Rheological characterization of Poly(ethylene oxide) and carboxymethyl cellulose suspensions with added solids

LWT - Food Science and Technology 64 (2015) 131e139

Contents lists available at ScienceDirect

LWT - Food Science and Technology journal homepage: www.elsevier.com/locate/lwt

Rheological characterization of Poly(ethylene oxide) and carboxymethyl cellulose suspensions with added solids O. Skurtys a, *, R. Andrade b, F. Osorio c Department of Mechanical Engineering, Universidad T
ecnica Federico Santa María, Santiago, Chile Department Food Engineering, Universidad de Cordoba, Montería, Colombia c Department of Food Science and Technology, Universidad de Santiago de Chile, Avenida Ecuador 3769, Santiago, Chile a

b

a r t i c l e i n f o

a b s t r a c t

Article history: Received 23 February 2015 Received in revised form 20 May 2015 Accepted 21 May 2015 Available online 4 June 2015

Many foods are suspensions of solid particles randomly distributed in a non-Newtonian polymeric fluid. The rheological properties of high molecular weight poly(ethylene oxide) (PEO) and carboxymethyl cellulose (CMC) suspensions by adding micro-metric solid particles such as fibres or spheres were studied. The particle volume fraction, F, was varied between 0 and 0.4. Their rheological properties were obtained after fitting a Cross model. Rheological behaviour of the solutions was compared with rheological behaviour of food reported in the literature. For PEO and CMC solutions with spherical particle, the behaviour of the normalized steady shear viscosity, m/m0, as function of the fraction volume was compared with a Thomas model. However, for PEO the multibody interactions were not well represented and for CMC suspensions, m/m0 seems to be lineal with F. To observe and explain more the influence of the particle concentrations on the rheological behaviour, dynamic rheological measurements (upon verification of the linearity limit) were also performed. A transition from a dominantly viscous fluid to a dominantly elastic material was observed when F was increased. © 2015 Elsevier Ltd. All rights reserved.

Keywords: Carboxymethyl cellulose Cross model Food texture Poly(ethylene oxide) Solid suspensions

1. Introduction Many foods are suspensions of solid particles randomly distributed in a continuous medium (Newtonian or non-Newtonian fluid) such as: tomato puree, peanut butter, salad dressing (Rao, 1999; Saeseaw, Shiowatana, & Siripinyanond, 2005; Tadros, 2010). Considerable attention is given in the literature to the rheology of suspensions of particles in Newtonian fluids like starch granules in water (Bertolini, 2010; Rao, 1999). In contrast, even if the rheology of suspensions in non-Newtonian media is in the food engineering field, from a technological point of view, more important than its counterpart in Newtonian media, relatively few studies are conducted on the rheology of dilute or semi-dilute suspensions of solid particles in non-Newtonian food fluids. The rheology behaviour of suspension (spheres, fibres etc.) in pure viscoelastic fluids like polystyrene melt, PDMS are further reported (Larson, 1999). Addition of solid particles to food fluids does not simply change the magnitude of the viscosity, it can modify strongly the rheological properties of the fluid. However, external variables such as

* Corresponding author. E-mail address: [email protected] (O. Skurtys). http://dx.doi.org/10.1016/j.lwt.2015.05.047 0023-6438/© 2015 Elsevier Ltd. All rights reserved.

temperature and pressure can also influence the rheological behaviour (Doi & Edwards, 1994). Thus, knowledge of the rheological behaviour of this class of complex fluid is fundamental to understand the relationship between the food processing behaviour and relations between structure and property. In food engineering, pseudo-plasticity or shear-thinning fluids as poly(ethylene oxide) (PEO) or carboxymethyl cellulose (CMC) are the most common type of time-independent non-Newtonian fluid (Chhabra, 2010). These fluids are characterized by an apparent viscosity (defined as the ratio between the shear stress s and the _ which decreases with increasing shear rate. The shear rate g), rheological properties of polymer solutions are strongly related to the chemical formulation, the molecular weight and the concentration of the polymer and external variables such as temperature and pressure (Doi & Edwards, 1994). Poly(ethylene oxide) (PEO) is a polymer of ethylene oxide, flexible and non-ionic water-soluble used in many applications from industrial manufacturing to medicine (Phillips & Williams, 2000). The shear rheology of PEO solutions has been characterized by several authors. Effects of concentrations, molecular weights, salt and anionic surfactants on the viscoelastic character of PEO in aqueous solutions were commented by Lance-Gomez and Ward (1986). Carboxymethyl

