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Viscosimetric study of aqueous solutions of glucosamine and its mixtures with glucose
Journal of Food Engineering 68 (2005) 403–408 www.elsevier.com/locate/jfoodeng
Viscosimetric study of aqueous solutions of glucosamine and its mixtures with glucose D. Go´mez-Dı´az, J.M. Navaza
*
Department of Chemical Engineering, ETSI, University of Santiago de Compostela, C/Lope Go´mez de Marzoa, Santiago de Compostela E-15782, Spain Received 4 January 2004; accepted 28 June 2004
Abstract At present, glucosamine is an important substance for its future use in food products to contribute therapeutical characteristics to the product. In the present paper, the viscosimetric behaviour of aqueous solutions of this solute has been carried out. For a deep characterization, the effect of composition and temperature have been analysed. Also the effect of addition of glucose upon the viscosity of the solution has been studied. The viscosimetric behaviour of aqueous solutions of glucosamine and the mixtures with glucose has been modelized with equations for one and two solutes obtaining suitable results. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Glucosamine; Viscosity; Density
1. Introduction In recent years, glucosamine and other products such as chondroitin have been widely promoted as a treatment for arthritis and placebo-controlled studies. Glucosamine has been shown to rehabilitate cartilage and reduce the progression of osteoarthritis, and significantly lessen pain from arthritis. Glucosamine is an amino sugar that is present in all human tissues and is thought to promote the formation and repair of cartilage. This substance is the principal compound of the glucosaminoglycans (GAGs) that form the matrix of the connective tissues. In some cases the glucosamine could be combined to others GAGs since this compound keeps the viscosity in the articulation and stimulates the cartilage recovery. The low molecular weight of the glucosamine means that it substance will be absorbed easily and in a high
*
Corresponding author. Fax: +34 81 595012. E-mail address: [email protected] (J.M. Navaza).
0260-8774/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.06.016
grade into the intestine. Also, an anti-inflammatory effect has been observed in relation to the cartilage metabolism. The use of this additive in animal and human food has become quite common and for this reason, the flow characteristics are interesting. The combined use of glucosamine with other solutes is an option to enrich food and has been examined in dairy products (Flood & Puagsa, 2000). In recent years, several authors have studied the effect of numerous solutes upon the physico-chemical properties with more interest in density and viscosity (Cibulkova, Vasiljev, Danek, & Simko, 2003; Moreiras et al., 2003; Palaiologou, Molinou, & ´ lvarez, Tsierkezos, 2002; Va´zquez, Varela, Cancela, A & Navaza, 1996). Solutes such as sucrose, glucose, glycerine, carbonates, phosphates, sulphates, etc., have been analysed on the basis of their physical properties in literature. The trends observed by these researchers have not been clear and different behaviours have been analysed. In most of cases, the effect of the solute presence produces an increase in the value of the property analysed when the solute concentration increases but Pereira,
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
404
Moreira, Va´zquez, and Chenlo (2001), found that the presence of certain solutes decreased the kinematic viscosity. Several authors have developed different equations that correlate the experimental values of density and viscosity for aqueous solutions of one solute. In the case of density, different formulations have been published. ´ lvarez, Varela, Cancela, and Navaza Va´zquez, A (1996), used an equation based on the value of the solvent (water) density and a polynomial contribution of the solute concentration. When this equation was applied to ternary mixtures (water + solute 1 + solute 2), the solvent density is the corresponding density of water + solute 1. On the other hand, other authors (Bettin, Emmerich, Spieweck, & Toth, 1998; Pereira et al., 2001), have contributed equations relating relative density to solvent density. The equation proposed by Pereira et al. (2001) included the effects of composition and temperature while the Bettin et al. (1998) equation only correlated density values with the composition. Also, the equation developed by Pereira et al. (2001) is a predictive model, based in characteristics parameters for each solute. Also, in recent years, studies based on neural networks to correlate data of multicomponent mixtures have produced some papers (Comesan˜a, Otero, Garcı´a, & Correa, 2003). ´ lvarez, and With regards to viscosity, Va´zquez, A Navaza (1998), contributed a similar equation to that previously mentioned by some of these authors for density. Kumar (1993), developed a complete equation for prediction absolute viscosity for binary mixtures (one solute). Pereira et al. (2001), completed these studies and modified the equation proposed by Kumar (1993) to obtain a predictive equation for kinematic viscosity based on characteristics parameters of the solutes employed. The present paper tries report density, kinematic viscosity and absolute viscosity behaviours for aqueous solutions containing glucosamine and the influence of the presence of glucose upon the trends observed.
