Flow behaviours of cellulose and carboxymethyl ...

Food Hydrocolloids 58 (2016) 235e245

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Flow behaviours of cellulose and carboxymethyl cellulose from grapefruit peel Mukaddes Karatas¸, Nurhan Arslan* , Turkey Faculty of Engineering, Department of Chemical Engineering, Fırat University, 23279 Elazıg

a r t i c l e i n f o

a b s t r a c t

Article history: Received 14 November 2015 Received in revised form 19 February 2016 Accepted 28 February 2016 Available online 3 March 2016

The viscosity of cellulose from defatted, protein, pectin and hemicellulose free, delignified grapefruit peel was measured at different temperatures (10e60 C) and concentrations (1e10 kg/m3) with a capillary flow technique. The effects of concentration and temperature on the viscosity of cellulose were examined by utilizing sixteen derived models describing the combined effects of temperature and concentration on the viscosity. The constants of models fitted to the experimental data were predicted by nonlinear regression analysis. The grapefruit peel cellulose was converted carboxymethyl cellulose (CMC) by etherification using sodium monochloroacetate and sodium hydroxide. The apparent viscosities of CMC from grapefruit peel cellulose were measured by using a rotational viscometer at concentrations varied from 15 kg/m3 to 35 kg/m3 for temperatures 10e60 C. Apparent viscosity decreased with increasing shear rate. Apparent viscosity increased with an increase in concentrations for all temperatures and decreased with the temperature at which viscosity was measured. The Arrhenius equation was used to describe the temperature dependence of viscosity. The power law, Bingham and Casson models were used for description of flow. The power model given a good fit for the experimental data of CMC at different temperatures and concentrations. The consistency coefficient and flow behaviour index were calculated by using the power-law model. The CMC solutions were found to exhibit pseudoplastic and thixotropic flow behaviours. At various stages of cellulose and CMC production that concentrations and temperatures changed, the best model among derived models may be used to estimate the viscosity of cellulose and CMC from grapefruit peel in the range of temperatures and concentrations studied. © 2016 Elsevier Ltd. All rights reserved.

Keywords: Grapefruit peel Cellulose Carboxymethyl cellulose Flow behaviour Chemical compounds studied in this article: Cellulose (PubChem CID: 24748) Carboxymethyl cellulose (PubChem CID: 6328154) Chloroform (PubChem CID: 6212) Methanol (PubChem CID: 887) Ammonium oxalate (PubChem CID: 14213) Sodium hydroxide (PubChem CID: 14718) Chloroacetic acid sodium salt (PubChem CID: 23665759) Isobutyl alcohol (PubChem CID 6560) Acetic acid (PubChem CID: 176) Hydrochloric acid (PubChem CID: 313)

1. Introduction Cellulose is a linear polymer of b-(1 / 4)-D-glucopyranose units in 4C1 conformation. Cellulose is the most abundant natural, renewable, biodegradable polymer. It constitutes about 33% of all plants' matter. Cellulose found in plants as microfibrils is the most important structural component of plant cell walls (Kirk & Othmer, 1967). There are potential sources of cellulose such as orange peel, palm kernel and pomelo peel (Bicu & Mustata, 2013; Chumee & Seeburin, 2014; Yan, Krishniah, Rajin, & Bono, 2009). The presence of polar carboxyl groups makes the cellulose soluble,

* Corresponding author. E-mail address: narslan2@firat.edu.tr (N. Arslan). http://dx.doi.org/10.1016/j.foodhyd.2016.02.035 0268-005X/© 2016 Elsevier Ltd. All rights reserved.

chemically reactive and strongly hydrophilic (Benyounes & Benmounah, 2012). Sodium carboxymethyl cellulose (CMC) is a water soluble negatively charged polysaccharide. CMC resulting from the interaction of salts of chloroacetic acid with alkali cellulose is the most widely used cellulose ether, with applications in the food, oil exploration, detergent, paper, textile, pharmaceutical and paint industries as thickener or a flocculating agent (Haleem, Arshad, Shahid, & Tahir, 2014; Chumee & Seeburin, 2014; Melander & Vuorinen, 2001; Oun & Rhim, 2015; Taubner, Synytsya, & Copikova, 2015). Many researchers have studied the production of CMC from agricultural waste cellulose sources such rul & Arslan, 2003, 2004), cashew tree gum as sugar beet pulp (Tog (Silva et al., 2004), Cavendish banana pseudo stem (Adinugraha, Marseno, & Haryadi, 2005), sago waste (Pushpamalar, Langford, Ahmad., & Lim, 2006), palm kernel cake (Bono et al., 2009),

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M. Karatas¸, N. Arslan / Food Hydrocolloids 58 (2016) 235e245

durian rind (Rachtanapun, Luangkamin, Tanprasert, & Suriyatem, 2012), pomelo peel (Chumee & Seeburin, 2014), cotton gin waste (Haleem et al., 2014), cotton linter pulp (Oun & Rhim, 2015) and office waste paper (Joshi et al., 2015), However, to date, to the best of our knowledge, no systematic work has been reported on the isolation of cellulose from grapefruit peel and then the carboxymethylation of isolated cellulose to CMC. CMC is the most widely used cellulose derivative, which composed of b-D-glucose and b-Dglucopyranosyl-2-O-(carboxymethyl)-monosodium salt connected via b-(1,4-glycosidic) bonds (Rachtanapun et al., 2012). Anhydrous glucopyranose unit enables some emulsifying or stabilizing functions, in addition to its thickening capacity, thermo-plasticity surface activity, film forming ability and suspending and stabilising characteristics. CMC at different concentrations can be used to increase viscosity, stabilise suspension or emulsions and maintain flow characteristics of foods (Bekkour, Sun-Waterhouse, & Wadhwa, 2014). CMC is abundantly available biopolymer with nontoxic, biodegradable, biocompatible, and good film forming properties (Almasi, Ghanbarzadeh, & Entezami, 2010). The viscosity of cellulose needs to be known to provide primary importance to the cellulose industry. The accurate viscosity data for cellulose solutions over wide temperature and concentration regions are needed for several engineering applications in the cellulose production industry. Both the temperature and concentration variations of the viscosity of fluids were combined by several investigators in a single equation (Magerramov, Abdulagatov, Azizov, & Abdulagatov, 2007). To our knowledge, no previous work on the rheological properties of cellulose from grapefruit peel has been reported. The flow curves of fluid are modelled by using the several models such as Newtonian, Bingham, power law, Casson and Herschel-Bulkley which are the most frequently used for engineering applications (Cancela, Alvarez, & Maceiras, 2005; Hojjat, Etemad, Bagheri, & Thibault, 2011; Singh & Sharma, 2013; Sopade & Kiaka, 2001; Steffe, 1992; Zhong, Oostrom, Truex, Vermeul, & Szecsody, 2013). The rheological properties of CMC depend on the concentration of CMC solutions and the degree of substitution , Farriol, Desbrie res, & Rinaudo, 2002). Since (Barba, Montane experimental viscosity data in production process of CMC from grapefruit peel cellulose are needed to make engineering calculations on heat-transfer coefficients, evaporation performance, pumping and pipe requirements, mixing requirements and equipment design, viscosity must be correlated with temperature and concentration. Viscosity data on the rheological behaviour of CMC from various sources have been reviewed by Cancela et al. (2005), Dapia, Tovar, Santos, and Parajo (2005); Edali, Esmail, and Vatistas (2001); Ghannam and Esmail, (1997), Kelessidis, Poulakakis, and Chatzistamou (2011) Lin and Ko (1995), Lindberg, € , and Martinmaa (1987) and Pilizota, Subaric and Lovric Sirvio (1996), but no published information is available on the rheological behaviour of CMC from grapefruit peel. The main objectives of the present study were: (1) to isolate the cellulose from grapefruit peel, (2) to develop the equations for correlation of the experimental viscosity data of grapefruit peel cellulose solutions as a function of temperature and concentration, (3) to synthesize CMC from grapefruit peel cellulose, (4) to investigate the rheological behaviours of CMC solutions at several temperatures, concentrations and shear rates, and (5) to discuss the behaviour of the temperature and concentration dependences of apparent viscosities of CMC from grapefruit peel in light of the various theoretical models describing the combined effect of temperature and concentration.