132

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

cellulose (CMC) is derived from cellulose, it is used as a viscosity modifier or thickener, and to stabilize emulsions in various food products including ice cream; it is known for its excellent water retaining capacity (Phillips & Williams, 2000). Moreover, it is the sodium salt of CMC (CH COONa) that promotes water solubility, which is not affected by the temperature of the water itself. The rheological properties of CMC solutions at high concentrations have both non-Newtonian and viscoelastic properties. Food suspensions are complex materials whose rheological characteristics with respect to the nature of the solid particles as well as those of the fluid media often are determined using experimental modelling. Generally, the sizes of the particles are micrometric. Various food use microspheres of polyethylene (sizes from 10 mm to 1000 mm) as component: chewing gum base, cheese, etc. (Nussinovitch, 2010). To model, the simplest suspensions are composed of hard spheres in which the only interactions between particles are rigid repulsion that occur when particles come into contact. A widely appreciated example of a solid suspension is chocolate. Chocolate is a polydisperse suspension (sugar, cocoa and/ or milk solids) in a Newtonian fluid (fat phase) (Afoakwa, Paterson, & Fowler, 2007). However, most foods are non-Newtonian fluids containing nonspherical particles, e.g. tomato or apple pulp, cassava paste etc. Thus, to understand more food fluid-solid particle interactions, it is advisable to use nonspherical particles like fibres. Therefore, the purpose of this article is to study the changes in apparent viscosity of high molecular weight of PEO and CMC suspensions by adding micro-metric solid particles such as fibres or spheres. Steady shear flow tests were done to measure the steadystate viscosity of the suspension. Flow curves were reported for two PEO and CMC concentrations and various particle volume fraction (0
F
0.4) and were fitted using a Cross model. For all experiments, the normalized steady shear viscosity, m/m0, was modelled as function of particle volume fraction. Dynamic rheological measurements (upon verification of the linearity limit) were also performed to observe and explain more the influence of the particle concentrations on the rheological behaviour. 2. Materials and methods 2.1. Suspending fluids Two different types of suspending fluids were used. Poly(ethylene oxide) (PEO) is used as shear-thinning fluid whereas sodium carboxymethyl cellulose (CMC) is, instead, used as viscoelastic carrier fluid. Both fluids have a density r ¼ 1000 kg m3 at C. PEO and CMC were provided by SigmaeAldrich. POE has a nominal molecular weight Mw of 4  106 g mol1 whereas CMC had Mw z 7  105 g mol1 with a degree of substitution of 0.80e0.95. The aqueous solutions of PEO and CMC were prepared by dissolving the appropriate amount of PEO and CMC in distilled water at room temperature. Sufficient time (>24 h) of continuous magnetic stirring was allowed to achieve complete homogenization. PEO concentrations were fixed in the range 1%e1.5% w/w whereas CMC concentrations were chosen in the range 1.5%e2.2% w/w. 2.2. Solid particles Two types of glass bead microspheres purchased from Sigmund Lindner GmbH (Germany) were used as solid suspensions: A-type (size range: 0e50 mm) and B-type (size range: 40e70 mm). Carbon fibres were purchased from Zoltek (Panex 35, USA). The density of the glass beads was rs ¼ 2448 kg m3 whereas for carbon fibres rf ¼ 1810 kg m3. Particle size distribution (PSD) of glass beads was determined using a laser scattering spectrometer Mastersizer S model MAM 5005 (Malvern Instruments Ltd., UK). The length and

diameter of the fibre was constant lp ¼ 100 mm and dp ¼ 7.2 mm, respectively. Therefore the aspect ratio, i.e. length/diameter, was rp ¼ 13.88. Particle volume fraction, F, was varied between 0 and 0.4 for each polymer concentration. 2.3. Preparation of the suspensions Preparation of the suspensions was done with care as homogeneous dispersion of non agglomerated particles is difficult to obtain especially for low solid concentrations. The solid particles were dried to remove moisture. The polymer solution and solid particles were then weighted and gently stirred (to avoid introducing air) in a beaker for 1 h at the desired proportion. Solutions of CMC and PEO were clear and colourless therefore transparent to light. Optical observation confirmed that the particles were well dispersed and did not form aggregates. 2.4. Rheological measurements All the rheological measurements were performed on a rheometer (Carri Med, CSL2 100, TA Instruments, UK) using a 40 mm diameter parallel plate fixture with a gap h ¼ 600 mm. The lower plate is equipped with a Peltier temperature control system; all tests were conducted at 20  C with 3 repetitions. The samples were carefully loaded to the measuring plate of the rheometer using a spatula and then the measuring plate was raised at a very slow speed, in order to prevent the disruption of the solution structure. Moreover, it was checked that in all cases the time scale associated with sedimentation was much larger than the time scale of both sample preparation and experiment (10 min). For spherical particle, the settling time required to migrate 10% of the rheometer gap, h, under the influence of gravity, g (acting perpendicular to the gap) can be calculated from the Stokes law:

tsettling ¼

0:45mo h
 R2 g rp  r

(1)

where g is the gravity, m0 is the dynamic viscosity of the suspending fluid, h is the gap, rp and r are the particle density and fluid density, respectively. For fibre particle, another settling time can be estimated from the settling vertical velocity (Happel & Brenner, 1965):