of glucosamine and glucose + glucosamine were prepared by mass using an analytical balance with a precision of ±107 kg. In all cases, the prepared solutions were filtered using Millipore filters with a pore diameter of 0.22 lm. For these solutions, doubly distilled water was employed. In the present paper, different concentrations of glucosamine in the aqueous solutions, in the range of solubility of this solute in water (0–0.4 mol dm3) were studied for this system in relation to density and viscosity. Also, the same concentration range was employed for glucose in the ternary solutions. Density measurements of the corresponding mixtures were carried out using pycnometers (Gay-Lussacs pycnometer with a bulb volume of 25 cm3). The pycnometers were placed into a thermostatic bath maintained a constant temperature with ±0.1 °C. The kinematic viscosity (m) was determined from the transit time of the liquid meniscus through a capillary viscosimeter supplied by Schott (Cap No. 0 c, 0.46 ± 0.01 mm of internal diameter, K = 0.003201 mm2 s1) using Eq. (1). The viscometer used was a Shott-Gera¨te AVS 350 Ubbelohde type m ¼ Kðt hÞ
where t is the transit time, K is the characteristic constant of the capillary viscosimeter, and h, is a correction value to prevent the final effects. An electronic stopwatch accurate to within ±0.01 s was used for measuring times. The glass capillary was immersed in a bath controlled to ±0.1 °C to determine the viscosity in the range temperature between 25 and 50 °C and then study the effect of the temperature on the viscosity. Each measurement was repeated at least six times. The dynamic viscosity (g) could be obtained by the product of kinematic viscosity (m) and the corresponding density (q) of the binary mixture in terms of Eq. (2) for each temperature and mixture composition. g¼qm
2. Materials and methods The solutes employed in the present paper, D (+) glucose and D (+) glucosamine hydrochloride (2-amino2-deoxy-D -glucose hydrochloride) (Fig. 1), were supplied by Fluka with a purity P99%. Aqueous solutions CH 2OH OH
O
ð1Þ
ð2Þ
Density and viscosity values for bi-distillate water and binary mixtures of water + glucose were determined and used to confirm that the methods employed in the present paper (picnometric and capillary methods) contributed suitable results for comparison with the literature values (Va´zquez et al., 1998).
3. Results and discussion OH HCl
HO NH 2
Fig. 1. Glucosamine structure.
3.1. Water + glucosamine system Figs. 2 and 3 show the results obtained for the value of these physical properties in the concentration range indicated in the materials and methods section. The
(Kumar, 1993). An example of this equation is shown in Eq. (3).
1.02
q ¼ q0 þ
4 X
Ai cj=2
ð3Þ
i¼2
1.01
1
0.99 0
0.02
0.04 ω
0.06
0.08
Fig. 2. Density values for aqueous solutions of glucosamine and glucose at t = 25 °C: (s) glucose solutions, (h) bibliographic data for glucose solutions, (d) glucosamine solutions.
1.08
ν. 10-6 / m2. s-1
405
1.03
1.04
where q, is the mixtures density, q0, is the solvent (water) density, c, is the solute concentration and Ai, are adjustable parameters. Other authors have proposed other models as Bettin et al. (1998) which has been used in different papers. This model is presented in Eq. (4). q b ¼ ð1 þ a cÞ ð4Þ q0 where a and b are fit parameters. Regarding the viscosimetric analysis, an equation developed by Kumar (1993) (Eq. (5)) is one of the more commonly employed models to fit experimental data as a function of mixture composition and operation temperature. Using this equation as starting point, Pereira et al. (2001) developed a predictive equation (Eq. (6)) that calculates the kinematic viscosity on the basis of the experimental data of the solute and pure solvent. g 1þbx ¼ g0 1 h x 1 1þBx mrel ¼ qrel 1 H x
1
0.96
0.92 0
0.02
0.04
0.06
0.08
ω
Fig. 3. Viscosity values for aqueous solutions of glucose and glucosamine at t = 25 °C: (s) glucose solutions, (h) bibliographic data for glucose solutions, (d) glucosamine solutions.
