC

40ºC

60ºC

80ºC

110ºC

An inverse power dependence of the complex viscosity was confirmed when

evaluated as a function of the angular frequency. However, all samples

demonstrated evident shear-thinning behavior, since the η∗ exhibited a negative

dependence on ω.

3.4. Ascertainment of the Cox-Merz rule

The Cox-Merz rule (Equation 3) is applied to correlate the dynamic and steady-

state shear properties of the solutions. The magnitude of complex viscosity (𝜂∗)

and apparent shear viscosity η are compared at equal values of shear rate and

frequency [13], [29].

𝜂∗ = 𝜂(�̇�)|𝜔=�̇� (3)

This rule has been studied for many polymers, solutions and complex food systems

[10], [30], [31]. In order to examine the applicability of the Cox–Merz rule, the

apparent viscosity (𝜂) and complex viscosity (𝜂∗) of squash pulp (Cucurbita

moschata) were plotted against shear rate (�̇�) and angular frequency (ω),

respectively (Figure 5).

1020 Somaris E. Quintana at al.

Figure 5. Comparison of Complex viscosity and apparent viscosity in function of

angular frequency and shear rate for squash (Cucurbita moschata) pulps at

different temperatures.

10-3

10-2

10-1

100

101

102

103

104

105

106

App

are

nt

vis

co

sity (

) and

com

ple

x v

isco

sity ()

/ P

a·s

Shear rate () / s-1 and frecuency ()/rad·s

-1

20ºC

40ºC

60ºC

80ºC

100ºC

*

20ºC

40ºC

60ºC

80ºC

100ºC

.·

It was observed that the magnitudes of the complex viscosity (𝜂∗) were higher than

apparent viscosity (𝜂), indicating that the Cox–Merz rule was not applicable to

squash pulp. Similar results were obtained in other investigations on the steady and

dynamic shear rheological properties of commercial tomato ketchup samples [32]

and it was found that the Cox–Merz rule was not applicable in ketchup–processed

cheese mixtures [33] and mango jam [34]. The non-applicability of the Cox–Merz

rule for complex dispersions is attributed to the presence of high-density

entanglements or to the development of structural and intermolecular aggregation

in solution [10].

Conclusions

Rheological analyses of the natural squash pulps showed that the viscosity of the

samples was influenced by the temperature applied. All samples showed shear

thinning behavior that could be adjusted to fit the Carreau-Yasuda model R2 >

0.9712. A dependence on temperature was observed, so the samples could behave

in accordance with the Arrhenius equation. Their viscoelastic properties present a

weak gel behavior. These gels were thermostable and show significant differences

as a function of temperature. Moreover, the Cox-Merz power rule was not

applicable to describe the rheological properties of the pulp because the viscosity

at a steady state was higher than complex viscosity. Considering the use of squash

Steady and shear dynamic rheological properties 1021

in different food products and preparations, the study of the rheological behavior of

its pulp have an important commercial value and should be used to promote further

applications and help design new products.

Acknowledgements. This work is part of a research project "Basic and applied

research projects in the agricultural sector (667 of 2014); Project 0487-2014 code

1107-667-44997" sponsored by the Administrative Department of Science,

Technology, and Innovation (CTeI) - Colciencias (Colombia). The authors are

grateful for their financial support.

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Received: March 21, 2018; Published: April 19, 2018