Shear viscosity measurements in the binary mixture butyl cellosolve-water near its upper and lower critical consolute points

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Shear viscosity measurements in the binary mixture butyl cellosolve-water near its upper and lower critical

consolute points

Y. Izumi, A. Dondos, C. Picot, H. Benoit

To cite this version:

Y. Izumi, A. Dondos, C. Picot, H. Benoit. Shear viscosity measurements in the binary mixture butyl

cellosolve-water near its upper and lower critical consolute points. Journal de Physique, 1981, 42 (2),

pp.353-358. �10.1051/jphys:01981004202035300�. �jpa-00209017�

Shear viscosity measurements in the binary ^mixture butyl cellosolve-water

near its _{upper and} lower critical consolute points

Y. Izumi (*). ^{A. Dondos} (**), ^{C. Picot and H. Benoit}

Centre de Recherches sur les Macromolécules (C.N.R.S.), 6, ^rue Boussingault, ⁶⁷⁰⁸³ Strasbourg Cedex, ^France

(Reçu ^{le 6} février 1979, révisé le 29 septembre 1980, accepté ^{le 6 octobre} 1980)

Résumé.

Afin de tester l’universalité des concepts régissant ^les phénomènes critiques, ^{la viscosité de} cisaillement de mélanges ^binaires n-butylglycol (1)-eau ^a été étudiée au voisinage ^{des deux} températures critiques ^{LCST et}

UCST respectivement d’origine entropique ^et enthalpique. ^Les valeurs des exposants critiques _~n ^{de la viscosité}

de cisaillement sont obtenues _par une analyse des résultats utilisant une renormalisation des coefficients de trans-

port. Soient, pour le mélange UCST, ~ ⁼ 0,039 ± 0,001 (30,14 % ^en poids ^de n-butylglycol) ^{et 0,036} ± 0,007 (24,78 %) ^tandis que pour le mélange LCST, ~ ⁼ 0,038 ± 0,001 (30,14 %) ^et 0,037 ± 0,003 (24,78 %). ^Ces expo- sants sont en bon accord avec le concept ^de couplage ^{mode-mode et les} prévisions ^du groupe de renormalisation.

Abstract.

To further probe ^the hypothesis ^of universality ^{of critical} phenomena, ^{the shear} viscosity ^{has been}

measured for a two-component ^critical liquid system, butyl cellosolve-water, ^{in the} region of both the entropy- driven lower (LCST) ^{and the} enthalpy-driven upper (UCST) critical solution temperature. The values of the critical exponents _~n for the shear viscosity ^{were obtained} by analysing the results from the viewpoint ^of multiplicative

renormalization of transport coefficients. We have obtained ~n ⁼ 0.038 ± ^0.001 (30.14 ^wt. %) and 0.036 ± 0.007 (24.78 ^wt. %) for the UCST mixture, ^and _~n, ^{= 0.038} ± ^0.001 (30.14 ^wt. %) ^{and 0.037} ± ^0.003 (24.78 ^wt. %) ^{for the}

LCST mixture. These exponent values agree well with mode-mode coupling ^and renormalization-group predictions

and satisfy ^the universality hypothesis.

Classification Physics ^Abstracts

64.70J

1. Introduction.

In recent years the shear visco-

sity ^{near the critical} point ^{has attracted an} increasing

amount of attention in this field [1]. ^{A number of}

studies ^{have been} reported ^on single component gas-

liquid systems ^{and two} component liquid-liquid

systems, ^{with the} universality ^and scaling-law ^relations being ^{well confirmed} [1-5]. Further work has been

performed ^{on the three} component system [6]. ^{All the} multicomponent ^{studies have been on} liquid-liquid systems which show either the _upper critical solution temperature (UCST) ^or the lower critical solution temperature (LCST).

Systems ^{with closed} solubility loops ^are relatively

rare and ^are the focus of the present investigation.

Rowlinson [7] has reviewed the excess thermody-

namic properties ^for phase separation ^{where the}

excess Gibbs free energy ^must exceed R T/2 ; ^for

UCST this free energy ^comes primarily ^{from the}

excess enthalpy, ^{while for LCST the} entropy ^{is the}

(*) ^{Now at the} Department ^of Polymer ^{Science, Faculty of} Science, University ^of Hokkaido, ⁰⁶⁰ Sapporo, Japan.