Vsettling ¼


 d2p g rp  r h

1 2 ln 2rp  1:614  0:355 ln 2rp 16mo 
 i 2 þ O ln 2rp (2)

where dp is the fibre diameter, rp is the aspect ratio, g is the gravity, m0 is the dynamic viscosity of the suspending fluid, and rp and r are the particle density and fluid density, respectively. The flow curves were obtained by applying an increasing shear stress ramp at a constant stress rate of 0.05 Pa s1. Storage G0 (u) and loss G00 (u) moduli were measured at frequencies ranging from 0.1 to 10 Hz and, by applying a chosen stress value, allowing measurements within the linear viscoelastic region. 3. Results and discussion 3.1. Spherical particle size measurements As, the De Brouckere mean diameter of the particles and the size distribution of the particles influence the flow behaviour

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

(Okechukwu & Rao, 1995), the particle size distribution (PSD) and the volume percentile in term of cumulative plot are shown in Fig. 1 for the two types of glass beads. Both samples are polydispersed with a monomodal PSD. The maximum particle diameter below which 50% of the sample volume exists, also known as the median particle size by volume, was for both the A-type and B-type, DA[5,0] ¼ 36.8 mm and DB[5,0] ¼ 58.2 mm respectively. The volume mean moment (De Brouckere Mean Diameter) was DA[4,3] ¼ 36.7 mm and DB[4,3] ¼ 59.8 mm. The relative difference of each statistical parameter X, DA[X]  DB[X]/DA[X], was about 60%. 3.2. Rheological properties of CMC and PEO suspensions The dynamic viscosity as function of the shear rate is presented in Fig. 2 for the four suspending fluids. Rheological behaviour of the suspending fluids can be modelled using the Cross model:

m  m∞ 1 ¼ m0  m∞ 1 þ ðlgÞm

133

degree of polymerisation of the cellulose molecules (DP) and the degree of substitution (DS) of the chain. For example, increasing DP very rapidly increases the viscosity of the modified cellulose in solution (Young & Shoemaker, 2001). The rheological properties of high molecular weight PEO aqueous are depending on polymer concentration and molecular weight (see Ortiz, Kee, and Carreau (1994)). The time constant, l, is a time constant related to the relaxation times of the polymer in solution. Thus when l increases with the polymer concentration, the entanglementdisentanglement process with shear rate is longer (Clasen & Kulicke, 2001; Dunstan, Hill, & Wei, 2004). Indeed, for pure PEO solution, l was equal to 0.44 s and 1.71 s for [PEO] ¼ 1% and [PEO] ¼ 1.5%, respectively. The characteristic time of pure CMC solutions was smaller than the pure PEO solutions. l was equal to 0.31 s and 0.51 s for [CMC] ¼ 1.5% and [CMC] ¼ 2.2%, respectively. In comparison, the time characteristic of the yogurt is close to [CMC] ¼ 1.5% since its Cross equation is m0 ¼ 10 Pa s, m∞ ¼ 0.004 Pa s, l ¼ 0.26 s and m ¼ 0.9 (Macosko, 1994).

(3)

_ m0 and where m is the dynamic viscosity at any given shear rate g, m∞ are the asymptotic values of viscosity at zero-shear rate and infinity shear rate, respectively. m the rate or rheological index i.e. a dimensionless constant indicating the degree of dependence of the viscosity on shear rate in the shear-thinning region. l is the characteristic time i.e. a constant parameter with the dimension of time. The Newtonian limit is recovered when l / 0. This model was chosen because it can describe both monotonic and non-monotonic flow curves. Their rheological properties obtained after fitting the Eq. (3) are reported in Table 1. For all cases, an excellent fit was obtained since the adjusted Rsquared was greater than 0.95. All pure solutions are shearthinning since m < 1, however, when the polymer concentration increases m was closer to 1. For example, m was equal to 0.77 and 0.83 for [CMC] ¼ 1.5% and [CMC] ¼ 2.2%, respectively. For PEO and CMC polymers, the viscous interactions between polymers chains are higher when the concentration increases since the viscosity at zero shear rate and infinity shear rate increases. When the concentration was fixed to 1.5%, the viscosity at zero shear rate of CMC is higher than PEO. It was reported by Edali, Esmail, and Vatista (2001) that rheological properties of CMC were influences by the type of substitution of the cellulose, the average chain length or