2. Materials and methods 2.1. Chemical analysis of grapefruit Grapefruit peel was analysed for protein and ash (AOAC, 1984). Fat content was measured by the Soxhlet method using petroleum ether. Polysaccharide was determined by difference. All results were calculated on an oven-dry matter basis. All analysis were performed in duplicate and the mean values were reported. 2.2. Isolation of cellulose from grapefruit peel Albedo and flavedo were obtained from grapefruit peels. Grapefruits were purchased from the open market. Grapefruit peels were segmented to a particle size of about 1 cm 1 cm, air-dried, and ground in a laboratory milling machine to pass a 50-mesh size screen. The ground pulp was heated to 97 C in a water bath for about 10 min to inactivate pectic enzymes. Then, it was washed with water, filtered through a suction filter, dried at 50 C and sieved. A 50-mesh fraction was used in experiments. The fat from dried and ground grapefruit peel (7 g) was removed by using conventional soxhlet extractor with chloroform:methanol (2:1, v/v) for 6 h. The defatted grapefruit peel was mixed with 0.1 M Na3PO4 (350 ml) to bring it to pH 7.5. Proteolysis was performed by the addition of protease (35 mg). After incubation overnight at 37 C, the sample was filtered. The deproteinated grapefruit peel was mixed with 750 ml of 0.25% ammonium oxalate (w/v) (pH:3.5). The mixture was shaken at 75 C in water bath for 60 min and filtered. 10% NaOH (1 g residue/20 ml NaOH) was added the depectinated grapefruit peel. The mixture was shaken at 35 C in water bath for 22 h, filtered and washed distilled water to remove the base. The hemicellulose-free grapefruit peel was mixed with 100 ml of distilled water, 5 ml of 10% acetic acid and 2 g NaCl. The mixture was shaken at 75 C in water bath for 60 min and filtered. The residue was washed with distilled water and ethanol to remove acid, and then dried at 50 C in an oven for 16 h (Kirk & Othmer, 1967). 2.3. Conversion of isolated cellulose into CMC The carboxymetylation of cellulose is a two step process and is accompanied by a undesired side reaction (Rajput, Pandey, & Joshi, 2015). The first step is activation of cellulose with an aqueous NaOH in the slurry of an organic solvent. The second step is reaction of cellulose with Na salt of chloroacetic acid. The main reaction comprises of Cell-OH þ NaOH / RcellOH$NaOH Cell-OH$NaOH þ ClCH2COONa / Cell-O-CH2COONa þ NaCl þ H2O The side reaction results in the formation of sodium glycolates from NaOH and sodium monochloroacetate. NaOH þ ClCH2COONa / HOeCH2COONa þ NaCl Isolated cellulose from grapefruit peel was converted to CMC in two steps: alkalization and etherification of cellulose. Carboxymethylation of the cellulose from grapefruit peel was performed as follows: Dried cellulose was ground to pass a 50-mesh size screen. Dried and ground cellulose (2 g) was dispersed in isobutyl alcohol (100 ml) containing NaOH of 30% (20 ml) at room temperature with continuous stirring for 90 min. The cellulose-NaOH activation reaction is generally performed at room temperature. The mixture was filtered to a weight of about 6.4 g and shredded for