(**) ^{Now at the} Faculty ^of Engineering, University ^of Patras, Patras, ^Greece.

(1) ^Ether monobutylique ^de l’éthylène glycol.

main contribution and the UCST and LCST in the

same mixture provided ^a special situation for the test of universality ^and scaling-law ^relations.

The purpose of our study ^is not to test the appli- cability ^{of the} scaling-law hypothesis per ^se but rather

to show that critical points ^of different fundamental

nature are described by identical critical exponents.

In this article, ^{we wish to} report measurements of the shear viscosity of critical binary ^mixture butyl ^cello-

solve (2-n-butoxyethanol-1, ethylene glycol ^mono-n- butyl ether, 2-hydroxyethyl butyl ether)-water.

This work represents ^{the first shear} viscosity ^inves- tigation ^{of two critical} points ^{in the same} binary system. ^{The UCST} investigated in this work is also the highest ^critical temperature employed ^{in a shear} viscosity study.

2. Experimental. ^{- The} materials used ^were purified

with special ^care, though impurities ^{added to a critical} system ^{have a small affect on at least some of its} thermodynamic ^and transport properties [8]. ^Merck Company ⁹⁹ % pure butyl cellosolve was fractionally

distilled under mild vacuum. The purity ^{of this compo-}

nent was at least 99.5 %. Freshly prepared ^three-fold

distilled water was used in our experiment. Preparation

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01981004202035300

354

of the critical mixture was carried out at once after the purification ^{of two} components.

The kinetic viscosity r/p (p : density) ^{was measured}

with a modified Ubbelohde viscometer. Samples ^were quickly prepared by filtering the mixtures into the

viscometer, freezing ^and subsequent sealing ^{of the}

viscometer with a torch under ^vacuum. The sealed viscometer was fixed on a rotary ^{mount and} placed

in a water (or silicone) ^bath along ^{with a thermostat}

which provided ^constant temperature within 0.005 OC for the LCST (or 0.02 OC for the UCST). ^The tempera-

ture was measured by ^{a HP} Model 2801A quartz ^ther-

mometer. The flow time of the required ^{volume of} liquid ^{between two} reference marks was recorded with

a chronometer, both _accuracy and reproducibility being ± 0.1 % for the LCST (or ± 0.4 % ^{for the} UCST). ^The viscometer was calibrated with _pure water so that a kinetic _energy correction could be

applied. ^{For the} purpose of comparison ^with theory,

the measured kinetic viscosity ^{has been} multiplied by

the density. The values of the density have been inter-

polated ^and extrapolated ^from existing ^data [9, 10].

Since the coexistence curves for butyl cellosolve- water system ^were determined years ago, ^we tried to test the purity ^{of our} samples by determining ^the

coexistence curve. First, ^Merck 99 % pure butyl

cellosolve was used without purification ^since the major impurity ^{was water.} The values obtained for the LCST location (27.5 ^wt. %, tc ⁼ 47.5 °C) ^{and the}

Fig. ^1.

Solubility ^of butyl cellosolve in water : D references [9]

and [10] ; a ^reference [11] ; ^{0 reference} [12] ; . present data ; ^{x cri-} tical point.

UCST location (30.0 ^wt. %, tc ^{= 131.5} °C) ^are compar- ed with the reported values of Cox and Cretcher [11]

(24.78 ^wt. %, tc ^{= 49.1} °C ; ^{24.78 wt.} %, tc ⁼ 128,DC),

of Poppe [12] (28.0 ^wt. %, tc ^{= 47.5 °C; 31.1 wt.} %,

tc ^{= 135} OC), and of Schneider et al. [10] (32.4 ^wt. %,

tc ^{= 49.2} °C ; ^{30.0 wt.} %, tc ^{= 130.3} oC). ^{These results}

are shown in figure ^{1. It is noted that the critical} compositions ^{in each} laboratory ^{are similar at both}

the UCST and the LCST, though ^the variations in the locations of the LCST and UCST will be attributed to different amount of impurities in the mixture studied

by ^each laboratory.

