Mar 16, 2015 - the two parameters of viscosity Arrhenius-type equation, such as the energy ... statistical correlations, thus allowing us to rewrite the Arrhenius ...
17TH ARAB CHEMISTRY CONFERENCE HAMMAMET 16-18 MARCH 2015 TUNISIA
A. Messaâdia, N. Dhouibia, M. Dallelb, H. Hamdac, F.B.M. Belgacemd, N. Ouerfellib, A.H. Hamzaouia a)
Laboratoire de Valorisation des Matériaux Utiles, Centre National des Recherche en Sciences des Matériaux, B.P.95, 2050 Borj Cedria Hammam Lif, Tunisia ; Université de Tunis El Manar, Laboratoire Biophysique et de Technologies Médicales LR13ES04, Institut Supérieur des Technologies Médicales de Tunis, 9 Avenue Dr. Zouhaier Essafi 1006 Tunis, Tunisia. c) Laboratoire d’Ingénierie Mathématique, Ecole Polytechnique de Tunisie, Université de Carthage, Rue El Khawarizmi, B.P.743, 2078 La Marsa, Tunisia. ; d) Department of Mathematics, Faculty of Basic Education, PAAET, Al-Ardhyia, Kuwait. b)
RESULTS
INTRODUCTION
Correlation between the Arrhenius parameters 60
0
0
(c)
ln As
(b)
(a)
50
lnAs
ln(As / Pa.s)
-1
40
30
20
0
-10
-15
0
50
100
150
200
250
300
350
-15
-25
-25 0
TA / K
-10
-20
-20
10
lnAs
-5
ln(As / Pa.s)
-5
Ea / kJ.mol
In transport phenomena, precise knowledge or estimation of fluids properties are necessary, for mass flow and heat transfer computations. Viscosity is one of the important properties which are affected by pressure and temperature. In the present work, based on statistical techniques for non linear regression analysis, we propose a novel equation modeling the relationship between the two parameters of viscosity Arrhenius-type equation, such as the energy (Ea) and the preexponential factor (As). Empirical validations, using about 90 data set of viscosity of pure solvents studied at different temperature ranges are provided from literature, give excellent statistical correlations, thus allowing us to rewrite the Arrhenius equation using a single parameter instead of two. Then, taking some mathematical considerations, we try in the present work to suggest an empirical exponential law-type equation valid even for the very viscous fluids (Ea < 40 kJ· mol-1) and (-20 < ln(As /Pa·s)). In addition, we have tried to give some physical meaning of the proposed equation parameters. Also, the suggested model is very beneficial for engineering data since it would permit to estimate the missing parameter value, if a well established estimate of the other is readily available.
50
100
1 50
200
250
3 00
0
3 50
10
20
30
Ea / kJ.mol
TA / K
40
50
60
-1
Figure 2. Scatter plots for pair-wise correlations between Arrhenius parameters. The Arrhenius temperature (TA = -Ea / R.lnAs),
Equation of Messaâdi-Dhoubi
METHODOLOGY Relationship between the activation energy and the Arrhenuis entropic factor
Table : Arrhenius parameters of some pure liquids studied at previous works. TA
Tb
Tm
/ kJ.mol-1
/K
/ K
/ K 178.45
Acetone
894.9
-11.097
7.4406
80.643
329.20
Acetic acid
1348.6
-11.308
11.213
119.26
391.15
289.75
60
Aniline
2405.1
-13.564
19.997
177.32
457.28
266.85
50
Butyl Alcohol
2298.9
-13.689
19.114
167.94
390.85
183.35
Carbone tetrachloride
1242.3
-11.152
10.329
111.39
349.87
250.23
Ethyl acetate
1192.9
-11.728
9.9183
101.72
350.15
189.55
Diethyl ether
904.48
-11.446
7.5203
79.021
307.75
156.85
n-heptane
1036.7
-11.302
8.6196
91.723
371.15
182.55
n-pentane
733.64
-10.886
6.0998
67.393
309.25
143.45
Toluene
1085.2
-11.135
9.0229
97.461
383.75
180.15
1052.2
-10.975
8.7485
95.872
412.25
225.35
3001.4
-14.945
24.955
200.83
468.15
257.15
Propylene Glycol
5744.8
-22.128
47.765
259.62
461.35
214.15
Butane-1,2-diol
5281.1
-20.681
43.910
255.36
465.15
159.15
Butane-1,4-diol
4012.2
-16.210
-1
cal
cal
20
33.359
247.51
503.15
0
10
20
Ea
30
exp
40
50
/ kJ.mol-1
60
293.15
(a )
214.15
] /σ
159.15
- (Ea) [(Ea)
1 /T
b
-1
X = 1 /T (K ) 1 /T A
0.5 0 -0 .5 -1 -1 .5 -2
10
20
30
40
50
60
70
80
0
10
20
30
40
50
60
70
80
O bse r va ti on nu m b e r
Figure 4. Normalized deviation plot related to (a): the activation energy: [(Ea)exp – (Ea)calc]/s and (b): the entropic factor: [(lnAs)exp – (lnAs)calc]/s against the number of observation (solvent).
CONCLUSION & PERSPECTIVE
-1 2 0
0 .0 0 3 7 5
0 .0 0 7 5
0 .0 1 1 2 5
0 .0 1 5
Figure 1. Graphical representation of the logarithm of the dynamic viscosity (lnη) methanol as a function of (1 / T) 1 00 0 0
Tb
T*
Ti / K
1 00 0
Figure 2. Classification of different mean temperatures used in this statistical investigation.
Conclusion
ln A s
Perspectives
-8
m
(b )
1
S l o p e = T * = E a /R
-1 0
T
-1
O bser v a ti on nu m b er
m
0
-6
A
-0 .5
0
A r r h e n iu s T e m p e r a tu r e
-4
T
0
-2
1 /T
T
0. 5
-1 .5
ln ( η /m P a . s )
1 /T
100
calc
461.35 465.15
- (lnAs)
247.25 257.32
exp
37.551 46.763
0
-10
/ m Pa.s)
1.5
[(lnAs)
-18.266 -21.857
calc
4516.3
-2
-15
exp
2
5624.3
2
-20
ln(A s
2 1. 5
1,2-Butanediol
4
-25 -25
Figure 3. Comparison between the experimental activation energy values (Ea)exp and the estimated ones (Ea)calc from Messaâdi-Dhouibi equation; (b): Comparison between the experimental entropic factor values (lnAs)exp and the estimated ones (lnAs)calc from Messaâdi-Dhouibi equation.
Propylene Glycol
Y =
-20
10
1
ArrheniusViscosity behavior
1 00
30
-15
] /σ
m-xylene
(b)
40
0
n-octanol
-10
(a)
/ mPa.s)
Ea
-
ln(As
lnAs
/ kJ.mol
T* /K
exp
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17
Pure Component
Ea
#
In this work, using statistical methods, we found a significant correlation between non-parametric statistical power of activity energy (Ea), the entropy factor (ln (As)) and Arrhenius temperature (TA). Thus, for facilities f programming and computing in hydraulic calculations fluid transport, and energy transfer calculations, we reduced the model using only a single variable without significant loss of accuracy.
Giving an extension and validation of the proposed equation for binary Newtonian liquid mixtures obeying the Arrhenius type equation viscosity to the whole range of the composition. It will also be very important in fluid engineering.