90 min in a shredder. The sodium chloroacetate (3 g) was added and stirred at 70 C for 6 h. The temperature was controlled within ±0.1 C using a circulating wash bath during carboxymethylation. The reaction product was neutralized using dilute glacial acetic acid. The mixture was then filtered and the residue was suspended in 70% methanol to remove undesired salts, filtered. The residue from the filtration was dried at 70 C overnight and the powder obtained was CMC (Kirk & Othmer, 1967). The degree of substitution (DS) of CMC was determined by potentiometric titration, the standard method (Jiang et al., 2011). 2.4. Rheological measurements The strong mineral acids dissolve cellulose in certain concentration ranges. This may be presumed to be due to the formation of the eOHþ 2 ion attached to the cellulose (Ott, 1946). Cellulose solutions were prepared by mixing the required amount of cellulose to produce cellulose solutions of the intended concentration (1, 2, 4, 6, 8 and 10 kg/m3) in HCl solution of 37%. Solutions were mechanically mixed to solubilize the cellulose and to disrupt any weakly flocculated aggregates prior to any measurements. Because diluted organic solutions are generally Newtonian in character, it has been assumed that the cellulose solutions studied were Newtonian (Kirk & Othmer, 1970). An Ubbelohde type capillary viscosimeter (capillary no: II, ID:1.13 mm) was immersed to water in glass cylindrical vessel connected to a thermostated heat bath circulator which can be adjusted to give the desired temperature. The temperature was maintained as desired with an accuracy of ±0.1 C. Flow times were recorded with a stopwatch with reproducibility ±0.2 s. The viscosity of cellulose solutions of different concentrations was calculated by means of flow times at 10 C intervals from 10 C to 60 C. CMC solutions were prepared by hydrating in distilled water the CMC from grapefruit peel for overnight. Before rheological measurements, solutions were mixed vigorously with a magnetic stirrer for 24 h to release air bubbles. To characterize the rheological properties, studies were carried out by rotational rheometry. The torque was measured by using a Brookfield viscometer (LVDV-E model; Brookfield Engineering Laboratories. Inc., Stoughton, MA, USA) with various spindle speeds (6, 10, 12, 20, 30, 50 and 60 rpm). A rotational steady shear flow measurement from shear rate of 1.32 s1 to shear rate of 13.2 s1 was performed. Spindle LV-1 was used to get readings within the scale. The rheological properties of CMC solutions were evaluated at different concentrations, ranging between 15 and 35 kg/m3 and at different temperatures (10, 20, 30, 40, 50 and 60 C). A 200-ml cylindrical vessel was used for all the measurements and sample was added to cover the immersion grooves on the spindle shafts. For each test, approximately 150 ml of sample was filled into the cylindrical vessel and allowed to equilibrate at desired temperature. In order to control the temperature, the water-jacketed stainless steel cylindrical vessel was connected to a constant temperature bath which was able to maintain temperature uniformity within ±0.1 C. The shear rate was increased continuously from 1.32 to 13.2 s1 giving seven readings. The torque readings were taken after 60 s in each sample, with a resting in time between the measurements at the different spindle speeds. CMC solutions were sheared at spindle speed of 30 rpm until an equilibrium state was reached to examine the change in the apparent viscosity with shearing time. All rheological tests were replicated two times in order to investigate the reproducibility of the results. The reproducibility was ±5% on an average. Shear rates for CMC solutions were calculated by using the cylindrical spindle factors given by Brookfield (Brookfield

237

Engineering Labs. Inc., Stoughton, MA, USA) for spindle LV-1.

dVf dr ¼ 0:22N

(1)

where dVf/dr (s1) is the shear rate, N is the spindle speed (rpm). To calibrate the viscometer, Brookfield silicone viscosity standard (nominal viscosity at 25 C: 1000 mPa s) was used. The following equation was used to calculate spindle calibration factor for any spindle speed.

f ¼ R=100

(2)

where f is the spindle calibration factor, R is the full scale viscosity range. Apparent viscosity values (ha) were calibrated using the following equation.

ha ¼ f ð% TorkÞ

(3)

Shear stress was found by the following relation.

trf ¼ ha dVf dr

(4)

where trf is the shear stress (mPa),ha is the apparent viscosity (mPas), dVf/dr is the shear rate (s1), Vf is the velocity in direction along the axis of rotation, r is the radial distance. 2.5. Statistical analysis The Statistical software package (Statistica for Windows 5.0, 1995) was used to carry out the nonlinear regression analysis of experimental viscosity data for both cellulose and CMC. The analysis of variance (ANOVA) was used to evaluate statistically the effect of concentration on the flow activation energy and the consistency index. 3. Results and discussion The composition of dried grapefruit peel was 3.86% ash, 6.23% crude protein, 2.25% crude fat (on a dry weight basis). Polysaccharide content calculated by difference was 87.66%. The yield percentage of cellulose production from dried grapefruit peel was found to be 20.04%. The degree of substitution (DS) of CMC is defined as the average number of carboxymethyl groups per repeating unit and is usually in the range of 0.4e1.5. CMC generally exists under the sodium salt form, a water-soluble product for DS > 0.5. A maximum degree of substitution of 1.5 is permitted, but more typically DS is in the range 0.60e0.95 for food applications (Schmitt, Sanchez, Desobry-Banon, & Hardy, 1998). The degree of CMC solubility depends on substitution of a carboxymethyl group instead of the hydroxyl groups in cellulose structure. The degree of substitution of CMC from grapefruit peel was found to be 0.798 ± 0.014 (average ± standard deviation of three replicate trials). 3.1. The combined effect of temperature and concentration on viscosity of cellulose The effect of concentration and temperature on the viscosity of cellulose solutions of 1, 2, 4, 6, 8 and 10 kg/m3 is given in Fig. 1. The cellulose viscosity decreased as the temperature at which the viscosities were measured increased and viscosity increased at higher concentrations (Fig. 1). Decrease in viscosity is due to the interactions of the molecules in solution, which are weaker at higher temperature. This effect is caused by the loss of hydradation water around the polymer molecule (Casas, Mohedano, & Ochoa,

238


descended for a higher concentration since the changes in viscosity at high concentrations was more than those at low concentrations for all temperatures. Temperature has an important influence on the flow behaviours of solutions. The effect of temperature on viscosity is generally expressed by Arrhenius and Andrade equations. The effect of temperature on the viscosity of cellulose solutions was determined by using Andrade equations (Constella, Lozano, & Crapiste, 1989; Speers & Tung, 1986):

Fig. 1. Effect of concentration and temperature on viscosity of cellulose solutions (temperature ( C): 10, :20, 30, -40, B50, C60).

▫

▵

2000). It was stated that dilute cellulose-NaOH complex solutions experienced a quite different rheological behaviour from those at higher concentrations and a Newtonian plateau was observed with decreasing cellulose concentration (Zhang, Li, & Yu, 2011). To point out the exponential dependence of fluid viscosity and temperature, the following linearized Arrhenius equation was used (Grigelmo, Ibarz, & Martin, 1999). The model is based on the assumption that the fluid flows obeys the Arrhenius equation for molecular kinetics.

ln h ¼ ln ho þ Ea =RT

(5)

The values of the flow activation energies were calculated from the linear plot of ln h versus 1/T in Eq. (4) for the measured viscosities of cellulose as a function of concentration. The intercepts and slopes of the linear plot are flow activation energy and parameter ln hο, respectively. The values of the parameter hο and the flow activation energy for cellulose from grapefruit peel were found to be 31.72 10336.40 103 mPas and 9.56e10.54 kJ/ mol, respectively (Table 1). It were found that the values of the parameter hο and the flow activation energy for cellulose from orange peel were 48.37 10351.39 103 mPas and rul, & Arslan, 2007). As 8.87e9.05 kJ/mol, respectively (Yas¸ar, Tog seen from Table 1, the flow activation energy increased with increasing concentration and the parameter hο decreased with an increase in concentration. Flow activation energy is a measure of viscosity sensitivity to temperature changes. Therefore, the cellulose solution at concentration of 10 kg/m3 is more sensitive to temperature in comparison with the cellulose solutions at other concentrations. As a result of the analysis of variance (ANOVA), it was revealed that the increasing concentration had insignificant effects on the activation energies (p > 0.05). The parameter hο Table 1 The values of the parameter hο and the flow activation energy for cellulose from grapefruit peel. C (kg/m3)

ho 103(mPa s)