Viscosity measurements were done with the frac-

tionally ^distilled butyl cellosolve at the LCST location

(wc ^{= 30.14 wt.} %, tc ⁼ 48.272°C), ^{which was deter-}

mined by ^the phase volume ratio method. The LCST location corresponds ^{to a} value of the UCST

(30.14 ^wt. %, tp ^{= 130.71 OC), where we} have used the

phase separation temperature tp ⁱⁿ place of tc. ^{It does}

specify ^{the exact location of the UCST, because the}

meniscus was not seen to appear in the middle of the

sample ^{at the UCST,} though ^{it is} comparable ^{to the}

results of Schneider et al. [10]. Especially, it should be noted that a few percent of volatile water at the UCST location was in the vapour phase ^{in our} viscometer,

which had dead _spaces of about 14 cm3. Consequently,

the concentration of butyl cellosolve in the liquid phase

was correspondingly increased, ^which explained ^the slight displacement of the UCST location. However,

we neglected this effect in the present analysis ^{of the} viscosity ^data.

The measurements were also made at both the location of LCST (24.78 ^wt. %, tp ^{= 48.010°C) and}

of UCST (24.78 ^wt. %, tp ⁼ 130.74°C), ^{which cor-} respond ^to the values of Cox and Cretcher [11].

3. Data analysis and results. -The _very complicated problem of the critical behaviour of transport ^coeffi- cients has been widely ^{studied. The recent refmement}

of mode-mode coupling theory [13-15] ^{and the success}

of renormalization _group theory [16,17] ^{have enabled}

the critical exponent z for the shear viscosity ^{to be}

examined more rigorously. ^{The theories} predict ^that

the shear viscosity along ^{with the} critical isochore _may be written as

with pn ^{= -} z" ^v, where A is a microscopic ^cut-off

wave number, , = ’0 e-v is the correlation length,

and e is given by (T /Tc - 1). # ^{is the critical} amplitude

for the diverging ^shear viscosity ^near equilibrium,

which ^can be identified as the bare (background) viscosity Y/id’ where the correction to # ^{of order e has}

been omitted. From mode-mode coupling theory, ^the

critical exponent _z,, ^{is found to be 0.054} using ^{the self-}

consistent approximation [13, 14] and 0.070 with

vertex corrections [15], while the renormalization-

group theory predicts z,, ^to be 0.053 in an e-expansion

to first order [16] and 0.065 in an e-expansion ^to

second order for the dimensionality ^{d = 3} [17].

A common feature of all these theories is that the shear viscosity ^{shows a weak} anomaly in the critical

region and that the renormalization of its anomalous part ^{is of a} multiplicative rather than of an additive type [18].

On the experimental side, equation (1) ^{has been}

confirmed by ^{a critical} reexamination of the existing viscosity ^data [4, 5] ^and by ^{a shear} viscosity ^measure-

ment in a large temperature range [19]. However, ^{it is} important ^{to note that} equation (1) ^is only ^{the first} approximation and, ⁱⁿ general, the existence of the correction terms is predicted theoretically, though fortunately ^{it has not} been needed to account for the behaviour of the shear viscosity ⁱⁿ many binary

critical mixtures [4, 5].

In interpreting viscosity ^data, much of the ambi-

guity ^{is due to different} methods of subtracting ^of llid.

It is natural that a systematic procedure ^{should be} developed for the evaluation of _llid. To gain ^some insight ^{into the} problem ^{we used two different} equa- tions to represent lid. The temperature dependence ^of

the viscosity ^of nearly ^all pure and multi component liquids ^{can be} adequately represented ^{over a limited}

range of temperature by the Arrhenius equation :

where A’ and B’ ^are constants independent ^{of tem-} perature. ^This equation gives ^an adequate description

of _tlid for the UCST, whereas, using ^this equation,

we obtained significant ^excess viscosities for the LCST. We think this was due to the inadequacy ^{of the}

Arrhenius equation ^{near the LCST} [20].

Since the butyl cellosolve-water system ^{at the} critical concentration is 93 mole % ^{water, we felt}

that the normal behaviour would be dominated by

water. Therefore, ^{as an} alternative method, ^{we used}

the Vogel equation :

where A, ^{B and C are constants} independent ^of tempe-

rature.

Equation (3) ^{has been} successfully ^{used to} present the behaviour ^{of the} viscosity ^{of water, which also}

shows large ,systematic deviations from the simple

Arrhenius équation ^[21].

Figure ^{2 shows the} temperature dependence ^{of the} viscosity for the UCST along ^with equation (2) ^and

that for the LCST along ^with equation (3).