experimental results show that when the solute concentration increases its value, the density and the kinematic viscosity increase too. Other authors have founded different behaviours for numerous solutes (Pereira et al., 2001) thought the more common trend was the same ´ lvarez that shown in the Figs. 2 and 3 (Va´zquez, A et al., 1996; Va´zquez, Varela et al., 1996). In Figs. 2 and 3 the values of the density and kinematic viscosity corresponding to aqueous solutions of glucosamine have been compared with the experimental data obtained to aqueous solutions of glucose and also compared with bibliographic data (Weast & Astle, 1982). For aqueous solutions formed by only one solute, different authors have developed equations (empiricals, semiempiricals or theoricals) that correlate with the experimental values for the properties analysed in the present studies. One of more typical equations for density values are based in polynomial development
ð5Þ
ð6Þ
where g is the viscosity of the mixture, g0, is the viscosity of water, mrel and qrel is the relative kinematic viscosity and density (respect water), respectively. b, h, B and H are adjustable parameters that depend on temperature. Eq. (6) has been employed to correlate the experimental data of the systems employed in present section with suitable results shown in Fig. 4.
1.2 Relative Kinematic viscosity
ρ / g. m c -3
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
1.16
1.12
1.08
1.04
1 0
0.02
0.04
ω
0.06
0.08
Fig. 4. Experimental values of relative viscosity for the binary solutions of glucose and glucosamine. Solid lines shown the behaviour of the model developed by Pereira et al. (2001): (s) glucose solutions, (d) glucosamine solutions.
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
406
Table 1 Parameters values for Eq. (6) using density and kinematic viscosity data corresponding to the binary mixture formed by water and glucosamine t (°C)
b
h
n
d
25 30 35 40 45 50
0.122 0.298 1.317 0.009 0.297 0.170
1.987 1.975 3.330 2.306 2.484 2.059
5 5 5 5 5 5
0.003 0.004 0.001 0.002 0.003 0.003
These equations have been employed to correlate the experimental data of the water + glucosamine system. Fit parameters and characteristic parameters of these equations are listed in Table 1. In these tables the medium-root-square has been included in order to check the goodness of fit of the equations to the experimental data. The medium-root-square is defined as shown in Eq. (7). 0P 2 11=2 zexp zcalc B C d¼@ i ð7Þ A ndata where d is the medium-root-square, ndata, is the number of data employed, zexp and zcalc, are the experimental and calculated values for the physical property. 3.2. Water + glucosamine + glucose system The ternary system formed by water + glucose + glucosamine, has been studied in the range of concentration between 0 and 0.4 mol dm3 for glucose and glucosamine. The experimental data and the behaviour observed for kinematic viscosity is shown in Fig. 5 at different values of solute concentration.
ν. 10-6 / m2.s-1
1.4
1.2
Fig. 6. Effect of mixture composition upon the value of relative dynamic viscosity at t = 25 °C.
In this figures, the experimental data have shown that the effect of the addition of both solutes increases the viscosity of the aqueous mixtures. In all cases this effect has been observed. Similar effect caused by the solutes presence upon the density mixture value was observed too. To analyse the joint effect of the concentration of both solutes, Fig. 6 has plotted solutes concentration on the X and Y axis and relative dynamic viscosity on the Z axis to show the density and kinematic viscosity simultaneously. This figure shows that the viscosity increases its value when the mixture is enriched in any solute and the maximum value of this physical property is reached for the higher concentrations of both solutes. Regarding a model to fit the experimental data of kinematic viscosity of the ternary mixtures employed in the present paper, for solutions of more than one solute, Pereira et al. (2001) showed that the terms b Æ w and h Æ w were assumed to be additive. Arising from these considerations, Eq. (6) adopt the form shown in Eq. (8). P 0 1 bk x k 1 @ k A P mrel ¼ ð8Þ 1þ qrel 1 hk x k k
1
0.8
[Glucose]
0
0.02
0.04
0.06
0.08
0.1
ω (glucosamine)
Fig. 5. Kinematic viscosity values for ternary mixtures formed by water + glucose + glucosamine at t = 25 °C: (m) x = 0; (s) x = 0.0177; (d) x = 0.0348; (h) x = 0.0514; (j) x = 0.0673.
where, mrel and qrel is the relative kinematic viscosity and density (respect water), respectively, b and h, are adjustable parameters. Fit parameters corresponding to Eq. (8) are listed in Table 2 for all temperatures studied. Fig. 7 shows the comparison between experimental and calculated data (using Eq. (8)) for the ternary system formed by glucosamine + glucose + water. This figure indicate that Eq. (8) allows to calculate viscosity values for the system analysed in the present paper.