Ea (kJ/mol)

r2

1 2 4 6 8 10

36.40 35.54 35.42 34.64 33.32 31.72

9.56 9.86 9.96 10.09 10.33 10.54

0.9918 0.9909 0.9950 0.9999 0.9982 0.9992

ln h ¼ A þ ðB=TÞ þ DT

(6)

log h ¼ ðA=TÞ B

(7)

h ¼ A BlogT

(8)

where h is the viscosity of cellulose solution (mPa s), ho is a preexponential factor (mPa s), Ea is the activation energy of flow (kJ/ mol), R is the universal gas constant (8.314 103 kJ/mol K), T is the absolute temperature (K) and A, B, D are constants. The effect of concentration on the viscosity is generally described by either an exponential or a power-law relationship (Speers & Tung, 1986).

h ¼ K1 ðCÞA1 h ¼ K2 expðA2 CÞ

(9) (10)

where K1 (mPa s ðkg=m3ÞA1 ), K2 (mPa s), A1 (dimensionless) and A2 (kg/m3)1 are constants and C is the concentration of cellulose solutions (kg/m3). Similarly, relationships between A, B, D constants in Eqs. (6)e(8) and concentration can be written in of forms of Eqs. (11) and (16).

A ¼ K3 ðCÞA3

(11)

A ¼ K4 exp ðA4 CÞ

(12)

B ¼ K5 ðCÞA5

(13)

B ¼ K6 exp ðA6 CÞ

(14)

D ¼ K7 ðCÞA7

(15)

D ¼ K8 exp ðA8 CÞ

(16)

The effect of temperature and concentration on viscosity could be combined into a single equation for use in applications where simultaneous heat and mass transfer takes place. Sixteen different theoretical models (eight different models by combining the Eq. (6) and Eqs. 11e16, four different models by combining the Eq. (7) and Eqs. 11e14, four different models by combining the Eq. (8) and Eqs. 11e14) were derived. In these models, the viscosity was related to temperature and concentration. Sixteen different theoretical models describing the temperature and concentration dependence of cellulose viscosity were applied to the experimental data to determine the best fit for the temperature range 10e60 C and the concentration range 1e10 kg/m3. The constants in models were determined by the nonlinear regression analysis to examine the goodness-of-fit of the models. Statistical software package (Statistica for Windows 5.0, 1995) was used to perform the nonlinear regression analysis of experimental viscosity data. The quality of the fit of the model was estimated using the various


statistical parameters such as root mean square error (RMSE), chisquare c2, mean bias error (MBE), mean percentage error (MPE) and the coefficient of determination r2. These parameters can be calculated as follows:

c2 ¼

N 2 1 X hpre;i h N i¼1 exp;i

#1 2 (17)

2 PN i¼1 hexp;i hpre;i Nn

MPE ¼

Table 3 Statistical test results of models derived for cellulose.

=

" RMSE ¼

(18)

N 1 X hexp;i hpre;i hexp;i 100 N

(19)

N 1 X hpre;i hexp;i N

(20)

i¼1

MBE ¼

i¼1

where hexp,i is the experimental viscosity, hpre,i is the predicted viscosity, N is the number of data points and n is the number of

239

Model

RMSE

c2

MBE

MPE

r2

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

0.030930 0.037197 0.042726 0.047956 0.035114 0.040334 0.035117 0.035070 0.035095 0.029418 0.029247 0.167800 0.065453 0.073581 0.073471 0.065324

0.001148 0.001660 0.002191 0.002760 0.001480 0.001952 0.001480 0.001476 0.001386 0.000974 0.000962 0.031676 0.004820 0.006091 0.006073 0.004801

0.000334 0.001065 0.000737 0.016249 0.000645 0.000972 0.000892 0.000763 0.000155 0.000229 0.000244 0.129563 0.000045 0.000059 0.000040 0.000108

0.026067 0.147791 0.083122 0.921487 0.100511 0.107023 0.118847 0.102663 0.004893 0.029095 0.029998 6.699714 0.011332 0.029376 0.027806 0.005709

0.9948 0.9924 0.9900 0.9874 0.9933 0.9911 0.9933 0.9933 0.9933 0.9953 0.9953 0.9930 0.9766 0.9704 0.9705 0.9767

model parameters. The models showing the combined effect of temperature and concentration on viscosity of cellulose and the values of the model

Table 2 Models showing the combined effect of temperature and concentration on viscosity of cellulose and values of model parameters. Model 1

Model 2

Model 3

lnh ¼ K3CA3 þ K5CA5/T þ K7CA7T K3 ¼ 0.0000034 (kg/m3)A3 A3 ¼ 4.117839 [e] K5 ¼ 655.0075 K(kg/m3)A5 A5 ¼ 0.042365 [e] K7 ¼ 0.005434 K1(kg/m3)A7 A7 ¼ 0.011451 [e]

lnh ¼ K3CA3 þ K5CA5/T þ K8exp(A8C)T K3 ¼ 4.648189 (kg/m3)A3 A3 ¼ 0.001865 [e] K5 ¼ 17.37174 K(kg/m3)A5 A5 ¼ 43.81278 [e] K8 ¼ 0.013536 K1 A8 ¼ 0.005424 (kg/m3)1

lnh ¼ K3CA3 þ K6exp(A6C)/T þ K7CA7T K3 ¼ 4.351418 (kg/m3)A3 A3 ¼ 0.044972 [e] K6 ¼ 8.362366 K A6 ¼ 0.066296 (kg/m3)1 K7 ¼ 0.012583 K1(kg/m3)A7 A7 ¼ 0.029882

Model 4

Model 5

Model 6

lnh ¼ K3CA3 þ K6exp(A6C)/T þ K8exp(A8C)T K3 ¼ 4.46853 (kg/m3)A3 A3 ¼ 0.001904 [e] K6 ¼ 10000 K A6 ¼ 6.352374 (kg/m3)1 K8 ¼ 0.013536 K1 A8 ¼ 0.005430 (kg/m3)1

lnh ¼ K4exp(A4C) þ K5CA5/T þ K7CA7T K4 ¼ 4.501287 [e] A4 ¼ 0.005614 (kg/m3)1 K5 ¼ 26.50706 K(kg/m3)A5 A5 ¼ 2.820219 [e] K7 ¼ 0.012955 K1(kg/m3)A7 A7 ¼ 0.009856 [e]

lnh ¼ K4exp(A4C) þ K5CA5/T þ K8exp(A8C)T K4 ¼ 4.190637 [e] A4 ¼ 0.052354 (kg/m3)1 K5 ¼ 10.73362 K(kg/m3)A5 A5 ¼ 1.511501 [e] K8 ¼ 0.012310 K1 A8 ¼ 0.032759 (kg/m3)1

