Surface Tension Prediction
of Organic Binary Liquid Mixtures
Prof. Dr. Ulhas Balkrishna Hadkar1*,
Miss. Munira Aunali
Loliwala2
1Director, Mumbai Education Trust’s, Institute of Pharmacy, Bandra (west), Mumbai- 400050, Maharashtra, India.
2Mumbai Education Trust’s, Institute of Pharmacy, Bandra (west), Mumbai- 400050, Maharashtra, India.
*Corresponding Author E-mail: ulhashadkar@yahoo.com,
mloliwala72@gmail.com
ABSTRACT:
Equations have been reported in the literature to predict the
surface tension of binary liquid mixtures. However, the equations involve large
number of variables and are very complex. In the present article an attempt is
made to propose an empirical equation to predict the surface tension of binary
organic liquid mixtures. A simple
equation, ‘Hadkar Equation’, has been proposed and
was used to calculate the surface tension of binary liquid mixtures that have
already been reported in the literature and was found to give the results close
to the reported values. To verify the utility of the equation for the
prediction of surface tension of liquid mixture, the surface tension of a few
organic binary liquid mixtures was determined using drop weight method. The ‘Hadkar Equation’, was found to be useful in the prediction
of surface tension of organic binary liquids having weak force of attraction.
KEY WORDS: Surface tension, Drop weight method, Dielectric constant,
Intermolecular forces.
INTRODUCTION:
Surface tension of a liquid is defined as the force in dynes
acting along the surface of the liquid at right angles to any line one
centimeter in length1. The various methods2 to determine
surface tension of a liquid are drop weight method, capillary rise method, Du-Nuoy ring method. The plot of surface tension versus
concentration has been used to determine critical micelle concentration of a
surfactant3. It is also used to determine the cross sectional area
of a surfactant molecule4. In general, surface tension is an
important physical property due to its influence on several natural phenomenon
as well as its industrial applications5, such a detergency,
lubrication, chemical reactions that occur at the fluid surfaces. Surface
tension of pure liquids such as heptanes, toluene, cyclohexane
etc and binary liquid mixtures has been determined by Hike Kahl,
Tinowadewitz and Jochem
Winkelmann6.
Surface tension has been shown to have a significant effect on the
dissolution rate of drugs and their release rate from solid dosage forms7.
Surfactants and wetting agents lower the contact angle and consequently improve
penetration by dissolution medium.
Finholt and Solvang8 compared the
dissolution behavior of phenacetin and phenobarbital tablets in human gastric juice to that in
dilute hydrochloric acid with and without various amounts of polysorbate 80 in the dissolution medium. The data showed
that both pH and surface tension have significant influence on the dissolution
kinetics of the drug studies.
Mixtures of liquids are often used in industry and it is necessary
to know the surface tension of liquid mixtures. The surface tension of binary
liquid mixtures 
m by ideal mixing rule is given by the equation
m= (
AA+BB). - - - - - - (1),
in which A and B are the mole fractions of components A and B and A and B are the surface tensions of pure components A and B
respectively. The equation (1) is valid if there is no interaction between the
components of the mixture. The difference in actual surface tension of the
mixture mix and that calculated using equation (1) is represented by E = mix– (AA+BB) and is the direct measure of interaction between the two
liquids.
The intermolecular attractive forces that exist between like or
unlike molecules are (a) Van der Waals Forces that
include dipole-dipole attractive forces, dipole-induced dipole attractive
forces (London forces). (b) Ion-ion dipole force of attraction. When two
liquids are mixed, the surface tension of the mixture is different from the
calculated values using equation (1) given above because of the intermolecular
forces of attraction between the molecules of the components of the mixture.
J.R Block and Bird9 found the following correlation
between critical constants and surface tension 
=
(Pc2.Tc)1/3
(-0.951 + 0.432/Zc) (1-Tr)11/9 ,
Where Pc, Tc and
Zc and Tr are the critical pressure,
critical temperature, critical compressibility factor and reduced temperature
respectively.
Zc = 
and
Tr= 
,
where Tr and R
are absolute temperature and gas constant respectively.
Glisniki10suggested the equation assuming additively
with the volume fractions 
of
the components as
cal= 
where cal = theoretical surface tension of binary liquid mixture.
1, 2 = surface tension of pure components liquids 1 and 2
respectively.