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408 Table 2 Parameters values for Eq. (8) using density and kinematic viscosity data corresponding to the ternary mixture formed by water, glucose and glucosamine
25 30 35 40 45 50
b2
3.031 3.042 3.637 3.757 4.650 5.412
2.283 1.984 1.524 1.523 0.729 0.690
h1
h2
0.545 0.432 1.583 2.239 5.793 9.285
2.392 3.222 4.664 4.698 7.432 8.471
n 17 17 17 17 17 17
d 0.012 0.010 0.014 0.012 0.020 0.023
1.4
1.04 1.02
1.2
1 1
0.98 0.96
ν. 10-6 / m2.s-1
b1
1.06
ρ / g . m c -3
t (°C)
407
0.8
0.94 0.92 20
0.6 30
40
50
t / ºC
Fig. 8. Effect of temperature and mixture composition upon the density: (s) x = 0.0212; (d) x = 0.0414; (h) x = 0.0609; (j) x = 0.0796.
( νrel)cal
1.4
1.2
1
1
1.2
1.4
b1,b2,h1,h2
10
0
( νrel)exp Fig. 7. Calculated and experimental values of relative kinematic viscosity of ternary aqueous solutions at t = 25 °C.
-10
20
30
3.3. Effect of temperature
50
Fig. 9. Parameters corresponding to Eq. (8): (s) b1; (d) b2; (h) h1; (j) h2.
1.5
1.4
( νrel)cal
In the present section, the effect of the operating temperature on the viscosimetric behaviour of the ternary mixture studied in the present paper has been analysed. The same behaviour has been observed for the density and kinematic viscosity in relation to the temperature at which the experiments were carried out. A decrease was observed for these properties when the temperature increases in value. These results agree with the published data obtained previously for our and other re´ lvarez search groups (Comesan˜a et al., 2003; Va´zquez, A et al., 1996; Va´zquez, Varela et al., 1996). For example, Fig. 8 shows the effect of temperature on these physical properties for this kind of mixture. Also, Eq. (8) has been employed to fit the kinematic viscosity and density data for the aqueous solutions of glucose plus glucosamine for all the temperatures employed in the present paper. The values for the parameters corresponding to Eq. (8) and their trend in relation to temperature are shown in Fig. 9. An example of the fit employing this Eq. (8) for all data at different temperatures is shown in Fig. 10 with a good agreement between experimental and calculated data.
40
T / ºC
1.3
1.2
1.1
1 1
1.1
1.2
1.3
1.4
1.5
( νrel)exp Fig. 10. Comparison between experimental and calculated values of relative kinematic viscosity for the ternary mixtures included all temperatures analysed in the present paper.
408
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
References Bettin, H., Emmerich, A., Spieweck, F., & Toth, H. (1998). Density data for aqueous solutions of glucose, fructose and invert sugars. Zuckerindustrie, 123(5), 341–348. Cibulkova, J., Vasiljev, R., Danek, V., & Simko, F. (2003). Viscosity of the system LiF + NaF + K2NbF7. Journal of Chemical and Engineering Data, 48(4), 938–941. Comesan˜a, J. F., Otero, J. J., Garcı´a, E., & Correa, A. (2003). Densities and viscosities of ternary systems of water + glucose + sodium chloride and several temperatures. Journal of Chemical and Engineering Data, 48(2), 362–366. Flood, A. E., & Puagsa, S. (2000). Refractive index, viscosity and solubility at 30 °C and density at 25 °C for the system fructose + glucose + ethanol + water. Journal of Chemical and Engineering Data, 45(5), 902–907. Kumar, A. (1993). A simple correlation for estimating viscosities of solutions of salts in aqueous, nonaqueous and mixed solvents applicable to high concentration, temperature and pressure. Canadian Journal of Chemical Engineering, 71, 139–142. Moreiras, A. F., Garcı´a, J., Lugo, L., Comun˜as, M. J. P., Lo´pez, E. R., & Ferna´ndez, J. (2003). Experimental densities and dynamic viscosities of organic carbonate + n-alkane or p-xylene systems at 298.15 K. Fluid Phase Equilibria, 204(2), 233–243.
