Fluid Phase Equilibria 157 Ž1999. 169–180
Molecular simulation of the phase behaviour of ternary fluid
mixtures: the effect of a third component on vapour–liquid and
liquid–liquid coexistence
Richard J. Sadus
)
Computer Simulation and Physical Applications Group, School of Information Technology, Swinburne UniÕersity of
Technology, P.O. Box 218, Hawthorn, Victoria 3122, Australia
Received 10 November 1998; accepted 27 January 1999
Abstract
The Gibbs ensemble algorithm is implemented to determine the vapour–liquid and liquid–liquid phase
coexistence of dilute ternary fluid mixtures interacting via a Lennard–Jones potential. Calculations are reported
for mixtures with a third component characterised by different intermolecular potential energy parameters.
Comparison with binary mixture data indicates that the choice of energy parameter for the third component
affects the composition range of vapour–liquid substantially. The addition of a third component lowers the
energy of liquid phase while slightly increasing the energy of the vapour phase. q 1999 Elsevier Science B.V.
All rights reserved.
Keywords: Theory; Molecular simulation; Vapour–liquid equilibria; Liquid–liquid equilibria; Ternary mixtures
1. Introduction
Historically, both experimental and theoretical studies of the phase behaviour of multicomponent
mixtures have concentrated mainly on binary mixtures. Considerable progress has been achieved in
understanding the phase behaviour of binary mixtures w1x. The phase behaviour of many mixtures has
been investigated up to high temperatures and pressures w2x and the observed critical behaviour has
been used to formulate a simple classification scheme w3,4x. A variety of theoretically based equations
)
Tel.: q61-3-9214-8773; fax: q61-3-9819-0823; e-mail: [email protected]
0378-3812r99r$ - see front matter q 1999 Elsevier Science B.V. All rights reserved.
PII: S 0 3 7 8 - 3 8 1 2 Ž 9 9 . 0 0 0 4 9 - 7
170
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
of state have been proposed w5x to model various aspects of phase equilibria and many molecular
simulation studies have been reported w6x using the Gibbs ensemble approach w7x. Binary mixture data
can provide valuable insights into the phase behaviour of multicomponent fluids but there is evidence
w1x that ternary mixtures may provide a better description of multicomponent equilibria in general.
In comparison to the extensive work on binary mixture equilibria, relatively little work has been
reported for ternary and higher multicomponent equilibria, particularly at high pressures and temperatures. The addition of a third component can have a profound effect on the phase equilibria of a fluid
mixture. Both upper and lower critical solution temperature behaviour is exhibited by some ternary
mixtures w8x and there are many examples w8x of ternary mixtures that exhibit closed-loop miscibility
curves. Various different types of tri-critical and other higher order critical phenomena can be
expected w9x in a ternary mixture. The addition of a small quantity of salt can shift w10x the phase
envelop substantially. Similarly, a small quantity of a surfactant can improve dramatically w11x the
mutual solubility of oil an water which under normal conditions of temperature and pressure are only
sparingly miscible. These phenomena can be qualitatively attributed to the different types of
interaction between unlike molecules in the ternary mixture. In a ternary mixture there are three
distinct types of unlike pair-interactions whereas there is only one unlike pair-interaction in a binary
mixture. Therefore, the phase behaviour of ternary mixtures is likely to be more indicative of
multicomponent fluid phase equilibria than phenomena exhibited by binary mixtures.
The Gibbs ensemble simulation algorithm w7x which has been employed extensively for binary
mixtures can also be employed to study ternary mixtures. An advantage of molecular simulation over
conventional calculations is that it enables us to link unambiguously the predicted behaviour to the
molecular properties. The effect on phase coexistence of various contribution to molecular interactions can be isolated and studied systematically using a suitable intermolecular potential. However,
few applications to ternary mixtures of either the Gibbs ensemble or other molecular simulation
methods have been reported. Panagiotopolous w12,13x reported simulations of the phase coexistence of
water, acetone and supercritical carbon dioxide. Tsang et al. w14,15x calculated phase equilibria of
some ternary Lennard–Jones mixtures and they compared the results to the predictions of the
one-fluid theory. Recently, de Miguel and Telo da Gama w16x have reported a simulation study of
ternary mixtures containing oil, water and a surfactant. It should be noted that the complete
experimental characterisation of a ternary mixture requires considerable effort. In it is in this context
that molecular simulation has a valuable role in elucidating the phase behaviour of ternary mixtures.