1, 2 = volume fractions of components 1 and 2 respectively.
A few equations have been proposed to predict the surface tension
of pure liquids and binary liquid mixtures, which are mostly derived from
statistical mechanics. The expression initially given by Escobedo and Mansoori11
for pure liquids has been extended to the mixtures of organic liquids by Joel
Escobedo and G. Ali Mansoori12. For the surface tension
, of pure liquids, Escobedo and Mansoori proposed,
=
[P (
l—v)]4- - - - - - - - (2)
and l and v are the densities of the liquid and its
vapor.
Where, P = Po (1 – Tr)0.37 Trexp
(0.30066/Tr+ 0.86442 Tr9)
----------- (3)
The equation reported by Joel Escobedo and G. Ali Mansoori for the prediction of surface tension of binary
liquid mixtures suffers from the serious defect of not having the same units of
the two sides of the equation. The equation is too complicated to include in
this introduction. Looking at the
complexity of the equation to predict the surface tension of binary liquid
mixtures used by Escobedo and Mansoori and the number
of parameters involved in the equation, the authors of the present article
tried to find a simple empirical equation to predict surface tension of binary
liquid mixture. One of the authors of the present article has proposed an
empirical equation which would be referred to as ‘Hadkar
Equation’ for the prediction of surface tension of a binary liquid mixture. It
involves only one parameter that is dielectric constant. The surface tension of
a few binary liquid mixtures was determined to verify the utility of the ‘Hadkar Equation’.
MATERIAL AND METHODS:
The liquids benzaldehyde, carbon
disulphide, carbon tetrachloride and toluene used were BDH quality, 10ml
graduated pipette. A 10ml graduated pipette held in vertical position was used
to determine the surface tension of the liquid and liquid mixture using drop
weight method. The drop rate was adjusted to about 15-20 drops per minute so
that each drop was detached from the tip of the pipette under its own weight.
The number of drops was determined for a fixed volume of the liquid and for the
same volume of distilled water. The surface tension of average of four readings
was recorded. The surface tension of liquid was calculated using equation
2= (n1/n2).
(ρ2/
ρ1). 1 ,
where n1, ρ1, 1 are the number of drops, density and surface tension of water
and n2, ρ2, 2 are the number of drops, density and surface tension of the
liquid or the binary liquid mixture. The surface tension of the following
binary liquid mixtures was determined using the drop weight method. Toluene and CS2
2. CCl4 and toluene and 3. Chloroform and benzaldehyde. The experimental values of surface tension
are compared with the theoretical value calculated using equation 1 and
calculated using ‘Hadkar Equation’ in Table 1.
Table 1: Comparison between surface tension
calculated using equation 1, experimental values and calculated using ‘Hadkar equation’ at 25 ±10C.
|
Binary mixture
|
Mole fraction
|
 m
dynes/cm
(Theoretical)
|
m
dynes/cm
(Experimental) (25 ±10C)
|
(m).(
H3)= mixH
dynes/cm
(Using ‘Hadkar eq’)
|
|
(A)
Toluene+ (B)CS2
|
 A B
|
 A=2.38
|
B=2.6
|
H3= 0.9770 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
32.30
|
34.25
|
32.30(H3=1 )
|
|
2.
|
0.2
|
0.8
|
31.52
|
30.02
|
30.795
|
|
3.
|
0.4
|
0.6
|
30.74
|
29.20
|
30.03
|
|
4.
|
0.6
|
0.4
|
29.96
|
28.54
|
29.27
|
|
5.
|
0.8
|
0.2
|
29.18
|
27.03
|
28.50
|
|
6.
|
1.0
|
0.0
|
28.40
|
25.92
|
28.40(H3=1 )
|
|
(A) CCL4+(B)Toluene
|
A B
|
A=2.238
|
B=2.38
|
H3=0.9856 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
28.40
|
25.92
|
28.40(H3=1 )
|
|
2.
|
0.2
|
0.8
|
27.74
|
27.12
|
27.340
|
|
3.
|
0.4
|
0.6
|
27.72
|
26.85
|
27.32
|
|
4.
|
0.6
|
0.4
|
27.38
|
26.42
|
26.98
|
|
5.
|
0.8
|
0.2
|
26.96
|
25.31
|
26.57
|
|
6.