Palaiologou, M. M., Molinou, I. E., & Tsierkezos, N. G. (2002). Viscosity studies on lithium bromide in water + dimethyl sulfoxide mixtures at 278.15 K and 293.15 K. Journal of Chemical and Engineering Data, 47(5), 1285–1289. Pereira, G., Moreira, R., Va´zquez, M. J., & Chenlo, F. (2001). Kinematic viscosity prediction for aqueous solutions with various solutes. Chemical Engineering Journal, 81, 35–40. ´ lvarez, E., & Navaza, J. M. (1998). Density, viscosity, Va´zquez, G., A and surface tension of sodium carbonate + sodium bicarbonate buffer solutions in the presence of glycerine, glucose, and sucrose from 25 to 40 °C. Journal of Chemical and Engineering Data, 43(2), 128–132. ´ lvarez, E., Varela, R., Cancela, A., & Navaza, J. M. Va´zquez, G., A (1996). Density and viscosity of aqueous solutions of sodium dithionite, sodium hydroxide, sodium dithionite + sucrose, and sodium dithionite + sodium hydroxide + sucrose from 25 °C to 40 °C. Journal of Chemical and Engineering Data, 41(2), 244–248. ´ lvarez, E., & Navaza, J. M. Va´zquez, G., Varela, R., Cancela, A., A (1996). Physical properties of aqueous solutions of NaHCO3, Na2CO3 and Na2CO3–NaHCO3 in the presence of sucrose and glucose. Afinidad, 53(461), 11–20. Weast, R. C., & Astle, M. J. (Eds.). (1982). CRC handbook of chemistry and physics (67th ed.). Boca Rato´n, FL: Chemical Rubber Publishing.
Viscosimetric study of aqueous solutions of glucosamine and its mixtures with glucose D. Go´mez-Dı´az, J.M. Navaza
*
Department of Chemical Engineering, ETSI, University of Santiago de Compostela, C/Lope Go´mez de Marzoa, Santiago de Compostela E-15782, Spain Received 4 January 2004; accepted 28 June 2004
Abstract At present, glucosamine is an important substance for its future use in food products to contribute therapeutical characteristics to the product. In the present paper, the viscosimetric behaviour of aqueous solutions of this solute has been carried out. For a deep characterization, the effect of composition and temperature have been analysed. Also the effect of addition of glucose upon the viscosity of the solution has been studied. The viscosimetric behaviour of aqueous solutions of glucosamine and the mixtures with glucose has been modelized with equations for one and two solutes obtaining suitable results. Ó 2004 Elsevier Ltd. All rights reserved. Keywords: Glucosamine; Viscosity; Density
1. Introduction In recent years, glucosamine and other products such as chondroitin have been widely promoted as a treatment for arthritis and placebo-controlled studies. Glucosamine has been shown to rehabilitate cartilage and reduce the progression of osteoarthritis, and significantly lessen pain from arthritis. Glucosamine is an amino sugar that is present in all human tissues and is thought to promote the formation and repair of cartilage. This substance is the principal compound of the glucosaminoglycans (GAGs) that form the matrix of the connective tissues. In some cases the glucosamine could be combined to others GAGs since this compound keeps the viscosity in the articulation and stimulates the cartilage recovery. The low molecular weight of the glucosamine means that it substance will be absorbed easily and in a high
*
Corresponding author. Fax: +34 81 595012. E-mail address: [email protected] (J.M. Navaza).