Unlike other theoretical methods such as equations of state, the results of molecular simulation are
exact and increasingly reliable.
The aim of this work is to use molecular simulation to investigate quantitatively the effect of a
small quantity of a third component on the vapour–liquid and liquid–liquid equilibria of fluid
mixtures. The Gibbs ensemble w7x is used to calculate the vapour–liquid and liquid–liquid phase
coexistence of ternary Lennard–Jones mixtures with components of different intermolecular interactions. Simulation data of this kind may have a valuable role in quantifying the effect of a third
component on phase behaviour specifically in terms of intermolecular interactions. In particular, they
enable us to examine the role of different unlike interactions on the observed phase equilibria.
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
171
2. Theory
2.1. Intermolecular potential
The Lennard–Jones potential was used to calculate interactions between pairs of molecules
separated by a distance ri j
u Ž ij . s 4´ i j
si j
12
si j
ž / ž /
ri j
y
ri j
6
Ž1.
where the ´ and s parameters are characteristic of the strength of intermolecular interaction and
molecular size, respectively.
2.2. Potential parameters
The calculations were performed in reduced units relative to component 1. Two different sets of
parameters for components 1 and 2 were used to obtain vapour–liquid and liquid–liquid equilibria.
For vapour–liquid equilibria Žmixtures I to IV. the Lennard–Jones parameters were ´ 22r´ 11 s 0.5,
s 22rs 11 s 1, ´ 12 s 0.7071 and s 12 s 1. For liquid–liquid equilibria Ž mixtures V to VIII. the
Lennard–Jones parameters were ´ 22r´ 11 s 0.75, s 22rs 11 s 0.95, ´ 12 s 0.6062 and s 12 s 0.975.
These combinations of parameters was chosen because earlier work w17,18x indicated that they are
associated with vapour–liquid and liquid–liquid equilibria in a binary mixture of Lennard–Jones
molecules. The contribution of interactions of molecules component 1 with molecules of component 3
and of molecules component 2 with molecules of component 3 were obtained from the following
combining rules.
(
´i j s ´i j ´j j
si j s
si j q sj j
2
Ž2.
Ž3.
2.3. Simulation details
The NPT-Gibbs ensemble w7x was used to simulate the coexistence of two liquid phases. A total of
200 molecules were partitioned between two boxes to simulate the two coexisting phases. To simulate
a dilute ternary mixture, only 10 of the 200 molecules were of component 3 with the remaining
molecules being either of component 1 or 2. The temperature of the entire system was held constant
and surface effects were avoided by placing each box at the centre of a periodic array of identical
boxes. Equilibrium was achieved by attempting molecular displacements Ž for internal equilibrium. ,
volume fluctuations Žfor mechanical equilibrium. and particle interchanges between the boxes Ž for
material equilibrium. .
The simulations were performed in cycles with each cycle consisting of 200 attempted displacements, a single volume fluctuation, and 2000 interchange attempts. The maximum molecular
displacement and volume changes were adjusted to obtain, where possible, a 50% acceptance rate for
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
172
the attempted move. It should be noted a lower acceptance rate is sometimes more efficient w19x.
Ensemble averages were accumulated only after the system had reached equilibrium. The equilibration period was typically 10,000 cycles and a further 20,000 cycles was used to accumulate the
averages. The calculations were truncated at intermolecular separations greater than half the box
length, and appropriate long-range corrections w20x were used to obtain the full contribution of pair
interactions to energy and pressure. A typical run required approximately 7 CPU h on a Cray
YMP-EL and 2 CPU h on a Fujitsu VPP300 supercomputer.
3. Results and discussion
The vapour–liquid Žat T U s 0.9. and liquid–liquid Žat P U s 1. coexistence data obtained from
molecular simulation data for different ternary mixtures are summarised in Tables 1 and 2,
respectively. The normal convention was adopted for the reduced density Ž r U s rs 3 ., temperature
Table 1
Gibbs ensemble simulations for the vapour–liquid equilibria of ternary mixtures at T U s 0.9 a
PU
Vapour phase
r
U
Liquid phase
rU
x1
x2
y EU
0.50Ž6.
0.58Ž5.
0.58Ž5.
0.63Ž7.
0.69Ž8.
0.69Ž8.
0.723Ž20.
0.718Ž22.
0.720Ž20.
0.705Ž26.
0.708Ž30.