|
1.0
|
0.0
|
26.7
|
23.15
|
26.7(H3=1 )
|
|
(A) Chloroform+
(B)Benzaldehyde
|
A B
|
A=4.806
|
B=17.8
|
H3=0.9154 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
38
|
36.42
|
38(H3=1 )
|
|
2.
|
0.2
|
0.8
|
35.9
|
33.27
|
32.862
|
|
3.
|
0.4
|
0.6
|
33.8
|
30.69
|
30.94
|
|
4.
|
0.6
|
0.4
|
31.7
|
28.28
|
29.01
|
|
5.
|
0.8
|
0.2
|
29.6
|
26.86
|
27.09
|
|
6.
|
1.0
|
0.0
|
27.50
|
25.17
|
27.50(H3=1 )
|
RESULTS
AND DISCUSSION:
The proposed ‘Hadkar Equation’ for the
prediction of surface tension of an organic binary liquid mixture is
mixH
= (AA+BB). H3 ----- (4)
where mixH = surface tension of the binary liquid
mixture
A= surface tension of component A
B= surface tension of component B
A= mole fraction of component A
B=mole fraction of component B
H3= (A/B) F and
F= ¼ (B/A) and 
A <B.
A= Dielectric constant of liquid A
B= Dielectric constant of liquid B and A<B.
It may be noted that the factor F and H3 are just
numbers, that is, dimensionless fractions and that the units of left hand side
as well as right hand side are that of the surface tension. The Hadkar equation (equation 4 above) can be used to predict
the surface tension of the organic binary liquid mixtures which do not have
strong interactions such as hydrogen bond formation. The equation is found to
be useful for organic liquids having low values of dielectric constants less
than 10. The Hadkar equation (equation 4) was used to
predict the surface tension of various organic liquid mixtures reported by Joel
Escobedo and G. Ali Mansoori13.
The calculated values agreed within 3% to 4% for almost all the liquid
mixtures. The values of the surface tensions of the liquid mixtures calculated
by using Escobedo et al equation and that calculated from Hadkar
equation are compared in the Tables 2 to 5.
Table No. 2: Comparison between surface
tension calculated using equation 1, reported value11 and calculated
using ‘Hadkar equation’ at 25 ±10C.
|
Binary mixture
|
Mole fraction
|
m
dynes/cm
(Theoretical)
|
m
dynes/cm
(Reported)
|
(m).(
H3)=mixH dynes/cm
(using ‘Hadkar eq’)
|
|
(A)
n- Dodecane +
(B)Benzene
|
|
A=2.002
|
B=2.275
|
H3= 0.9337 (For mixtures 2 to 5)
|
|
|
A
|
B
|
|
|
|
|
1.
|
0.0
|
1.0
|
27.5
|
27.5
|
27.5 (H3=1 )
|
|
2.
|
0.2
|
0.4
|
26.84
|
25.8
|
25.06
|
|
3.
|
0.4
|
0.6
|
26.18
|
24.6
|
24.44
|
|
4.
|
0.6
|
0.4
|
25.52
|
24.2
|
23.82
|
|
5.
|
0.8
|
0.2
|
24.86
|
24.2
|
23.21
|
|
6.
|
1.0
|
0.0
|
24.4
|
24.4
|
24.4(H3=1 )
|
|
(A)
n-Hexane + (B) Benzene
|
A
B
|
A=1.89
|
B=2.275
|
H3= 0.962 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
27.5
|
27.5
|
27.5(H3=1 )
|
|
2.
|
0.2
|
0.8
|
25.6
|
23.6
|
24.67
|
|
3.
|
0.4
|
0.6
|
23.7
|
21
|
22.79
|
|
4.
|
0.6
|
0.4
|
21.8
|
19.2
|
20.97
|
|
5.
|
0.8
|
0.2
|
19.9
|
17.6
|
19.14
|
|
6.
|
1.0
|
0.0
|
18
|
18
|
18(H3=1 )
|
|
(A)
Benzene + (B) O-xylene
|
A B
|
A=2.275
|
B=2.57
|
H3= 0.9733 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
29.4
|
29.4
|
29.4(H3=1 )
|
|
2.
|
0.2
|
0.8
|
29.15
|
29.15
|
28.37
|
|
3.
|
0.4
|
0.6
|
28.9
|
28.75
|
28.12
|
|
4.
