Viscosity Measurements and Modelling ofAqueous Polyvinyl Alcohol Mixtures

AHaake viscometer was used for viscosity measurements of aqueous polyvinylalcohol mixtures at temperatures of 288, 298, and 308 K. It was observed that atlow concentration of polyvinyl alcohol, variations of the measured shear stress ()versus shear rate () were linear and therefore, the Newtonian behaviour of the studiedmixtures is considered. The modified Eyring viscosity model previously proposed by theauthors were used to test the measured data for aqueous polyvinyl alcohol mixtures. Itwas shown that the model is well capable to fit the data and the parameters, of the modleare evaluated.

Hamid Modarress1, Mohsen Mohsen Nia2, and Raana Mostafa3

(1) Department of Chemical Engineering, Amir-Kabir University of TechnologyTehran, I.R. Iran

(2) Department of Science, Kashan University, Kashan, I.R. Iran(3) Department of Chemistry, Amir-Kabir University of Technology, Tehran, I.R. Iran

Recived: 4 April 2004; accepted: 11 August 2004

polyvinyl alcohol;

viscosity;

Haake viscometer;

Eyring equation.

A B S T R A C T

Key Words:

For designing and optimizing ofchemical industrial processes, vis-cosity is an essential parameter. Thelack of experimental viscosities dataled researchers to propose the model-ling equations for estimating the vis-cosities of liquids and their mixtures.

In this respect Eyring theory [1] forviscosity, played a central role. Someauthors attempted to combine theUNIFAC model with Eyring theory[2]. The others used group contribu-tion methods [3, 4] and the equationof state approach, to make this theo-

(*)To whom correspondence should be addressed.E-mail: hmodares @cic.aku.ac.ir

INTRODUCTION

Iranian Polymer Journal14 (2), 2005, 181-184

ry applicable to fluids and their mixtures [5]. Recentlythe authors of this paper modified and extended theEyring theory and used it to fit the experimental data forseveral liquids and their mixtures [6, 7].

The propose of this paper is to apply this model tothe measured viscosities data of aqueous polyvinylalcohol mixtures and to evaluate parameters of themodel for predicting the viscosities of these mixtures atvarious temperatures and concentrations in engineeringapplications.

TheoryThe Eyring viscosity model which has been derivedfrom the reaction rate theory [1] provides a valuableroute for calculating the viscosities of pure liquids.

= h/ (2mkT/h2)1/2ea/kT (1)

As M = N0m, R = N0k, V = N0 and Ea = N0a , thefinal Eyring viscosity model will be expressed as [2]:

= (2MRT/V2)1/2eEa/RT (2)

where M, R, T, V and Ea are the molar mass, gas con-stant, absolute temperature, liquid molar volume, andmolar activation energy, respectively.

For a c-component mixture of total molecules oftype Ni, where, , the following equation is derived as [6]:

where, xi is the mole fraction of component i. Also thisequation can be written in terms of molar properties as:

Since xi = 1.0, for a binary mixture, we have [6, 7]:

= (2RT)1/2[M1x1/2M2x2/2/V1x1/2V2x2/2] eEam/RT] (5)

In above equation, we have introduced the activationenergy of the binary mixture Eam as [7]:Eam = x1Ea1 + x2Ea2 (6)

and the temperature functionality for Eam in the fol-lowing form:

Eam = am + bmT (7)

By considering low concentration of polymer in poly-mer-solvent mixtures (x2

adding enough double distilled water. A Haake vis-cometer, rotovisco RV 100 with the CV 100 system,was used for the viscosity measurements at tempera-tures 288, 298, and 308 K.

The viscometer consisted of two rotating coaxialcylinders in which the fluid under investigation wasplaced in the space between them and the flow curveswere recorded. The usual experimental procedure wasutilized to obtain the viscosity results. First the viscome-ter was calibrated by the standard fluid and the instru-ments constant was measured. Then the instrument sconstant was used to calculate shear rates and shearstresses. The final results were presented as flow curves, = / vs. , where, is the viscosity of fluid and and are the shear stress and shear rate, respectively. TheNewtonian behaviour of studied mixtures was con-firmed as expected by the linear flow curves ( vs. ) atlow polymer concentrations of aqueous polyvinyl alco-hol mixtures and therefore no further corrections forNon-Newtonian behaviour was required.

RESULTS AND DISCUSSION

The dilute solution of a polymer in a solvent is definedas the concentration, which is much lower than c* [8].The quantitative definition of c* is c* = 1/[], where[] is the intrinsic viscosity of solution. The intrinsicviscosity is related to molecular weight of polymer asthe following form:

[] = kMa (12)

The values of k and a in Equation (12) for polyvinylalcohol at 298 K, which is the average temperature inour viscosity measurements are 0.30 (ml/g) and 0.50,respectively [9]. For studied aqueous polyvinyl alcoholmixtures, where Mn = 49000, the value of relative con-centrations (c/c*) for the studied mixtures fall in therange of 0.157-0.813. Therefore, polymer-solvent mix-tures are considered as dilute solutions and their New-tonian behavioures in regard to viscosities of mixturesare expected. The Newtonian behaviour is confirmedby the linearity of variations of measured shear stress-es () versus shear rates (). Figure 1, as an example,shows the linear variations of () versus () for threeaqueous polyvinyl alcohol mixtures at 288K.

The measured viscosities of aqueous polyvinylalcohol mixtures at temperatures 288, 298, and 308 Kare reported in Table 1. By substituting the measuredviscosities in Equation (9), values of parameters am andbm were calculated and the percent average absolutedeviation (AAD%) of experimental and calculated vis-cosities are reported in Table (2).