Model 7

Model 8

Model 9

lnh ¼ K4exp(A4C) þ K6exp(A6C)/T þ K7C T K4 ¼ 4.498836 [e] A4 ¼ 0.005617 (kg/m3)1 K6 ¼ 215.479 K A6 ¼ 2.135604 (kg/m3)1 K7 ¼ 0.012959 K1(kg/m3)A7 A7 ¼ 0.009475 [e]

lnh ¼ K4exp(A4C) þ K6exp(A6C)/T þ K8exp(A8C)T K4 ¼ 4.416049 [e] A4 ¼ 0.008447 (kg/m3)1 K6 ¼ 10000 K A6 ¼ 6.437849 (kg/m3)1 K8 ¼ 0.012766 K1 A8 ¼ 0.004895 (kg/m3)1

logh ¼ K3CA3/T ¡ K5CA5 K3 ¼ 501.565 K(kg/m3)A3 A3 ¼ 0.033787 [e] K5 ¼ 1.438065 (kg/m3)A5 A5 ¼ 0.0122704 [e]

Model 10

Model 11

Model 12

logh ¼ K3CA3/T ¡ K6exp(A6C) K3 ¼ 518.271 K(kg/m3)A3 A3 ¼ 0.012216 [e] K6 ¼ 1.493355[e] A6 ¼ 0.003397 (kg/m3)1

logh ¼ K4exp(A4C)/T ¡ K5CA5 K4 ¼ 519.037 K A4 ¼ 0.002966 (kg/m3)1 K5 ¼ 1.49576 (kg/m3)A5 A5 ¼ 0.013936 [e]

logh ¼ K4exp(A4C)/T ¡ K6exp(A6C) K4 ¼ 523.772 K A4 ¼ 0.004452 (kg/m3)1 K6 ¼ 1.508491[e] A6 ¼ 0.005206 (kg/m3)1

Model 13

Model 14

Model 15

h ¼ K3CA3 ¡ K5CA5logT

h ¼ K3CA3 ¡ K6exp(A6C) logT

h ¼ K4exp(A4C) ¡ K5CA5logT

K3 A3 K6 A6

K4 A4 K5 A5

A7

K3 ¼ 36.41702 mPa s(kg/m3)A3 A3 ¼ 0.117734 [e] K5 ¼ 13.99496 mPa s(kg/m3)A5 A95 ¼ 0.118825 [e] Model 16

h ¼ K4exp(A4C) ¡ K6exp(A6C) logT

K4 ¼ 36.5626 mPa s K6 ¼ 14.0466 mPa s A4 ¼ 0.030421 (kg/m3)1 A6 ¼ 0.030762 (kg/m3)1 [e]: dimensionless; h, mPas; T, K; C, kg/m3.

¼ ¼ ¼ ¼

42.891 mPa s(kg/m3)A3 0.001816 [e] 16.5978 mPa s 0.000557 (kg/m3)1

¼ ¼ ¼ ¼

42.8657 mPa s 0.000596 (kg/m3)1 16.5873 mPa s(kg/m3)A5 0.001638 [e]

240


constants (K3e8 ve A3e8) in Eqs. 11e16 are given in Table 2. Table 3 shows the statistical test results for models. As seen from Table 3, model 10 and model 11 has the lowest RMSE, c2 values and the highest regression coefficient values. In operations where both the temperature and concentration change during the process, the combined effect of temperature and concentration on the viscosity of cellulose from grapefruit peel can be modelled by model 10 and 11. The constants in Table 2 assist in the calculation of viscosity of cellulose from grapefruit peel within the temperatures and concentrations used in this work. Fig. 2 illustrates the comparison of experimental viscosity and predicted viscosity calculated by using model 11. The predicted results agree reasonably well with experimental data (r2: 0.9953). 3.2. Flow behaviour of carboxymethyl cellulose Flow curves for CMC solutions were obtained by fitting experimental data (shear stress-shear rate) with power law, Bingham and Casson models, which are the most frequently used for engineering applications (Hecke, Nguyen, Clausse, & Lanoiselle, 2012; Singh & Sharma, 2013; Sopade & Kiaka, 2001). These models being the most widely used viscosity models in engineering analysis and scientific computation are given below:

n Power law model : trf ¼ m dVf dr

(21)

Bingham model : trf ¼ tB þ hB dVf dr

(22)

0:5 Casson model : t0:5 rf ¼ tC þ hC dVf dr

(23)

where m is the consistency index (mPasn) and n is the flow behaviour index (dimensionless), tB and hB are the Bingham model parameters, tC and hC are the Casson model parameters. The values of model parameters of Power law, Bingham and Casson equations were obtained by non-linear regression at different temperatures and concentrations (Table 4). 0.5 Plots of trf versus dVf/dr and t0.5 for rf versus (dVf/dr) Bingham and Casson models, respectively give straight lines. Intercept values (tB in Bingham model and tC in Casson model) are yield stress which should be rather greater than zero. The power law model fitted well the experimental data since tB in Bingham model and tC in Casson model were nearly zero. Since the flow behaviour index values were less from 1, the flow behaviour of CMC

Fig. 2. Comparison of experimental viscosity and predicted viscosity values of cellulose from model 11.