|
0.6
|
0.4
|
28.65
|
28.6
|
27.88
|
|
5.
|
0.8
|
0.2
|
28.4
|
28.3
|
27.64
|
|
6.
|
1.0
|
0.0
|
28.15
|
28.15
|
28.15(H3=1 )
|
|
(A)
CCL4 + (B) Benzene
|
A B
|
A=2.238
|
B=2.275
|
H3= 0.9959 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
28.15
|
28.15
|
28.15(H3=1 )
|
|
2.
|
0.2
|
0.8
|
27.86
|
28.0
|
27.74
|
|
3.
|
0.4
|
0.6
|
27.57
|
27.8
|
27.45
|
|
4.
|
0.6
|
0.4
|
27.28
|
27.4
|
27.17
|
|
5.
|
0.8
|
0.2
|
26.99
|
27.05
|
26.88
|
|
6.
|
1.0
|
0.0
|
26.70
|
26.70
|
26.70(H3=1 )
|
|
(A)
Cyclopentane
+ (B) Benzene
|
A B
|
A=1.96
|
B=2.275
|
H3= 0.9684 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
28.1
|
28.1
|
28.1(H3=1 )
|
|
2.
|
0.2
|
0.8
|
26.82
|
26.4
|
25.94
|
|
3.
|
0.4
|
0.6
|
25.54
|
24.6
|
24.73
|
|
4.
|
0.6
|
0.4
|
24.26
|
23.5
|
23.49
|
|
5.
|
0.8
|
0.2
|
22.98
|
22.4
|
22.25
|
|
6.
|
1.0
|
0.0
|
21.7
|
21.7
|
21.7(H3=1 )
|
|
|
|
|
|
|
|
Table 3: Comparison between surface tension
calculated using equation 1, reported value11 and calculated using ‘Hadkar equation’ at 25 ±10C.
|
Binary mixture
|
Mole fraction
|
m
dynes/cm
(Theoretical)
|
m
dynes/cm
(Reported)
|
(m).(
H3)=mixH dynes/cm
(using ‘Hadkar eq’)
|
|
(A)
Cyclopentane
+ (B)CCL4
|
A
B
|
A=2.238
|
B=2.275
|
H3= 0.9959 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
26.2
|
26.2
|
26.2(H3=1 )
|
|
2.
|
0.2
|
0.8
|
25.32
|
25.3
|
24.59
|
|
3.
|
0.4
|
0.6
|
24.4
|
24.2
|
23.70
|
|
4.
|
0.6
|
0.4
|
23.56
|
23.4
|
22.88
|
|
5.
|
0.8
|
0.2
|
22.68
|
22.6
|
22.03
|
|
6.
|
1.0
|
0.0
|
21.8
|
21.8
|
21.8(H3=1 )
|
|
(A)
Cyclopentane
+ (B)Toluene
|
A B
|
A=1.96
|
B=2.38
|
H3= 0.9608 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
0.0
|
28
|
28
|
28(H3=1 )
|
|
2.
|
0.2
|
0.8
|
26.76
|
26.4
|
25.71
|
|
3.
|
0.4
|
0.6
|
25.52
|
25.1
|
24.52
|
|
4.
|
0.6
|
0.4
|
24.28
|
24.0
|
23.33
|
|
5.
|
0.8
|
0.2
|
23.04
|
22.8
|
22.13
|
|
6.
|
1.0
|
0.0
|
21.8
|
21.8
|
21.8(H3=1 )
|
|
(A)
Cyclopentane
+(B) Tetrachloroethylene
|
A B
|
A=1.96
|
B=2.30
|
H3= 0.9665 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
31.4
|
31.4
|
31.4(H3=1 )
|
|
2.
|
0.2
|
0.8
|
29.48
|
29.25
|
28.49
|
|
3.
|
0.4
|
0.6
|
27.56
|
27.0
|
26.63
|
|
4.
|
0.6
|
0.4
|
25.64
|
25.0
|
24.78
|
|
5.
|
0.8
|
0.2
|
23.72
|
23.2
|
22.92
|
|
6.
|
1.0
|
0.0
|
21.8
|
21.8
|
21.8(H3=1 )
|
|
(A)
Cyclohexane
+ (B)Benzene
|
A B
|
A=1.9890
|
B=2.275
|
H3= 0.9709 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
28.8
|
28.8
|
28.8(H3=1 )
|
|
2.