It is easily ^{seen that the excess} viscosity ^{at 30.14 wt.} %

is much larger ^{than that at 24.78 wt.} %, ^{which means}

that the latter does not correspond ^{to the critical}

concentration and it is consistent with the present result of the coexisting ^curve. Indeed, Chakhouskoy [22]

and Onken [10] ^have previously inferred the presence of impurities ⁱⁿ butyl cellosolve used by ^{Cox and}

Cretcher [11].

Fig. ^2.

^{The shear} viscosity ^{as a function of} temperature ^{at two} différent composition : a) ^{the UCST} along ^with equation (2) ^where

A’ = - 6.914 and B’ ⁼ 2.48 ^x 103 at 30.14 wt. % ; A’= - 6.846 and B’ ⁼ 2.40 x 103 at 24.78 wt. %. b) ^{The LCST} along ^with equation (3) ^{where A = -} 1.498, ^{B =} 208.97 and C ^{= -} 212.5 at 30.14 wt. % ; A ^{= -} 1.331, ^{B =} 160.91 and C ^{= -} 222.5 at 24.78 wt. %.

Fig. ^3.

^{Plot of In} ’1/ lid ^vs. ln 1 a at ^{30.14 wt.} % : ^{0 UCST and}

e LCST. The broken and solid lines, respectively, ^{are before and}

after correcting for the non-linear viscosity ^effect.

356

The excess viscosities obtained using ^{two methods}

of characterizing background behaviours are shown in figure ^{3 of In} tif tlid ^vs. ln 1 B 1. Figure 3 shows that In tif tlid ^at first increases linearly, ^{then starts to level}

off as one approaches the critical point, ^whereas equation (1) suggests ^a straight ^{line of} slope - _(pl

in the plot ^{of ln} tif tlid ^vs. ln 1 e along ^{with the critical}

isochore. Although ^{such a} levelling-off (cusp-like behaviour) ^of viscosities could be attributed to the presence of impurities [23], ^a result of non-linear

viscosity ^effects [24], and other effects [25, 26], ^nowa- days ^{it is} mainly attributed to the second effect in the measurement of the capillary method. As pointed ^out by Oxtoby [24], ^{such a method} introduces ^a non-linear effect causing ^an apparent levelling-off of the data as one approaches ^{the critical} point. Depending ^{on the} type ^of viscometer used and on the correlation length

of the system the effect can become _very important.

Unfortunately, ^the correlation length ^{for the} present system ^{has not been} reported in either the _upper or

lower critical regions. ^{Therefore we tried to estimate}

the correlation length ^{under the} assumption ^{that the} theory ^of Oxtoby ^{could be} applied ^{to the} present system. According ^to Oxtoby, the non-linear effect

A(Â) ^is expressed ^{as a} function of  (= tlç3 D/kB T,

where D is the magnitude of the shear gradient),

which should be a universal function of À, independent

of A. The values of A(Â) ^were calculated by using ^an

extension of the microscopic ^mode coupling theory,

and were graphically given ^{in the} original ^text [24].

In order to compare the theory ^{with the} present results we need further to determine an effective average value Deff ^{in terms of the} experimentally

known Dmax. ^{If we assume a} parabolic velocity profile

in the capillary tube, Deff ^is given by (8/15) Dmax,

where Dmax ⁼ hpgr/2 ill, h, height ^of pressure head

(7.15 cm), l, length ^of capillary (5.7 cm), ^{r, radius of} capillary (0.0353 cm), and g ^{is 980} cm/s2. ^{Thus we have}

determined the correlation length from the shift factor between the plot ^of A(Â,,ff) ^vs. log Àeff ^{and that}

of { q(0) - l(Âr ,ff) I/ il(O) ^{vs. - 3 v} log E 1. ^{The res-} pective ^{values for} jo ^{and v at the LCST are 5.5 ± 1.0 A}

and 0.62 ± 0.02 ; ^at the UCST the corresponding

values are 6.7 + ^1.5 A and 0.64 + ^0.03. Other inde-

pendent measurement on the same system ^{will be} needed to examine the validity ^{of these} values, though

these exponent ^{values are in} good agreement ^{with the} results obtained from the light scattering ^{and the} Rayleigh line width measurements for the 3-methyl- pyridine-D20 binary liquid system ^{in the} region ^of

both the LCST and the UCST [27].