0.685Ž18.
0.700Ž31.
0.684Ž35.
0.687Ž27.
0.656Ž49.
0.654Ž52.
0.611Ž37.
0.197Ž38.
0.215Ž45.
0.210Ž35.
0.250Ž56.
0.251Ž65.
0.304Ž43.
4.64Ž25.
4.55Ž29.
4.57Ž25.
4.35Ž32.
4.38Ž40.
4.06Ž24.
0.739Ž12.
0.755Ž20.
0.768Ž16.
0.775Ž13.
0.50Ž4.
0.52Ž6.
0.62Ž6.
0.68Ž6.
0.719Ž9.
0.705Ž26.
0.693Ž21.
0.671Ž14.
0.756Ž17.
0.732Ž45.
0.697Ž35.
0.648Ž22.
0.182Ž16.
0.210Ž48.
0.247Ž37.
0.299Ž24.
4.51Ž11.
4.34Ž30.
4.15Ž24.
3.87Ž14.
0.258Ž23.
0.230Ž19.
0.214Ž20.
0.199Ž14.
0.243Ž27.
0.679Ž20.
0.701Ž17.
0.709Ž15.
0.718Ž9.
0.685Ž24.
0.45Ž5.
0.50Ž6.
0.56Ž5.
0.61Ž7.
0.90Ž11.
0.723Ž9.
0.709Ž10.
0.683Ž15.
0.670Ž15.
0.699Ž19.
0.833Ž21.
0.790Ž17.
0.728Ž29.
0.694Ž25.
0.733Ž35.
0.161Ž21.
0.204Ž17.
0.264Ž28.
0.296Ž24.
0.258Ž33.
4.60Ž12.
4.37Ž11.
4.03Ž17.
3.86Ž16.
4.14Ž22.
0.233Ž17.
0.226Ž10.
0.216Ž11.
0.225Ž15.
0.208Ž14.
0.210Ž16.
0.198Ž20.
0.663Ž13.
0.673Ž7.
0.678Ž9.
0.701Ž10.
0.680Ž9.
0.704Ž8.
0.703Ž14.
0.39Ž3.
0.50Ž3.
0.53Ž5.
0.58Ž4.
0.56Ž5.
0.69Ž6.
0.74Ž12.
0.728Ž13.
0.718Ž5.
0.717Ž9.
0.712Ž14.
0.703Ž14.
0.686Ž23.
0.660Ž16.
0.850Ž18.
0.815Ž15.
0.791Ž24.
0.779Ž22.
0.764Ž28.
0.712Ž39.
0.658Ž16.
0.145Ž18.
0.179Ž15.
0.203Ž24.
0.216Ž22.
0.230Ž27.
0.282Ž39.
0.334Ž23.
4.69Ž14.
4.52Ž7.
4.44Ž13.
4.37Ž16.
4.26Ž17.
4.01Ž25.
3.70Ž15.
x1
x2
yE
Mixture I (´ 33 s 1.25)
0.075
0.122Ž13.
0.08
0.131Ž10.
0.085
0.130Ž11.
0.09
0.143Ž16.
0.092
0.157Ž19.
0.098
0.165Ž21.
0.202Ž17.
0.204Ž24.
0.211Ž22.
0.184Ž20.
0.203Ž28.
0.180Ž21.
0.787Ž17.
0.784Ž25.
0.777Ž22.
0.794Ž22.
0.785Ž29.
0.809Ž11.
Mixture II (´ 33 s 0.95)
0.07
0.107Ž9.
0.08
0.114Ž13.
0.085
0.139Ž14.
0.09
0.154Ž13.
0.237Ž12.
0.222Ž19.
0.210Ž15.
0.204Ž12.
Mixture III (´ 33 s 0.25)
0.07
0.099Ž7.
0.08
0.116Ž15.
0.09
0.137Ž13.
0.1
0.150Ž16.
0.11
0.211Ž22.
Mixture IV (´ 33 s 0.1)
0.07
0.093Ž6.
0.08
0.111Ž7.
0.09
0.134Ž13.
0.095
0.143Ž7.
0.1
0.147Ž12.
0.11
0.175Ž13.
0.12
0.198Ž20.
a
U
Values in brackets represent the uncertainty in the last digit.
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
173
Table 2
Gibbs ensemble simulations for the liquid–liquid equilibria of ternary mixtures at P U s1a
TU
Phase A
Phase B
rU
x1
x2
y EU
3.66Ž4.