|
0.2
|
0.8
|
28.04
|
27.0
|
27.22
|
|
3.
|
0.4
|
0.6
|
27.28
|
26.2
|
26.48
|
|
4.
|
0.6
|
0.4
|
26.52
|
25.4
|
25.74
|
|
5.
|
0.8
|
0.2
|
25.76
|
25.2
|
25.01
|
|
6.
|
1.0
|
0.0
|
25
|
25
|
25(H3=1 )
|
|
(A)
Cyclohexane
+ (B)Toluene
|
A B
|
A=1.9890
|
B=2.38
|
H3= 0.9632 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
31.2
|
31.2
|
31.2(H3=1 )
|
|
2.
|
0.2
|
0.8
|
29.84
|
29.4
|
28.74
|
|
3.
|
0.4
|
0.6
|
28.48
|
24.6
|
27.43
|
|
4.
|
0.6
|
0.4
|
27.12
|
26.2
|
26.12
|
|
5.
|
0.8
|
0.2
|
25.76
|
25.1
|
24.81
|
|
6.
|
1.0
|
0.0
|
24.4
|
24.4
|
24.4(H3=1 )
|
Table 4: Comparison between
surface tension calculated using equation 1, reported value11 and
calculated using ‘Hadkar equation’ at 25 ±10C.
|
Binary mixture
|
Mole fraction
|
m
dynes/cm
(Theoretical)
|
m
dynes/cm
(Reported)
|
(m).(
H3)=mixH dynes/cm
(using ‘Hadkar eq’)
|
|
(A)
CCL4 + (B) iodomethane
|
A B
|
A=2.238
|
B=7.0
|
H3= 0.9128 (For
mixtures 2 to 5)
|
|
1.
|
0.0
|
1.0
|
31.0
|
31.0
|
31.0(H3=1 )
|
|
2.
|
0.2
|
0.8
|
30.16
|
29.2
|
27.53
|
|
3.
|
0.4
|
0.6
|
29.32
|
28.0
|
26.76
|
|
4.
|
0.6
|
0.4
|
28.48
|
27.6
|
26.00
|
|
5.
|
0.8
|
0.2
|
27.64
|
27.0
|
25.23
|
|
6.
|
1.0
|
0.0
|
26.8
|
26.8
|
26.8(H3=1 )
|
|
(A)
Benzene + (B) Carbon disulphide
|
A B
|
A=2.275
|
B=2.641
|
H3= 0.969 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
32.7
|
32.7
|
32.7(H3=1 )
|
|
2.
|
0.2
|
0.8
|
31.8
|
30.6
|
30.83
|
|
3.
|
0.4
|
0.6
|
30.94
|
29.4
|
29.98
|
|
4.
|
0.6
|
0.4
|
30.06
|
28.7
|
29.12
|
|
5.
|
0.8
|
0.2
|
26.18
|
28.3
|
28.27
|
|
6.
|
1.0
|
0.0
|
28.3
|
28.3
|
28.3(H3=1 )
|
|
(A)
Isooctane + (B) n-Dodecane
|
A B
|
A=1.95
|
B=2.00
|
H3= 0.9938 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
24.4
|
24.4
|
24.4(H3=1 )
|
|
2.
|
0.2
|
0.8
|
23.08
|
23.0
|
22.93
|
|
3.
|
0.4
|
0.6
|
21.76
|
21.6
|
21.62
|
|
4.
|
0.6
|
0.4
|
20.44
|
20.7
|
20.31
|
|
5.
|
0.8
|
0.2
|
19.12
|
19.2
|
19.10
|
|
6.
|
1.0
|
0.0
|
17.8
|
17.8
|
17.8(H3=1 )
|
|
(A)
Isooctane + (B) n-Cyclohexane
|
A B
|
A=1.95
|
B=1.989
|
H3= 0.995 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
23.7
|
23.7
|
23.7(H3=1 )
|
|
2.
|
0.2
|
0.8
|
22.56
|
21.3
|
22.44
|
|
3.
|
0.4
|
0.6
|
21.42
|
20.4
|
21.31
|
|
4.
|
0.6
|
0.4
|
20.28
|
19.2
|
20.17
|
|
5.
|
0.8
|
0.2
|
19.14
|
18.3
|
19.04
|
|
6.