3.3. Shear flow measurements of suspensions with added particles 3.3.1. Shear flow measurements of PEO suspensions with added particles For two PEO concentrations and five particle volume fractions (A-type, B-type and fibres), the dynamic viscosity as function of shear rate is plotted over a logelog scale in Fig. 3. For a fixed PEO concentration, the influence of the solid particles concentrations on the dynamic viscosity is clear, when the dynamic viscosity was increased with the particle volume fraction. Moreover, at low shear rate a shear-thickening behaviour was observed. The apparent viscosity increases with increasing shear rate, followed at a given shear rate by a shear-thinning behaviour. This phenomenon had been reported by Vrahopoulou and McHugh (1987) and Georgelos and Torkelson (1988) for pure poly(ethylene oxide) in water. In our case, the phenomenon was also observed when solid particles were added. At high shear rate, i.e. when m ¼ m∞, it is noted that the viscosity varied slightly with the solid particle concentration. In practice, at high shear rate this means that the flow encounters less resistance at high shear rates. The rheological flow curves were also well represented by the Cross model (Eq. (3)) for all PEO concentrations and particle volume fractions. Indeed, for all cases, the adjusted R-squared was greater than 0.95.

Fig. 1. For A-type and B-type particles, particle size distribution (PSD) and the volume percentile in term of cumulative plot.

134

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

Fig. 2. For four suspending fluids, dynamic viscosity as a function of shear rate. Table 1 Cross model constants of pure suspending solutions (m0 and m∞ are the dynamic viscosity at zero-shear rate and at infinity shear rate, l the characteristic time, m the rate index). Fluid

m∞ (Pa.s)

m0 (Pa.s)

l (s)

m

POE 1% POE 1.5% CMC 1.5% CMC 2.2%

0.04 0.11 0.24 0.58

1.49 11.25 14.25 62.69

0.439 1.711 0.318 0.514

0.741 0.757 0.773 0.827

In Fig. 4, for both PEO solutions and various type of particles (Atype, B-type and fibre), the rate index m and the characteristic time l is plotted as function of particle volume fraction, F. For all solutions m is also lower than 1, thus the fluids (pure solution with solid particles) can classified as shear-thinning. Moreover, it was observed that the influence of the particle volume fraction on the

rate index m was weak. Except for [PEO] ¼ 1.5% with A-type particles, m remains nearly constant, close to 0.73, when the particle volume fraction was increased. Indeed, for [PEO] ¼ 1.5% with Atype particles, the fluid was slightly more pseudoplastic: m z 0.68. For each type of particles, the characteristic time l, which may be considered as a relaxation time, was found to increase with the particle volume fraction. When fibres with a particle volume fraction of 0.4 were added to pure solution, l increased threefolds when the suspending fluid was [PEO] ¼ 1.5% and more than one order of magnitude when the concentration of PEO was 1%. An increasing of the relaxation times may suggest the existence of viscoelastic effects, modifications in the microstructure of nonNewtonian suspension e.g. a “strengthening” of the solution. Moreover, it can be observed that when the glass bead diameter was modified, the characteristic time was not modified significantly, i.e. the structure of the solution was only slightly changed.

Fig. 3. For two PEO concentrations and five particle volume fractions, dynamic viscosity as a function of shear rate: (A) A-type particles, (B) B-type particles, (C) fibre particles.

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

135

Fig. 4. For two PEO concentrations and various type of particles (A-type, B-type and fibres), the rate index m and the characteristic time l as function of particle volume fraction, F.

This important feature will be discussed in more detail in dynamic rheological measurements section. At intermediate g_ the Cross model shows a power law behaviour m  m∞ zðm0  m∞ Þlm g_ m . Thus, for m[m∞ and m0 [m∞ , it is possible to compare our results with the power law models reported in the literature, in particular with the rheological properties of processed fluid and semisolid foods like fruit juices, purees, salad dressings etc. Indeed, the Cross model can be written:

mzm0 lm g_ m zK g_ n1

(4)

where: n ¼ 1  m is the flow behaviour index and K ¼ m0lm is the consistency coefficient (Pa.sn). For [PEO] ¼ 1.5% solutions n z 0.27 whereas K varied between 7 Pa.sn (pure solution) and 15 Pa.sn (40% of fibres). In comparison, the rheological behaviour of [PEO] ¼ 1.5% with a volume fraction of 20% fibres had the same rheological behaviour as mango pulp (3.49% db pectin, pH 3.56) with a 20  Brix at a temperature T ¼ 30  C: K ¼ 7.9 Pa.sn and n ¼ 0.28. While, [PEO] ¼ 1% with 40% fibre had the rheological behaviour of the same mango pulp at a temperature 70  C: K ¼ 3.6 Pa.sn and n ¼ 0.26 (see Rao, 1999). Thus, it can be noted that it may be possible to reproduce rheological behaviour of foods using a polymeric solution and solid particles. For example, our results can be interesting for food engineers who test or design processes where the food product could be replaced by an equivalent fluid. The reader can find various others food rheological behaviours in Rao (1999).