As it is seen from reported results in Table (2), thecalculated AAD% for mixtures are less than 0.33%,which indicate the accuracy of calculations and theapplicability of the modified viscosity model, based onthe Eyring theory, to polymer-solvent mixtures. Byconsidering the activation energy expressed by Equa-tion (7) and values of activation energy parameters amand bm reported in Table (2), some interesting pointsabout the physical interpretation of these parametersbecome clear. Higher values of these parameters meanhigher values of activation energy as a result of molec-ular frictions and retardations in molecular motion ofpolymer chains, that in turn cause higher measured vis-cosities of polymer-solvent mixtures. Another parame-ter in the modified Eyring viscosity model is A, which

Viscosity Measurements and Modelling of Aqueous...Modarress H. et al.

Iranian Polymer Journal / Volume 14 Number 2 (2005) 183

Table 1. The measured viscosities ( * 103 Pa.s) of aqueouspolyvinyl alcohol mixtures.

C (g/20 mL) 15oC 25oC 35oC0.6107

0.5381

0.2467

0.1180

3.91

3.20

1.41

1.11

3.00

2.40

1.11

0.90

2.31

1.80

0.90

0.74

Figure 1. The linear variation of () versus () for three aque-ous polyvinyl alcohol mixtures at 288K.

(s-1)

0 100 200 3000

0.4

0.8

1.2C = 0.6107 (g/20 mL)C = 0.5381 (g/20 mL)C = 0.1180 (g/20 mL)

is expressed by Equation (11). This parameter not onlyis effectively temperature dependent but also, dependson molecular weights of polymer and solvent. Thushigher molecular weight of polymer causes retardationin molecular motions of polymer chain and then led tohigher viscosity for polymer-solvent mixture.

The parameters am and bm are expressed in term ofpolymer concentration, C, as follows:

am = -9425.35C2 + 15841.37C + 14403.37 (13)

bm = 48.87C2 - 45.52C - 193.32 (14)

By using the above correlations the calculated AAD%is 0.84%. By rearranging Equation (10) and writing itin the logarithmic form we have:

ln (/T1/2) = lnA + (am + bmT)/RT (15)

where lnA is constant for a fixed concentration of poly-mer-solvent mixture. According to Equation (15), thevariation of ln (/T1/2) versus 1/T should be linear.

Linearity of the plots in Figure 2 indicates consistencyof measured and calculated results.

CONCLUSION

The linear relation between shear stress, , and shearrate , indicates the Newtonian behaviour of studiedaqueous polyvinyl alcohol mixtures. Viscosities ofaqueous polyvinyl alcohol mixtures are calculated byusing the modified Eyring viscosity model. The param-eters of the model are correlated in terms of polymerconcentrations. The total AAD% for viscosity calcula-tions by the proposed model is 0.84%.

REFERENCES

1. Glastone S., Laidler K. J., and Eyring, H., The theory of rateprocesses, McGraw-Hill, New York, Ch. 9, 477 (1941).

2. Cao W., Knudsen K., Fredenslund A., and Rasmussen P.,Group-contribution viscosity predictions of liquid mix-tures using UNIFAC-VLE parameters, Ind. Eng. Chem.Res., 32, 2088-2092 (1993).

3. Wu D. T., Prediction of viscosities of liquid mixtures by agroup contribution method, Fluid Phase Equilibria, 30,149-156 (1986).

4. Chevalier J.L.E., Petrino P.J., and Gaston-Bonhomme Y.,Estimation method for kinematic viscosity of a liquid-phase mixture, Chem. Eng. Sci., 43, 1303-1309 (1988).

5. Lee M.J. Chiu J.Y., Hwang S.M., and Lin T.K., Viscositycalculations with the Eyring-Patel-Teja model for liquidmixtures, Ind. Eng. Chem. Res., 38, 2867-2876 (1998).

6. Mohsen-Nia M., Modarress H., and Mahdavi M.A., A newtwo parameters equation for viscosity calculations, Amirk-abir, J. Sci. Technol., 15, 120-132 (2004).

7. Modarress H., Mohsen-Nia M., and Mahdavi M. A.,Experimental and theoretical studies of polymer-solventmixtures, viscosity, Appl. Polym. J., 91, 1724-1929 (2004).

8. Teraoka I., Polymer Solutions: An introduction to physicalproperties; dilute solution, John Wiley, Inc., (2002).

9. Brandrup J. and Immerqut E.H., Viscosity-molecularweight relationship, Polymer Handbook, 2nd Ed., JohnWiley Inc, Ch. IV (1975).

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Iranian Polymer Journal / Volume 14 Number 2 (2005)

-3.5

-3.7

-3.9

-4.1

-4.3

-4.53.2 3.3 3.4 3.5

(1/T) x 1000

C = 0.6107 (g/20 mL)C = 0.5381 (g/20 mL)C = 0.2467 (g/20 mL)C = 0.1180 (g/20 mL)

Figure 2. The linear variation of ln (/T1/2) versus 1/T for theaqueous polyvinyl alcohol mixtures.

Table 2. The parameters of viscosity activation energy foraqueous polyvinyl alcohol mixtures.

C (g/20mL) am bm AAD%0.6107

0.5381

0.2467

0.1180

20645.52

22453.97

17792.55

16189.92

-203.18

-211.13

-201.75

-198.18

0.24

0.33

0.23

0.01