|
1.0
|
0.0
|
18.0
|
18.0
|
18.0(H3=1 )
|
|
(A)
Cyclohexane
+ (B) cis-Decalin
|
A B
|
A=1.9890
|
B=2.219
|
H3= 0.975 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
32.2
|
32.2
|
32.2(H3=1 )
|
|
2.
|
0.2
|
0.8
|
30.64
|
30.4
|
29.89
|
|
3.
|
0.4
|
0.6
|
29.08
|
29.1
|
28.35
|
|
4.
|
0.6
|
0.4
|
27.52
|
27.6
|
26.86
|
|
5.
|
0.8
|
0.2
|
25.96
|
25.9
|
25.31
|
|
6.
|
1.0
|
0.0
|
24.4
|
24.4
|
24.4(H3=1 )
|
Table 5: Comparison between
surface tension calculated using equation 1, reported value11 and
calculated using ‘Hadkar equation’ at 25 ±10C.
|
Binary mixture
|
Mole fraction
|
m
dynes/cm
(Theoretical)
|
m
dynes/cm
(Reported)
|
(m).(
H3)=mixH dynes/cm
(using ‘Hadkar eq’)
|
|
(A)
Cyclohexane
+ (B) trans-Decalin
|
A
B
|
A=1.9890
|
B=2.184
|
H3= 0.979 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
30.0
|
30.0
|
30.0(H3=1 )
|
|
2.
|
0.2
|
0.8
|
28.88
|
28.8
|
28.27
|
|
3.
|
0.4
|
0.6
|
27.76
|
27.8
|
27.17
|
|
4.
|
0.6
|
0.4
|
26.64
|
26.7
|
26.7
|
|
5.
|
0.8
|
0.2
|
25.52
|
25.5
|
25.5
|
|
6.
|
1.0
|
0.0
|
24.4
|
24.4
|
24.4(H3=1 )
|
|
(A)
CCL4 + (B) Carbon disulphide
|
A B
|
A=2.238
|
B=2.641
|
H3= 0.9656 (For mixtures 2 to 5)
|
|
1.
|
0.0
|
1.0
|
32.6
|
32.6
|
32.6(H3=1 )
|
|
2.
|
0.2
|
0.8
|
31.2
|
30.2
|
30.31
|
|
3.
|
0.4
|
0.6
|
30.2
|
28.96
|
29.16
|
|
4.
|
0.6
|
0.4
|
29
|
27.8
|
28
|
|
5.
|
0.8
|
0.2
|
27.8
|
26.66
|
26.84
|
|
6.
|
1.0
|
0.0
|
26.60
|
26.60
|
26.60(H3=1 )
|
|
(A)
Benzene + (B) Ethylacetate
|
A B
|
A=2.275
|
B=6.02
|
H3= 0.9122 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
23.8
|
23.8
|
23.8(H3=1 )
|
|
2.
|
0.2
|
0.8
|
24.72
|
24.4
|
23.98
|
|
3.
|
0.4
|
0.6
|
25.64
|
25.2
|
23.38
|
|
4.
|
0.6
|
0.4
|
26.56
|
26.0
|
24.22
|
|
5.
|
0.8
|
0.2
|
27.48
|
27.0
|
25.06
|
|
6.
|
1.0
|
0.0
|
28.4
|
28.4
|
28.4(H3=1 )
|
|
(A)
Carbon disulphide +(B) Dichloromethane
|
A B
|
A=2.641
|
B=9.08
|
H3= 0.914 (For mixtures 2 to
5)
|
|
1.
|
0.0
|
1.0
|
27.3
|
27.3
|
27.3(H3=1 )
|
|
2.
|
0.2
|
0.8
|
28.16
|
27.3
|
25.74
|
|
3.
|
0.4
|
0.6
|
29.02
|
27.4
|
26.52
|
|
4.
|
0.6
|
0.4
|
29.88
|
28.2
|
27.31
|
|
5.
|
0.8
|
0.2
|
30.74
|
29.2
|
28.09
|
|
6.
|
1.0
|
0.0
|
31.6
|
31.6
|
31.6(H3=1 )
|
LIMITATION:
The ‘Hadkar Equation’ to predict surface
tension of organic binary liquid mixtures is applicable only if there is weak
interaction between the two liquids such as London force of attraction between
the molecules of the liquids. For example, the surface tension values
calculated for the mixture of ethyl alcohol and water using ‘Hadkar Equation’ and the practical values differ
significantly because of strong interaction between the molecules of the two
liquids due to formation of hydrogen bond. The surface tension values obtained
for the liquid mixtures having weak interactions reported in the tables 2-5,
were in good agreement (within 3-4%) with the calculated values using ‘Hadkar Equation’.