solutions were pseudoplastic. Pseudoplasticity is believed to be caused by the orientation of the CMC macromolecules as they align in the direction of the shearing force (Rozema & Beverloo, 1974). The power law model was used to characterize the flow behaviour of CMC solutions. Similarly, power law model was used due to the fact that consistency coefficient and behaviour index showed excellent representation of the data for all range of shear rate used in a work conducted by Cancela et al. (2005). Diaz and Navaza (2003) noted that the rheological properties of CMC dispersions were explained by power law model. Westra (1989) stated that the rheological behaviour of CMC with xanthan gum was pseudoplastic. Lin and Ko (1995) stated that when the CMC solutions were tested by a viscometer under the steady shear conditions, the viscosities of CMC solutions versus shear rate exhibited a well-known power-law region covering a wide shear rate range. Kelessidis et al. (2011) stated that the experimental apparent viscosity data for the CMC solutions of 0.4e2.0% fitted power law model. Consistency index is a measure of the consistency of the substance. Flow behaviour index indicates the degree of nonNewtonian characteristics of the fluid. Plots of calculated m values against concentration at various temperatures are in Fig. 3. The results indicate an increased consistency index with increasing concentration at the same temperature. The consistency index values at different concentrations were found to be insignificantly different for all the temperatures considered (p > 0.05). This was probably caused by the increase of particleeparticle interaction (Vitali & Rao, 1982). Similar flow properties were observed for common fluids (Chakrabandhu & Singh, 2005; €g üs¸, 2000; Sopade & Kiaka, 2001). The consistency Maskan & Go index showed a decreasing trend with increasing temperature, which indicates a decrease in viscosity at higher temperatures. No harmonious variation was observed at n values with increase in temperature and concentration. Hassan and Hobani (1998) expressed that the flow behaviour index is almost independent of the concentration and temperature, unlike the consistency index. The apparent viscosity as a function of the shear rate at 20 C and concentrations of 15e35 kg/m3 is depicted in Fig. 4. Similar behaviour was obtained at other temperatures (graphs not shown). The plot of shear rate and shear stress for different concentrations of CMC at 20 C is given in Fig. 5. The apparent viscosity is inversely correlated to the shear rate, which indicates that the samples exhibit shear-thinning flow (Amin, Abadi, & Katas, 2014; Casas et al., 2000). Shear-thinning behaviour is classically encountered with heterogeneous systems containing a dispersed phase. The particles are linked together by weak forces. When the hydrodynamic forces during shear are sufficiently high, the interparticle linkages are broken, resulting in reduction in size of the structural units that, in turn, offer lower resistance to flow during shear (Mewis, 1979). The flow curves of the CMC solutions exhibited a shear-thinning behaviour when viscosity decreased with the increase in shear rate. The flow curves of the CMC solutions are similar to those previously reported by several researchers (Benchabane & Bekkour, 2008; Hojjat et al., 2011; Valenza, Merle, Mocanu, Picton, & Müller, 2005). The decrease in viscosity with increasing shear rate is mainly related to the disentanglement of macromolecular chains under shear field and breaking of possible structure in solution. The decrease in apparent viscosity can be attributed to the break of macromolecular aggregates (Almedia & Dias, 1997). At low shear rates, apparent viscosity decreased more sharply. At high shear rates, apparent viscosity decreased more slowly. Because viscosity is a measure of resistance to flow, resistance to flow was less in high shear rates due to breaking of aggregate. As expected, the CMC solutions at higher concentrations exhibited higher viscosity than the CMC solutions at lower


241

Table 4 Power law, Bingham and Casson model parameters for CMC at different concentrations and temperatures. T ( C)

C (kg/m3)

Power law model

Bingham model

Casson model

n

m (Pasn)

r2

hB (Pas)

tB (Pa)

r2

tC (Pa)0.5

hC(Pas)0.5

r2

15 20 25 30 35

0.8822 0.8577 0.8480 0.8281 0.7999

0.1179 0.1347 0.1511 0.1749 0.1973

0.9966 0.9922 0.9937 0.9953 0.9965

0.0870 0.0938 0.1007 0.1078 0.1099

0.0400 0.0498 0.0679 0.1002 0.1349

0.9998 0.9994 0.9982 0.9966 0.9941

0.2802 0.2869 0.2957 0.3046 0.3044

0.0673 0.0848 0.1021 0.1262 0.1552

0.9988 0.9968 0.9979 0.9983 0.9967

15 20 25 30 35

0.8918 0.8822 0.8785 0.8771 0.8274

0.1012 0.1179 0.1342 0.1525 0.1794

0.9992 0.9966 0.9936 0.9961 0.9968

0.0753 0.0870 0.0987 0.1082 0.1095

0.0379 0.0400 0.0441 0.0692 0.1073

0.9998 0.9998 0.9996 0.9961 0.9964

0.2622 0.2802 0.2964 0.3118 0.3075

0.0622 0.0673 0.0747 0.0883 0.1281

0.9995 0.9988 0.9977 0.9969 0.9981

15 20 25 30 35

0.8817 0.8918 0.8822 0.8833 0.8664

0.0816 0.1012 0.1179 0.1419 0.1577

0.9980 0.9992 0.9966 0.9977 0.9970

0.0599 0.0753 0.0870 0.1045 0.1091

0.0290 0.0379 0.0400 0.0500 0.0728

0.9999 0.9998 0.9998 0.9998 0.9980

0.2487 0.2622 0.2802 0.3075 0.3125

0.0302 0.0622 0.0673 0.0767 0.0939

0.9917 0.9995 0.9988 0.9990 0.9977

15 20 25 30 35

0.7950 0.8954 0.8343 0.8769 0.8530

0.0797 0.0941 0.1135 0.1347 0.1508

0.9900 0.9962 0.9914 0.9938 0.9941

0.0467 0.0724 0.0742 0.0987 0.1023

0.0409 0.0266 0.0486 0.0441 0.0641

0.9990 0.9996 0.9995 0.9996 0.9993

0.1962 0.2570 0.2539 0.2964 0.2982

0.0906 0.0526 0.0869 0.0747 0.0972

0.9958 0.9985 0.9974 0.9977 0.9981

15 20 25 30 35

0.8591 0.8817 0.8527 0.8822 0.8735

0.0585 0.0816 0.0973 0.1179 0.1349

0.9970 0.9980 0.9979 0.9966 0.9939

0.0400 0.0599 0.0649 0.0870 0.0970

0.0268 0.0290 0.0466 0.0400 0.0499

0.9994 0.9999 0.9997 0.9998 0.9994

0.1894 0.2334 0.2379 0.2802 0.2939

0.0561 0.0562 0.0817 0.0673 0.0791

0.9990 0.9994 0.9994 0.9988 0.9979

15 20 25 30 35

0.7177 0.7950 0.8179 0.8390 0.8658

0.0584 0.0797 0.0934 0.1121 0.1218

0.9862 0.9899 0.9897 0.9895 0.9937

0.0271 0.0467 0.0586 0.0745 0.0867

0.0397 0.0409 0.0424 0.0457 0.0436

0.9988 0.9990 0.9990 0.9993 0.9996

0.1423 0.1962 0.2242 0.2551 0.2781

0.1058 0.0906 0.0842 0.0828 0.0734

0.9963 0.9958 0.9966 0.9966 0.9982

10

20

30

40

50

60

Fig. 3. Consistency index as a function of concentration of CMC (temperature ( C): -10, 20, C30, B40, :50, 60).