3.3.2. Shear flow measurements of CMC suspensions with added particles For two CMC concentrations and five particle volume fractions (A-type, B-type and fibres), the dynamic viscosity as function of shear rate is plotted over a logelog scale in Fig. 5. As previous cases (PEO solutions), for both concentrations and each volume fraction, an initial shear-thickening behaviour was observed, followed at a given shear rate by a shear-thinning behaviour. This behaviour was yet reported for pure CMC solution by Benchabane and Bekkour (2008). Clearly, adding fibres to the CMC solution increased the dynamic viscosity more than when spherical particles were added to the pure solution. The values of the rate index m and characteristic time l obtained after fitting the rheological flow curves with a Cross-Model are presented in Fig. 6. The adjusted R-squared was greater than 0.95. In the same way as PEO solutions, the rate index m was not significantly modified when the particle volume fraction was increased and the characteristic time l was increased with the

particle volume fraction. Indeed, adding fibres to pure the pure solution strongly modified the value of l. Moreover, m and l were higher for [CMC] ¼ 2.2% solutions. At a fixed CMC concentration, a modification of the spherical diameter had little influence on the value of the characteristic time. At intermediate g_ for [CMC] ¼ 2.2% solutions, the Cross model showed a power law behaviour with a flow index n z 0.17 and a consistency coefficient K varying between 108 Pa.sn (pure solution) and 160 Pa.sn (40% of fibres). In comparison, the rheological behaviour of [CMC] ¼ 2.2% with a volume fraction of 40% fibres had a rheological behaviour close to a tomato paste with a solid volume fraction of 54%: K ¼ 164.5 Pa.sn and n ¼ 0.22 (see Rao, 1999). 3.4. Rheological models of the suspensions with added particles 3.4.1. Rheological models of PEO suspensions with added particles With the aim of studying more the influence of the particle volume fraction on the rheological behaviour of the fluid, the normalized steady shear viscosity as function of particle volume fraction is plotted for both PEO concentrations in Fig. 7. As it is generally observed, adding solid particles increased the viscosity over that of pure polymeric solutions. It is possible to express the normalized viscosity in terms of third order polynomials in the particle volume fraction:

m ¼ 1 þ a1 F þ a2 F2 þ a3 F3 m0

(5)

where F is particle volume fraction, a1, a2, and a3 are constant coefficients, m and m0 are the dynamic viscosity at any given shear rate g_ and the asymptotic values of viscosity at zero-shear rate, respectively. The values of the coefficients (a1, a2, and a3) and the standard deviations are presented in Table 2. The polynomial fits of the experimental data are shown as solid lines in Fig. 7. For spherical particles, it can be noticed that the fit on the first order coefficient is quite robust and always in good agreement with Einstein's prediction since a1 z 2.5. The maximum deviation from the theoretical value of 2.5 is 3%. The 2.5 value confirmed for non Newtonian suspensions by our results, as theoretically reported by Palierne (1990). For fibre particles, a1 also has a value close to 2.5. Moreover, the fitting can be compared with the Thomas's model. Indeed, for particle volume fraction slightly higher than 0.3, for Newtonian fluid, Thomas and Muthukumar (1991) considered a third term in the polynomial expansion that takes into account full hydrodynamic interactions between hard-spheres:

136

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

Fig. 5. For two CMC concentrations y five particle volume fractions, dynamic viscosity as a function of shear rate: (A) A-type particles, (B) B-type particles, (C) fibre particles.

m ¼ 1 þ 2:5F þ 4:83F2 þ 6:4F3 m0

(6)

where F is particle volume fraction, m and m0 are the dynamic viscosity at any given shear rate g_ and the asymptotic values of viscosity at zero-shear rate, respectively. The second term is the Einstein limit, the third term accounts for hydrodynamic (twobody) interaction, while the fourth term relates to multibody interaction. For all solution with spherical spheres, the coefficient a2 of our fitting was found close to 4.83. Even if the suspending fluid was non-Newtonian, the hydrodynamic interaction between two spheres was well described by the Thomas's model. However, as expected, when the solid particles are fibres, the model (Eq. (6))

was not correct: a2 ¼ 11.83 and a2 ¼ 6.87 for [PEO] ¼ 1% and [PEO] ¼ 1.5%, respectively. The multibody interactions were not well represented by the Thomas model's since the values of a3 were different of 6.4. This may be due to no-Newtonian effects and also because our suspensions of spherical particles were not monodispersed. For polydispersed suspensions, the maximum packing volume fraction is higher, since small particles may occupy the space between the larger particles. Moreover, even with modest amount of smaller particles, smallest particles may act as a lubricant for the flow of the larger particles, reducing the overall viscosity. In the same way as the continuous phase the small particles are lubricating the flow of the large particles. More experimental

Fig. 6. For two CMC concentrations and various type of particles (A-type, B-type and fibres) the rate index m and the characteristic time l as function of particle volume fraction, F.