CONCLUSION:
The ‘Hadkar Equation’ proposed for
predicting the surface tension of organic binary liquid mixtures was found to
give results close to the reported literature values. The predicted values of
surface tension are in close agreement (within 3-4%) with the reported
literature values.
ACKNOWLEDGEMENTS:
The authors wish to thank the Trustees Mr. Chhagan
Bhujbal, Mrs. Meenatai Bhubjbal, Mr. Sameer Bhujbal, Mr. Pankaj Bhujbal for the laboratory
facilities provided to complete the work.
REFERENCES:
1.
A. Bahl, B. Bahl, G. Tuli “Essentials of Physical Chemistry” S. Chand and company Ltd, New Delhi, 2009, Pg 423.
2.
http://zzm.umcs.lublin.pl/Wyklad/FGF-Ang/2A.F.G.F.%20Surface%20tension.pdf
3.
Handbook
of detergents, Part A, Edi Guy Broze, Marcel Dekker,
INC. New York. Basel, 1998, Pg 51.
4.
A.
Martin, P. Bustamante, A.H.C. Chun “physical Pharmacy” Indian Edition, Lippincott
Williams and Wilkins, 2005, Pg375
5.
M.L.L.
Paredes, J.M.T. Santos and E.S. Bezerra
Latin American Applied Research 2012 42: Pg 389-395
6.
Hike Kahl, Tinowadewitz and JochemWinkel Mann J. Chem. Engg.
Data, 2003, 48(3) Pp 580-586.
7.
Remington
“The Science and Practice of Pharmacy” 22nd Edition, Philadelphia
College of Pharmacy 2013, Pg 442.
8.
Finholt,
Solvang S. “Effect of tablet processing and formulation factors on dissolution
rate of the active ingredients in human gastric juice”. J.Pharm
Sciog 1970, 59(1) Pg 49 to 52
9.
J.R.
Block and R.B. Bird, Am. Inst.Chem.Engg.J.1, 74 (1965).
10. J. Glinski, J.
Chem.Phy.Vol.18 p.2301-2307, 2003.
11. Joel Escobedo and Ali Mansoori
AICHE Journal Vol 44, No.10, Pp 2324-2332, (1998).
12. J. Escobedo and G. Ali Mansoori
AIChE.J. 42(5), 1425. 19.96.
13. ibid
11.
ABBREVIATION:
Abbreviation used in the Tables no. 1 to 5
Binary liquid mixture of A and B
A= Surface tension of liquid A at 25 ± 1 degrees Celsius in
dynes/ cm.
B= Surface tension of liquid B at 25 ± 1 degrees Celsius in
dynes/ cm.
A= Mole fraction of liquid A in the binary mixture of A and B.
B= Mole fraction of liquid B in the binary mixture of A and B.
Note: A =
(1 - B )
A= Dielectric constant of liquid A at 25 degrees Celsius.
B= Dielectric constant of liquid B at 25 degrees Celsius.
m (Theoretical)= surface tension of the mixture using
equation 1.
m (Experimental)
= surface tension
determined using drop weight method.
m (Reported)= Surface tension of liquid mixture
reported in Ref No.11
mixH= Surface tension of liquid mixture using Hadkar equation (equation 4) for prediction of the surface
tension of the binary mixture.
Hadkar equation for the surface tension of a
binary liquid mixture is
mixH
= (AA+BB).H3 -- - - (4),
where, H3 is
the Hadkar Factor given by
H3=
(A/B) F and F= ¼ (B/A) and A <B.
It may be noted that for pure liquid A or B, the Hadkar Factor H3=1
Note:
(1)H3= (A/B) F and F= ¼ (B/A) and A <B.
(2) Pure liquid A may be considered as mixture of liquid A and
liquid A and A =B.
The value of H3 = 1 for pure liquid A or pure liquid B.
Asian J. Pharm.
Tech. 2015; Vol. 5: Issue 2, Pg 107-114