▫

▵

concentrations for all temperatures due to the increase in the local intermolecular interactions between the polymer chains. The decrease in the viscosity is well-known and usually is explained by an increase in thermal activity of molecules causing an increase in molecule free volume and a simultaneous decrease in intermolecular and/or intramolecular interactions (Abraham, Ratna, Siengechin, & Karger-Kocsis, 2008). It was observed that the apparent viscosity decreased with an increase at temperature for all concentrations (graphs not shown). These changes in rheological behaviour are likely due to inner structural changes in polymer

Fig. 4. Typical flow curves for different concentrations of CMC at 20 C (concentration (kg/m3): 15, :20, B25, C30, 35).

▵

▫

solutions. The Arrhenius model has been successfully used by many researchers to describe the temperature dependency of rheological parameters (Grigelmo et al., 1999; Hecke et al., 2012; Marcotte, Taherian, Trigui, & Ramaswamy, 2001). The effect of temperature on the apparent viscosity of CMC solutions at a specified shear rate was determined by using the Arrhenius model. The non-linearized form of equation (1) is:

242

M. Karatas¸, N. Arslan / Food Hydrocolloids 58 (2016) 235e245 Table 5 Shear rate and flow activation energy relationship for CMC solutions. Shear rate (s1)

Ea (kJ/mol)

r2

1.32 2.20 2.64 4.40 6.60 11.0 13.2

6.519e11.412 6.106e12.790 6.271e14.635 6.487e15.197 6.525e16.246 4.777e16.646 3.766e16.956

0.9458e0.9688 0.9291e0.9874 0.9824e0.9901 0.9519e0.9841 0.9537e0.9916 0.9084e0.9833 0.8359e0.9779

ho ¼ d1 expðε1 CÞ

(26)

Fig. 5. Plot of shear rate and shear stress for different concentrations of CMC at 20 C (concentration (kg/m3): 15, :20, B25, C30, 35).

where d, d1, ε and ε1 are constants. A single equation combining the effects of temperature and concentration on viscosity of CMC solutions would be useful. Incorporating Eqs. (25) and (26) into Eq. (24), the following models involving the effect of concentration and temperature on viscosity are obtained.

ha ¼ ho exp ðEa =RTÞ

ha ¼ dðCÞε expðEa =RTÞ

(27)

ha ¼ d1 expðε1 CÞexpðEa =RTÞ

(28)

▵

▫

(24)

where ha is the apparent viscosity with increasing shear rate (mPas), ho is a constant(mPas), Ea is the activation energy of flow (kJ/mol), R is the universal gas constant (8.314 103 kJ/mol K), T is the absolute temperature (K). Flow activation energies were determined from the plot of ln h versus 1/T. An Arrhenius plot for shear rate of 6.6 s1 is given in Fig. 6. Ea values increased with an increase in the concentration of CMC and show a change in slope with an increase in concentration. The change in activation energy values of CMC solutions at concentrations ranging from 10 kg/m3 to 35 kg/m3 for different shear rate is given in Table 5. Activation Energy, Ea, is important in deducing the sensitivity of a process towards temperature. The higher the activation energy, the more sensitive process will be (Singh & Sharma, 2013). The concentration dependency of the viscosity at each temperature was examined using a power-law model and an exponential model (Vitali & Rao, 1982). These equations can also be used for ho. ho are function of concentration and can be described as below:

ho ¼ dðCÞε

(25)

Fig. 6. Arrhenius plot for CMC at shear rate of 6.6 s1 (concentration (kg/m3): :20, B25, C30, 35).

▫

▵15,

These rheological models would be useful to predict the apparent viscosities of CMC from grapefruit peel at different concentration and temperature values. The statistical package, Statistica for Windows 5.0, was used to perform the nonlinear regression analysis of experimental viscosity data. The various statistical parameters such as root mean square error (RMSE), chi-square c2, mean bias error (MBE), mean percentage error (MPE), modelling efficiency (EF) and r were used to determine the goodness of the fit. Parameter EF was calculated as following:

PN EF ¼

i¼1

2 P 2 hexp;i hexp;ave N i¼1 hpre;i hexp;i 2 PN i¼1 hexp;i hexp;ave

(29)

where hexp,i is the experimental viscosity, hpre,i is the predicted viscosity, hexp,ave is the average of the experimental viscosity values, N is the number of data points. Estimated constants of the Eqs. (27) and (28) and values of RMSE, c2, MBE, EF and r are presented in Tables 6 and 7, respectively. Statistical analysis indicated that Eq. (27) is more adequate than Eq. (28) in fitting apparent viscosity data as a function of temperature and concentration. The higher the values of the EF and r, the better the goodness of the fit. The lower the values of the RMSE, c2 and MBE, the better the goodness of the fit. The results have shown that highest values of EF and r and the lowest RMSE, c2 and MBE values could be obtained with the statistically fitted model of Eq. (27). Validation of the established model was evaluated by comparing the computed apparent viscosity values with the observed apparent viscosity values. The performance of the model was illustrated in Fig. 7 (r2:1). The predicted data generally banded around the straight line which showed the suitability of the Eq. (27) in describing rheological behaviour of CMC solutions from grapefruit peel. The data obtained in this study are applicable only in designing equipment for handling of CMC solutions at the temperature range studied. The apparent viscosities at the other temperatures and concentrations in the ranges of temperatures and concentrations examined in this study can be obtained by using constants in the


243

Table 6 The combined effect of temperature and concentration on apparent viscosity of CMC solutions (Eq. (27)). Shear rate (s1)

ha ¼ d(C)ε exp(Ea/RT) d mPas(kg/m3)ε

ε []

Ea (kJ/mol)

Statistical tests

1.32

0.5211

0.7700

7.6076

2.20

0.5688

0.7020

7.5698

2.64

0.4768

0.6793

7.9972

4.40

0.4108

0.7311

7.8285

6.60

0.3370

0.7498

8.0842

11.00

0.5073

0.6943

7.4337

13.20

0.7103

0.6490

6.8801

RMSE ¼ 5.9873; c2 ¼ 39.830 MBE ¼ 0.1260; EF ¼ 0.9713 r RMSE ¼ 5.8662; c2 ¼ 38.235 MBE ¼ 0.1394; EF ¼ 0.9594 r RMSE ¼ 5.6744; c2 ¼ 35.776 MBE ¼ 0.6401; EF ¼ 0.9561 r RMSE ¼ 5.9783; c2 ¼ 39.711 MBE ¼ 0.1836; EF ¼ 0.9506 r RMSE ¼ 6.0607; c2 ¼ 40.814 MBE ¼ 0.1946; EF ¼ 0.9487 r RMSE ¼ 7.1841; c2 ¼ 57.346 MBE ¼ 0.2386; EF ¼ 0.9155 r RMSE ¼ 7.9500; c2 ¼ 70.225 MBE ¼ 0.2318; EF ¼ 0.8802 r