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

137

Fig. 7. For PEO suspensions, normalized steady shear viscosity (m/m0) as function of particle volume fraction (F).

results are necessary to confirm these results but clearly the Thomas model was not adequated to model the rheological behaviour of spherical particles in non-Newtonian fluid. Our results show that the normalized steady shear viscosity depends on solid particle but also on polymer concentration. Indeed, when particle volume fraction of A-type was fixed to F ¼ 0.4, for [PEO] ¼ 1% the ratio m/m0 increase 2-fold whereas when the PEO concentration was higher [PEO] ¼ 1.5%, the influence of the spherical particle on the dynamic viscosity was smaller, the ratio m/m0 only increased 20%. The same phenomenon is observed if A-type particles were replaced by B-type particles. 3.4.2. Rheological models of CMC suspensions with added particles In Fig. 8, the normalized steady shear viscosity is plotted as function of particle volume fraction. For both CMC concentrations, the normalized steady shear viscosity as function of particle volume fraction seems to be linear, i.e. m/m0 ¼ a1F þ a2. Four linear lines (guides to the eyes) are shown as dot lines in Fig. 8. To the best of our knowledge, this result was not reported in the literature. The values of the both coefficients (a1 and a2) and the standard deviations are presented in Table 3. For all solutions, the value of a2 was close to 1. At fixed CMC concentration, the value of a1, i.e. the slope of the line, increased with the sphere diameter and was maximum for fibre particles. The addition of fibres suspended in the pure solution allowed to increase the viscosity of the pure solution more than the addition of spherical particles. 3.5. Dynamic rheological measurements of the suspensions with added particles To observe and explain more the influence of the particle concentrations on the rheological behaviour, dynamic rheological measurements were carried out. Indeed, dynamic rheometry is an efficient tool to investigate the properties of food or polymer solutions with or without particles under conditions close to the atrest state, i.e. when small amplitude oscillatory shear are applied Table 2 Fit values of the polynomial coefficients of deviations are also shown. Fluids

Particles

a1

PEO 1%

A-type B-type Fibre A-type B-type Fibre

2.47 2.53 2.48 2.49 2.51 2.53

PEO 1.5%

m m0

¼ 1 þ a1 F þ a2 F2 þ a3 F3 . Standard

a2 ± ± ± ± ± ±

0.27 0.41 0.09 0.17 0.14 0.12

4.79 4.83 11.83 4.90 4.82 6.37

R2

a3 ± ± ± ± ± ±

0.31 0.23 0.94 0.31 0.72 0.58

5.34 6.87 19.29 2.32 5.84 6.64

± ± ± ± ± ±

0.20 0.017 0.20 0.01 0.74 1.03

0.994 0.999 0.996 0.990 0.999 0.997

(Deshpande, 2010). Indeed, this allows the determination of the viscoelastic properties without the disruption of the internal structure of the sample. Under this condition, the sinusoidal stress applied to a non-Newtonian fluid sample can be represented as (Deshpande, 2010; Rao, 1999):

s ¼ s0 sinðutÞ

(7)

and the linear response of the solution in terms of strain can be monitored and written as

g ¼ g0 sinðut þ dÞ

(8)

Here u is the frequency of oscillation in rad.s (u ¼ 2pf and f is the frequency in Hz), s0 is the strain amplitude, g0 is the stress amplitude, d is the phase angle between the stress and the strain (i.e., the loss angle) and t is the time. In theory, a phase angle of d ¼ 0 describes a purely elastic behaviour, whereas d ¼ p/2 describes a purely viscous behaviour. The storage modulus G0 and loss modulus G00 are defined as ratios of stress and strain amplitudes, respectively, given by G0 ¼ s0/g0cos(d) and G00 ¼ s0/g0sin(d). The storage modulus G0 is a measure of the reversible, elastic energy, while the loss modulus G00 is a measure of the viscous dissipation. Since the type of spherical particle modified only slightly the rheological properties on the suspensions, the measurements were only carried out for B-type. Moreover, only high CMC and PEO concentrations were considered. 3.5.1. Dynamic rheological behaviour for one PEO concentration and various particle volume fractions For [PEO] ¼ 1.5%, the variation of elastic (G0 ) and loss (G00 ) moduli as function of particle volume fraction at different frequencies is plotted for B-type particles and fibres in Fig. 9A and B, respectively. At lower frequency i.e. 0.1 Hz, pure PEO solution had G00 > G0 . This means that viscous properties are dominant compared to the elastic ones. This result is in good agreement with that reported by Ebagninin, Benchabane, and Bekkour (2009). When a sufficient B-type volume fraction was added to pure PEO solution, e.g. F > 0.3, G0 was slightly higher than G00 (see Fig. 9A). Thus, it is possible to modify, the dynamic rheological behaviour of this nonNewtonian fluid by increasing the volume fraction of spherical particles from a dominantly viscous fluid to a dominantly elastic material. For a food, a modification of the dynamic rheological behaviour may imply a modification of the product texture in the mouth (Sahin & Sumnu, 2006). However, the type of particles was important since in Fig. 9B, at 0.1 Hz, it is observed that the rheological behaviour of pure PEO solution can be modified by adding a smaller volume fraction of fibre: F z 0.1. For higher frequency, i.e. 1

138

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

Fig. 8. For CMC suspensions, normalized steady shear viscosity (m/m0) as function of particle volume fraction (F).