0260-8774/$ - see front matter Ó 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2004.06.016
grade into the intestine. Also, an anti-inflammatory effect has been observed in relation to the cartilage metabolism. The use of this additive in animal and human food has become quite common and for this reason, the flow characteristics are interesting. The combined use of glucosamine with other solutes is an option to enrich food and has been examined in dairy products (Flood & Puagsa, 2000). In recent years, several authors have studied the effect of numerous solutes upon the physico-chemical properties with more interest in density and viscosity (Cibulkova, Vasiljev, Danek, & Simko, 2003; Moreiras et al., 2003; Palaiologou, Molinou, & ´ lvarez, Tsierkezos, 2002; Va´zquez, Varela, Cancela, A & Navaza, 1996). Solutes such as sucrose, glucose, glycerine, carbonates, phosphates, sulphates, etc., have been analysed on the basis of their physical properties in literature. The trends observed by these researchers have not been clear and different behaviours have been analysed. In most of cases, the effect of the solute presence produces an increase in the value of the property analysed when the solute concentration increases but Pereira,
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
404
Moreira, Va´zquez, and Chenlo (2001), found that the presence of certain solutes decreased the kinematic viscosity. Several authors have developed different equations that correlate the experimental values of density and viscosity for aqueous solutions of one solute. In the case of density, different formulations have been published. ´ lvarez, Varela, Cancela, and Navaza Va´zquez, A (1996), used an equation based on the value of the solvent (water) density and a polynomial contribution of the solute concentration. When this equation was applied to ternary mixtures (water + solute 1 + solute 2), the solvent density is the corresponding density of water + solute 1. On the other hand, other authors (Bettin, Emmerich, Spieweck, & Toth, 1998; Pereira et al., 2001), have contributed equations relating relative density to solvent density. The equation proposed by Pereira et al. (2001) included the effects of composition and temperature while the Bettin et al. (1998) equation only correlated density values with the composition. Also, the equation developed by Pereira et al. (2001) is a predictive model, based in characteristics parameters for each solute. Also, in recent years, studies based on neural networks to correlate data of multicomponent mixtures have produced some papers (Comesan˜a, Otero, Garcı´a, & Correa, 2003). ´ lvarez, and With regards to viscosity, Va´zquez, A Navaza (1998), contributed a similar equation to that previously mentioned by some of these authors for density. Kumar (1993), developed a complete equation for prediction absolute viscosity for binary mixtures (one solute). Pereira et al. (2001), completed these studies and modified the equation proposed by Kumar (1993) to obtain a predictive equation for kinematic viscosity based on characteristics parameters of the solutes employed. The present paper tries report density, kinematic viscosity and absolute viscosity behaviours for aqueous solutions containing glucosamine and the influence of the presence of glucose upon the trends observed.
of glucosamine and glucose + glucosamine were prepared by mass using an analytical balance with a precision of ±107 kg. In all cases, the prepared solutions were filtered using Millipore filters with a pore diameter of 0.22 lm. For these solutions, doubly distilled water was employed. In the present paper, different concentrations of glucosamine in the aqueous solutions, in the range of solubility of this solute in water (0–0.4 mol dm3) were studied for this system in relation to density and viscosity. Also, the same concentration range was employed for glucose in the ternary solutions. Density measurements of the corresponding mixtures were carried out using pycnometers (Gay-Lussacs pycnometer with a bulb volume of 25 cm3). The pycnometers were placed into a thermostatic bath maintained a constant temperature with ±0.1 °C. The kinematic viscosity (m) was determined from the transit time of the liquid meniscus through a capillary viscosimeter supplied by Schott (Cap No. 0 c, 0.46 ± 0.01 mm of internal diameter, K = 0.003201 mm2 s1) using Eq. (1). The viscometer used was a Shott-Gera¨te AVS 350 Ubbelohde type m ¼ Kðt hÞ
where t is the transit time, K is the characteristic constant of the capillary viscosimeter, and h, is a correction value to prevent the final effects. An electronic stopwatch accurate to within ±0.01 s was used for measuring times. The glass capillary was immersed in a bath controlled to ±0.1 °C to determine the viscosity in the range temperature between 25 and 50 °C and then study the effect of the temperature on the viscosity. Each measurement was repeated at least six times. The dynamic viscosity (g) could be obtained by the product of kinematic viscosity (m) and the corresponding density (q) of the binary mixture in terms of Eq. (2) for each temperature and mixture composition. g¼qm
2. Materials and methods The solutes employed in the present paper, D (+) glucose and D (+) glucosamine hydrochloride (2-amino2-deoxy-D -glucose hydrochloride) (Fig. 1), were supplied by Fluka with a purity P99%. Aqueous solutions CH 2OH OH
O
ð1Þ
ð2Þ
Density and viscosity values for bi-distillate water and binary mixtures of water + glucose were determined and used to confirm that the methods employed in the present paper (picnometric and capillary methods) contributed suitable results for comparison with the literature values (Va´zquez et al., 1998).
3. Results and discussion OH HCl
HO NH 2
Fig. 1. Glucosamine structure.
3.1. Water + glucosamine system Figs. 2 and 3 show the results obtained for the value of these physical properties in the concentration range indicated in the materials and methods section. The
(Kumar, 1993). An example of this equation is shown in Eq. (3).