¼ 0.9855 ¼ 0.9795 ¼ 0.9780 ¼ 0.9750 ¼ 0.9740 ¼ 0.9568 ¼ 0.9382

Table 7 The combined effect of temperature and concentration on apparent viscosity of CMC solutions (Eq. (28)). Shear rate (s1)

ha ¼ d1exp(ε1C)exp(Ea/RT) d1 (mPas)

ε1 (kg/m3)1

Ea(kJ/mol)

Statistical tests

1.32

2.7692

0.0309

7.6191

2.20

2.5787

0.0285

7.5872

2.64

2.0545

0.0274

8.0194

4.40

1.9928

0.0295

7.8498

6.60

1.7060

0.0302

8.1048

11.00

2.2832

0.0279

7.4488

13.20

2.8942

0.0260

6.8987

RMSE ¼ 6.6017; c2 ¼ 48.425 MBE ¼ 0.1282; EF ¼ 0.9651 r RMSE ¼ 5.7041; c2 ¼ 36.152 MBE ¼ 0.1518; EF ¼ 0.9616 r RMSE ¼ 6.0362; c2 ¼ 40.484 MBE ¼ 0.2245; EF ¼ 0.9503 r RMSE ¼ 6.2135; c2 ¼ 42.898 MBE ¼ 0.3351; EF ¼ 0.9467 r RMSE ¼ 6.3447; c2 ¼ 44.728 MBE ¼ 0.3616; EF ¼ 0.9438 r RMSE ¼ 7.6075; c2 ¼ 64.305 MBE ¼ 0,3344; EF ¼ 0.9053 r RMSE ¼ 8.3906; c2 ¼ 78.225 MBE ¼ 0.1864; EF ¼ 0.8666 r

¼ 0.9824 ¼ 0.9806 ¼ 0.9748 ¼ 0.9730 ¼ 0.9715 ¼ 0.9515 ¼ 0.9309

The empirical Weltman model has been used to model timedependent flow behaviour of natural food products to describe the thixotropic behaviour of CMC solutions (Battacharya, 1999; Hecke et al., 2012; Weltman, 1943).

ha ¼ AþB lnðtÞ

Fig. 7. Comparison of experimental apparent viscosity and predicted apparent viscosity values of CMC from equation (27).

derived model given for each shear rate in Table 6. Hydrocolloid solutions may exhibit time-dependent properties, mainly thixotropy. When a material is sheared at a constant shear rate, the viscosity of a thixotropic material will decrease over a period of time, implying a progressive breakdown of the structure (Abu-Jdayil & Mohameed, 2004). Modelling of the thixotropic behaviour has been based on equations such as Weltmann, firstorder stress decay models and structural kinetic model (Karazhiyan et al., 2009).

(30)

where t is the shearing time (s), A (mPas) and B (mPas) are the Weltman constants. Time-dependent flow properties of CMC solutions were assessed by examining apparent viscosity versus shear time in Weltman model. CMC solutions were sheared at constant shear rate of 6.60 s1 and the apparent viscosities were recorded as a function of shearing time until a steady state was reached. The apparent viscosity of CMC solutions as a function of time for spindle speeds of 30 rpm (shear rate: 6.60 s1) at concentrations from 15 kg/m3 to 35 kg/m3 and 30 C is shown in Fig. 8. At a constant spindle speed, the apparent viscosity decreased with time. Towards the end of the 6 min shearing period, the apparent viscosity tended towards a plateau. From these results, the CMC solutions were found to be slightly thixotropic. Ghannam and Esmail (1997) have shown that the CMC dispersions exhibited thixotropic and viscoelastic behaviour at high CMC concentrations. Similar thixotropic behaviour was found for amorphouse cellulose suspensions (Jia et al., 2014) and carrot puree (Hecke et al., 2012). Dolz, Jimenez, Hernandez, Delegido, and Casanovas (2007) stated that the CMC solutions having different concentrations showed thixotropic behaviour.

244


exhibited a thixotropic flow behaviour at all the concentrations. This study provides essential data for design of processes relating CMC solutions from grapefruit peel within the temperatures (10e60 C), the concentrations (15e35 kg/m3) and the shear rates (1.32e13.2 s1) studied. References

Fig. 8. Apparent viscosity of CMC as a function of shearing time at 30 C for shear rate of 6.6 s1 (concentration (kg/m3): 15, :20, B25, C30, 35).

▵

▫

Table 8 Weltman model parameters for different CMC concentrations. C (kg/m3)

A (mPas)

B (mPas)

r2

15 20 25 30 35

0.9118 1.0943 1.1935 1.3602 1.8261

67.723 85.364 96.682 118.230 132.170

0.9845 0.9200 0.9867 0.8900 0.9674

Weltman model parameters used to describe the change in apparent viscosity with shearing time for different CMC solutions are showed in Table 8 A and B constants characterize the time dependent behaviour of CMC. It was found that an increase in the CMC concentration caused a decrease in magnitude of A, which is an indication of resistance of the fluid against the flow. A zero value of B (the coefficient of breakdown) indicates that the apparent viscosity of the fluid is independent of time (Abu-Jdayil, Azzam, & Al-Malah, 2001). A negative B value measures the degree of destruction of aggregates arising from shear rate. In other words, it measures how fast the apparent viscosity drops from the initial value to the final equilibrium value (Abu-Jdayil & Mohameed, 2004). The magnitude of B increased with increasing concentration. 4. Conclusions The isolated cellulose from grapefruit peel was converted to CMC by etherification using sodium monochloroacetic acid and NaOH. The empirical equations were developed to predict the viscosity of cellulose from grapefruit peel as a function of temperature and concentration. CMC solutions exhibited shear thinning or pseudoplastic rheological behaviour that was well described by the power-law model with a consistency index and a flow behaviour index lower than 1. It was found that the consistency index values increased with the concentration while the opposite trend was observed with temperature. For the prediction of the apparent viscosity of CMC solutions, a power law and exponential models for concentration and the Arrhenius relationship for temperature were combined to simultaneously describe the effects of concentration and temperature. The model with the best performance can be applied to predict the apparent viscosity of CMC solutions. The activation energy calculated with the Arrhenius model indicated that CMC solutions were most sensitive to temperature change at low shear rates. The time-dependent viscosity decreased rapidly with time and reached an equilibrium state. CMC solutions were adequately described by the Weltman model. CMC solutions

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