Table 3 Fit values of the polynomial coefficients of also shown. Fluids

Particles

a1

CMC 1.5%

A-type B-type Fibre A-type B-type Fibre

1.23 1.66 4.54 1.84 2.28 4.36

CMC 2.2%

m m0

¼ a1 F þ a2 . Standard deviations are R2

a2 ± ± ± ± ± ±

0.08 0.04 0.16 0.12 0.03 0.05

0.98 1.01 0.97 0.98 0.994 1.00

± ± ± ± ± ±

0.02 0.01 0.04 0.03 0.008 0.01

0.987 0.997 0.995 0.986 0.999 0.999

and 10 Hz, pure PEO solution was naturally elastic, G0 > G00 . However, when a sufficient volume fraction of particles (B-type or fibre) was added (for example, F > 0.3), G0 < G00 , the rheological behaviour of the solution was changed, i.e. the viscous properties are dominant compared to the elastic ones. 3.5.2. Dynamic rheological behaviour for one CMC concentration and various particle volume fractions For [CMC] ¼ 2.2%, the variation of elastic (G0 ) and loss (G00 ) moduli as function of volume fraction at different frequencies is plotted for B-type particles and fibres in Fig. 10A and B, respectively. Unlike to pure PEO solution, pure CMC solution showed, for all frequencies, i.e. 0.1 Hz, 1 Hz and 10 Hz, that G00 > G0 . This means that pure CMC solution was mainly viscous. This result is in good agreement with those reported by Benchabane and Bekkour (2008). When B-type particles or fibres were added to a pure CMC solution a transition from a dominantly viscous fluid to a

dominantly elastic material was observed. Values G00 and G0 were slightly higher for pure solution with fibres. The volume fraction of particles, F, was frequency-dependent. However, F was only slightly different if the particles were B-type particles or fibres. It would be very interesting to study the transition between both behaviours: dominantly viscous to dominantly elastic. 4. Conclusion The rheological properties of high molecular weight PEO and CMC suspensions by adding micro-metric solid particles such as fibres or spheres were studied experimentally. PEO concentrations were fixed in the range 1%e1.5% w/w whereas CMC concentrations were 1.5%e2.2% w/w. Particle volume fraction, F, was varied between 0 and 0.4 for each polymer concentration. For each solution, the rheological properties were shear-thinning and were described using a Cross model. The addition of solid particles increased the viscosity over those of the pure polymeric solutions. The increase of viscosity was more notorious when using fibres. The rate index m was not modified significantly when the particle volume fraction was increased but the characteristic time l was increased with the particle volume fraction. Rheological behaviour of suspensions can be compared with food fluids. For suspensions with spherical particles, the behaviour of the normalized steady shear viscosity, was compared with a Thomas model (for Newtonian fluid). For PEO the multibody interactions were not well described. Our results are consistent with those reported theoretically. For CMC suspensions, the normalized steady shear viscosity seems to lineal with F. To the

Fig. 9. For [PEO] ¼ 1.5%, variation of elastic (G0 ) and loss (G00 ) moduli as function of volume fraction at different frequencies for two suspending fluids: A) B-type particles; B) fibres.

O. Skurtys et al. / LWT - Food Science and Technology 64 (2015) 131e139

139

Fig. 10. For [CMC] ¼ 2.2%, variation of elastic (G0 ) and loss (G00 ) moduli as function of fibre volume fraction different frequencies for two suspending fluids: A) B-type particles; B) Fibres.