Now we can estimate the critical temperature ^{in the}

presence of flow Tc(D) which is shifted downward

below its equilibrium ^value Tc(O) ^as [28]

where 1-rs(D) ^{is the crossover reduced} température ^at

which kc ç ^{= 1 holds, and is} given by

Thus we found 0.011° at the LCST and 0.020 at the UCST as thé values of Tc(0) - ^Tc(D) 1.

Since these values are comparable ^to the accuracy of the thermal stability ^{in the} present experiment,

we have neglected the shift of the critical temperature in the presence of flow.

The shear viscosity in the absence of the shear

gradient ^{effect is} given by

A plot ^{of In} ’1(0)/ r¡id ^vs. ln 1 B 1 ^{is shown} by ^{a solid}

line in figure ^3.

It can be seen that the levelling-off ^{is now} quite insignificant compared ^{with the} plot ^of

though ^{we find two} distinguishable straight ^{lines with}

the same values of slope (- ^{0.038 ±} 0.001), ^within

the experimental ^{error. Thus we can determine the}

critical exponent _z,, ^{for the} viscosity by combining

with the results obtained through ^the analysis ^{of non-}

Newtonian effects : the respective values for z,, ^{and A}

at the LCST are 0.061 ± ^{0.002 and} 0.017, and at the UCST the corresponding ^{values are 0.059 ± 0.003}

and 0.010.

Since r/ rid ^{and ç} along ^the non-critical isochore would diverge ^{on the} spinodal ^curve introduced by

Benedek [29], ^the following extension of equation (1)

has been proposed [5] ;

where 8gp ⁼ T /T Sp - ^{1. Straight lines of slopes -} ç in plots ^{of ln} r¡/ r¡id ^{as a function of ln} Esp ^{are obtained} and applied ^{to the} viscosity ^{data at 24.78 and}

Fig. ^4.

Plot of In tif tlid ^vs. ln 1 Bsp 1 ^{0 UCST and. LCST at}

30.14 wt. % ; A ^{UCST and V LCST at 24.78 wt.} %.

Table I.

Values of Ço, v, A ^and z,, ^at Wc ⁼ 30.14 wt. %.

Table II.

Characteristics of ^the samples ^{and values} of tp

tsp ^and cp".

(’) Butyl cellosolve % by weight.

(b) lp,,(theot.) ^was calculated with the v value (0.627) of Baker et al. [31].

30.14 wt. %, ^{as shown in} figure ^{4. All the} exponent values obtained are listed in tables 1 and II, including phase separation ^and pseudo-spinodal temperatures.

From our values for the viscosity exponents qJ", Zm and the v exponents, the LCST exhibits basically ^the

same type ^of viscosity anomaly ^{as the} UCST, ^whose exponents ^are consistent with the theoretical _pre- dictions mentioned above [13-17]. ^{Such a result}

agrees well with the hypothesis ^of universality, ^irres- pective ^{of the} particular system under examination.

However, ^{due to} hydrogen bonding, ^the temperature dependence ^of viscosity for the LCST _away from the critical point ^{is more} complex ^{than that} represented by

a simple ^Arrhenius equation.

Finally it is worthwhile to attempt ^{a more} general

test of the homogeneity ^and scaling laws with the

viscosity ^data. According ^to the initial approach ^of

Green and co-workers [30], ^the scaling relation of

equation (1) ^{takes a form}

where X ⁼ eo/1 AX2* Il AX2* ⁼ (x2 - x2c)/x2c, x2c is the mole fraction at the critical concentration, and

is the critical exponent ^{of the} coexisting ^curve

The function f(X) ^{has a universal} asymptotic ^beha- viour, i.e.,

The results applied ^{to the} present system ^{are shown} in figure 5.

As is evident from figure 5, ^the analysis presented

here seems to be applicable ^to both the UCST and the LCST. However, it would be desirable to have more

extensive data for a more stringent ^{test of the} scaling hypothesis.

Fig. ^5.

Scaling plot of the shear viscosity ^{as a} function of X : 0 UCST; 0 ^LCST.

Acknowledgments.

One of the authors (Y.I.T

would like to express thanks for a fellowship ^{from the}

French Government.

358

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