1.02
q ¼ q0 þ
4 X
Ai cj=2
ð3Þ
i¼2
1.01
1
0.99 0
0.02
0.04 ω
0.06
0.08
Fig. 2. Density values for aqueous solutions of glucosamine and glucose at t = 25 °C: (s) glucose solutions, (h) bibliographic data for glucose solutions, (d) glucosamine solutions.
1.08
ν. 10-6 / m2. s-1
405
1.03
1.04
where q, is the mixtures density, q0, is the solvent (water) density, c, is the solute concentration and Ai, are adjustable parameters. Other authors have proposed other models as Bettin et al. (1998) which has been used in different papers. This model is presented in Eq. (4). q b ¼ ð1 þ a cÞ ð4Þ q0 where a and b are fit parameters. Regarding the viscosimetric analysis, an equation developed by Kumar (1993) (Eq. (5)) is one of the more commonly employed models to fit experimental data as a function of mixture composition and operation temperature. Using this equation as starting point, Pereira et al. (2001) developed a predictive equation (Eq. (6)) that calculates the kinematic viscosity on the basis of the experimental data of the solute and pure solvent. g 1þbx ¼ g0 1 h x 1 1þBx mrel ¼ qrel 1 H x
1
0.96
0.92 0
0.02
0.04
0.06
0.08
ω
Fig. 3. Viscosity values for aqueous solutions of glucose and glucosamine at t = 25 °C: (s) glucose solutions, (h) bibliographic data for glucose solutions, (d) glucosamine solutions.
experimental results show that when the solute concentration increases its value, the density and the kinematic viscosity increase too. Other authors have founded different behaviours for numerous solutes (Pereira et al., 2001) thought the more common trend was the same ´ lvarez that shown in the Figs. 2 and 3 (Va´zquez, A et al., 1996; Va´zquez, Varela et al., 1996). In Figs. 2 and 3 the values of the density and kinematic viscosity corresponding to aqueous solutions of glucosamine have been compared with the experimental data obtained to aqueous solutions of glucose and also compared with bibliographic data (Weast & Astle, 1982). For aqueous solutions formed by only one solute, different authors have developed equations (empiricals, semiempiricals or theoricals) that correlate with the experimental values for the properties analysed in the present studies. One of more typical equations for density values are based in polynomial development
ð5Þ
ð6Þ
where g is the viscosity of the mixture, g0, is the viscosity of water, mrel and qrel is the relative kinematic viscosity and density (respect water), respectively. b, h, B and H are adjustable parameters that depend on temperature. Eq. (6) has been employed to correlate the experimental data of the systems employed in present section with suitable results shown in Fig. 4.
1.2 Relative Kinematic viscosity
ρ / g. m c -3
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
1.16
1.12
1.08
1.04
1 0
0.02
0.04
ω
0.06
0.08
Fig. 4. Experimental values of relative viscosity for the binary solutions of glucose and glucosamine. Solid lines shown the behaviour of the model developed by Pereira et al. (2001): (s) glucose solutions, (d) glucosamine solutions.
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
406
Table 1 Parameters values for Eq. (6) using density and kinematic viscosity data corresponding to the binary mixture formed by water and glucosamine t (°C)
b
h
n
d
25 30 35 40 45 50
0.122 0.298 1.317 0.009 0.297 0.170
1.987 1.975 3.330 2.306 2.484 2.059
5 5 5 5 5 5
0.003 0.004 0.001 0.002 0.003 0.003
These equations have been employed to correlate the experimental data of the water + glucosamine system. Fit parameters and characteristic parameters of these equations are listed in Table 1. In these tables the medium-root-square has been included in order to check the goodness of fit of the equations to the experimental data. The medium-root-square is defined as shown in Eq. (7). 0P 2 11=2 zexp zcalc B C d¼@ i ð7Þ A ndata where d is the medium-root-square, ndata, is the number of data employed, zexp and zcalc, are the experimental and calculated values for the physical property. 3.2. Water + glucosamine + glucose system The ternary system formed by water + glucose + glucosamine, has been studied in the range of concentration between 0 and 0.4 mol dm3 for glucose and glucosamine. The experimental data and the behaviour observed for kinematic viscosity is shown in Fig. 5 at different values of solute concentration.
ν. 10-6 / m2.s-1
1.4
1.2
Fig. 6. Effect of mixture composition upon the value of relative dynamic viscosity at t = 25 °C.