best of our knowledge, these results were never reported. At low frequency, 0.1 Hz, pure PEO solution was viscous whereas at higher frequency, i.e. 1 and 10 Hz, pure PEO solution was naturally elastic, G0 > G00 . When a sufficient volume fraction of particles (B-type or fibre) was added (for example, F > 0.3), the rheological behaviour of the solution can be modify. Pure CMC solution was viscous for all frequencies. However, if particles were added (B-type or fibres) a transition from a dominantly viscous fluid to a dominantly elastic material was observed. The volume fraction of particles, F, was frequency-dependent but independent of the kind of particles (Btype or fibre). Finally, more experiments are necessary especially for low particles volume fraction and we believe that our results reported here can potentially impact in food engineering. Indeed, the knowledge of the rheological properties of polymeric solutions with added solid particles is very important in various unit operation processes: design of a pipe network, etc. Acknowledegment O.S wishes to thanks the financial support provided by Fondecyt (project 1120661). FAO would like to thank DICYT-Usach. References Afoakwa, E. O., Paterson, A., & Fowler, M. (2007). Factors influencing rheological and textural qualities in chocolate e a review. Trends in Food Science & Technology, 18(6), 290e298. Benchabane, A., & Bekkour, K. (2008). Rheological properties of carboxymethyl cellulose (cmc) solutions. Colloid & Polymer Science, 286, 1173. Bertolini, A. C. (2010). Starches: Characterization, Properties, and Applications, chapter Trends in starch applications (pp. 1e20). Taylor and Francis Group, LLC. Chhabra, R. P. (2010). Rheology of complex fluids, chapter non-Newtonian fluids: An introduction (pp. 3e34). Springer-Verlag. Clasen, C., & Kulicke, W. M. (2001). Determination of viscoelastic and rheo-optical material functions of water-soluble cellulose derivatives. Progress in Polymer Science, 26, 1839e1919. Deshpande, A. P. (2010). Rheology of complex fluids, chapter oscillatory shear rheology for probing nonlinear viscoelasticity of complex fluids: Large amplitude (pp. 87e110). Springer-Verlag. Doi, M., & Edwards, S. F. (1994). The theory of polymer dynamics. Oxford University Press.

Dunstan, D. E., Hill, E. K., & Wei, Y. (2004). Direct measurement of polymer segment orientation and distortion in shear: semi-dilute solution behavior. Polymer, 45, 1261e1266. Ebagninin, K. W., Benchabane, A., & Bekkour, K. (2009). Rheological characterization of poly(ethylene oxide) solutions of different molecular weights. Journal of Colloid and Interface Science, 336, 360e367. Edali, M., Esmail, M. N., & Vatista, G. H. (2001). Rheological properties of high concentrations of carboxymethyl cellulose solutions. Journal of Applied Polymer Science, 79, 1787e1801. Georgelos, P. N., & Torkelson, J. M. (1988). The role of solution structure in apparent thickening behavior of dilute peo/water systems. Journal of Non-Newtonian Fluid Mechanics, 27, 191e204. Happel, J., & Brenner, H. (1965). Low Reynolds number hydrodynamics with special applications to particulate media. Englewood Cliffs, N.J: Prentice Hall, Inc. Lance-Gomez, E., & Ward, T. (1986). Viscoelastic character of poly(ethylene oxide) in aqueous solutions: effect of shear rate, concentration, salt, and anionic surfactant. Journal of Applied Polymer Science, 31, 333e340. Larson, R. G. (1999). The structure and rheology of complex fluids (pp. 279e297). Oxford University Press, Inc. Macosko, C. W. (1994). Rheology: Principles, measurements and applications, chapter viscous liquid (pp. 65e108). Wiley. Nussinovitch, A. (2010). Polymer macro- and micro-gel beads: Fundamentals and applications, chapter food and biotechnological applications for polymeric beads and carriers (pp. 75e116). Springer. Okechukwu, P. E., & Rao, M. A. (1995). Influence of granule size on viscosity of cornstarch suspension. Journal of Exture Study, 26, 501e516. Ortiz, M., Kee, D. D., & Carreau, P. (1994). Rheology of concentrated poly (ethylene oxide) solutions. Journal of Rheology, 38, 519e539. Palierne, J. F. (1990). Linear rheology of viscoelastic emulsions with interfacial tensions. The Journal of Chemical Physics, 29, 204e214. Phillips, G. O., & Williams, P. A. (2000). Handbook of hydrocolloids. CRC e Woodhead Publishing. Rao, M. A. (1999). Rheology of fluid and semisolid foods: Principles and applications. Aspen Publishers, Inc. Saeseaw, S., Shiowatana, J., & Siripinyanond, A. (2005). Sedimentation field-flow fractionation: size characterization of food materials. Food Research International, 38, 777e786. Sahin, S., & Sumnu, S. G. (2006). Physical properties of foods. Springer. Tadros, T. F. (2010). Rheology of dispersions: Principles and applications. Wiley-VCH Verlag. Thomas, C. U., & Muthukumar, M. (1991). Three-body hydrodynamic effects on viscosity of suspensions of sphere. The Journal of Chemical Physics, 94, 5180e5189. Vrahopoulou, E., & McHugh, A. (1987). Shear-thickening and structure formation in polymer solutions. Journal of Non-Newtonian Fluid Mechanics, 25, 157e175. Young, S. L., & Shoemaker, C. F. (2001). Measurements of shear-dependent intrinsic viscosities of carboxymethyl cellulose and xanthan gum suspensions. Journal of Applied Polymer Science, 42, 2405e2408.