In this figures, the experimental data have shown that the effect of the addition of both solutes increases the viscosity of the aqueous mixtures. In all cases this effect has been observed. Similar effect caused by the solutes presence upon the density mixture value was observed too. To analyse the joint effect of the concentration of both solutes, Fig. 6 has plotted solutes concentration on the X and Y axis and relative dynamic viscosity on the Z axis to show the density and kinematic viscosity simultaneously. This figure shows that the viscosity increases its value when the mixture is enriched in any solute and the maximum value of this physical property is reached for the higher concentrations of both solutes. Regarding a model to fit the experimental data of kinematic viscosity of the ternary mixtures employed in the present paper, for solutions of more than one solute, Pereira et al. (2001) showed that the terms b Æ w and h Æ w were assumed to be additive. Arising from these considerations, Eq. (6) adopt the form shown in Eq. (8). P 0 1 bk x k 1 @ k A P mrel ¼ ð8Þ 1þ qrel 1 hk x k k
1
0.8
[Glucose]
0
0.02
0.04
0.06
0.08
0.1
ω (glucosamine)
Fig. 5. Kinematic viscosity values for ternary mixtures formed by water + glucose + glucosamine at t = 25 °C: (m) x = 0; (s) x = 0.0177; (d) x = 0.0348; (h) x = 0.0514; (j) x = 0.0673.
where, mrel and qrel is the relative kinematic viscosity and density (respect water), respectively, b and h, are adjustable parameters. Fit parameters corresponding to Eq. (8) are listed in Table 2 for all temperatures studied. Fig. 7 shows the comparison between experimental and calculated data (using Eq. (8)) for the ternary system formed by glucosamine + glucose + water. This figure indicate that Eq. (8) allows to calculate viscosity values for the system analysed in the present paper.
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408 Table 2 Parameters values for Eq. (8) using density and kinematic viscosity data corresponding to the ternary mixture formed by water, glucose and glucosamine
25 30 35 40 45 50
b2
3.031 3.042 3.637 3.757 4.650 5.412
2.283 1.984 1.524 1.523 0.729 0.690
h1
h2
0.545 0.432 1.583 2.239 5.793 9.285
2.392 3.222 4.664 4.698 7.432 8.471
n 17 17 17 17 17 17
d 0.012 0.010 0.014 0.012 0.020 0.023
1.4
1.04 1.02
1.2
1 1
0.98 0.96
ν. 10-6 / m2.s-1
b1
1.06
ρ / g . m c -3
t (°C)
407
0.8
0.94 0.92 20
0.6 30
40
50
t / ºC
Fig. 8. Effect of temperature and mixture composition upon the density: (s) x = 0.0212; (d) x = 0.0414; (h) x = 0.0609; (j) x = 0.0796.
( νrel)cal
1.4
1.2
1
1
1.2
1.4
b1,b2,h1,h2
10
0
( νrel)exp Fig. 7. Calculated and experimental values of relative kinematic viscosity of ternary aqueous solutions at t = 25 °C.
-10
20
30
3.3. Effect of temperature
50
Fig. 9. Parameters corresponding to Eq. (8): (s) b1; (d) b2; (h) h1; (j) h2.
1.5
1.4
( νrel)cal
In the present section, the effect of the operating temperature on the viscosimetric behaviour of the ternary mixture studied in the present paper has been analysed. The same behaviour has been observed for the density and kinematic viscosity in relation to the temperature at which the experiments were carried out. A decrease was observed for these properties when the temperature increases in value. These results agree with the published data obtained previously for our and other re´ lvarez search groups (Comesan˜a et al., 2003; Va´zquez, A et al., 1996; Va´zquez, Varela et al., 1996). For example, Fig. 8 shows the effect of temperature on these physical properties for this kind of mixture. Also, Eq. (8) has been employed to fit the kinematic viscosity and density data for the aqueous solutions of glucose plus glucosamine for all the temperatures employed in the present paper. The values for the parameters corresponding to Eq. (8) and their trend in relation to temperature are shown in Fig. 9. An example of the fit employing this Eq. (8) for all data at different temperatures is shown in Fig. 10 with a good agreement between experimental and calculated data.
40
T / ºC
1.3
1.2
1.1
1 1
1.1
1.2
1.3
1.4
1.5
( νrel)exp Fig. 10. Comparison between experimental and calculated values of relative kinematic viscosity for the ternary mixtures included all temperatures analysed in the present paper.
408
D. Go´mez-Dı´az, J.M. Navaza / Journal of Food Engineering 68 (2005) 403–408
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