3.64Ž6.
3.58Ž4.
3.56Ž5.
3.55Ž3.
3.52Ž4.
0.820Ž8.
0.819Ž6.
0.809Ž7.
0.807Ž7.
0.804Ž6.
0.790Ž7.
0.852Ž31.
0.846Ž16.
0.830Ž25.
0.824Ž30.
0.813Ž37.
0.730Ž80.
0.104Ž31.
0.109Ž16.
0.125Ž26.
0.129Ž29.
0.143Ž36.
0.226Ž83.
5.30Ž20.
5.26Ž11.
5.12Ž17.
5.09Ž16.
4.99Ž16.
4.60Ž32.
0.851Ž32.
0.845Ž37.
0.780Ž32.
0.823Ž25.
0.789Ž41.
0.803Ž47.
3.60Ž3.
3.58Ž4.
3.53Ž4.
3.50Ž4.
3.45Ž4.
3.41Ž4.
0.813Ž4.
0.809Ž6.
0.804Ž5.
0.799Ž6.
0.792Ž5.
0.791Ž9.
0.833Ž27.
0.833Ž45.
0.810Ž29.
0.835Ž28.
0.786Ž19.
0.742Ž93.
0.126Ž26.
0.126Ž41.
0.132Ž26.
0.125Ž27.
0.174Ž20.
0.219Ž90.
5.07Ž14.
5.04Ž22.
4.98Ž13.
4.96Ž15.
4.72Ž10.
4.52Ž36.
Mixture VII (´ 33 s 0.25)
0.95
0.796Ž5.
0.120Ž16.
0.96
0.793Ž8.
0.115Ž22.
0.98
0.792Ž10.
0.119Ž23.
1.0
0.774Ž10.
0.191Ž29.
1.02
0.762Ž5.
0.221Ž43.
0.798Ž17.
0.802Ž22.
0.826Ž22.
0.756Ž28.
0.727Ž42.
3.16Ž3.
3.14Ž4.
3.20Ž5.
3.13Ž4.
3.10Ž5.
0.802Ž6.
0.800Ž4.
0.795Ž7.
0.787Ž4.
0.775Ž5.
0.830Ž24.
0.831Ž15.
0.832Ž36.
0.826Ž26.
0.779Ž45.
0.129Ž22.
0.129Ž13.
0.139Ž33.
0.147Ž24.
0.191Ž43.
4.77Ž13.
4.76Ž8.
4.74Ž19.
4.66Ž12.
4.40Ž19.
Mixture VIII (´ 33 s 0.1)
0.96
0.793Ž7.
0.109Ž27.
0.98
0.780Ž10.
0.137Ž29.
0.99
0.779Ž11.
0.149Ž35.
1.01
0.764Ž11.
0.183Ž46.
1.03
0.758Ž7.
0.189Ž45.
0.829Ž26.
0.803Ž2.
0.792Ž34.
0.761Ž47.
0.756Ž42.
3.09Ž3.
3.05Ž5.
3.04Ž5.
3.00Ž5.
3.00Ž7.
0.807Ž13.
0.792Ž10.
0.790Ž4.
0.777Ž7.
0.762Ž10.
0.874Ž13.
0.828Ž47.
0.818Ž33.
0.806Ž57.
0.704Ž85.
0.105Ž12.
0.148Ž42.
0.149Ž35.
0.168Ž51.
0.263Ž80.
4.97Ž9.
4.67Ž27.
4.61Ž16.
4.48Ž28.
4.01
r
U
x1
x2
yE
Mixture V (´ 33 s 1.25)
0.95
0.832Ž9.
0.96
0.829Ž12.
0.97
0.818Ž7.
0.98
0.816Ž7.
0.99
0.804Ž8.
1.0
0.805Ž9.
0.115Ž39.
0.114Ž29.
0.106Ž18.
0.115Ž19.
0.153Ž39.
0.146Ž47.
0.850Ž40.
0.851Ž31.
0.859Ž20.
0.852Ž18.
0.810Ž39.
0.820Ž47.
Mixture VI (´ 33 s 0.95)
0.95
0.829Ž8.
0.96
0.825Ž10.
0.98
0.805Ž7.
0.99
0.807Ž9.
1.01
0.797Ž9.
1.02
0.791Ž9.
0.109Ž31.
0.116Ž34.
0.157Ž32.
0.137Ž24.
0.170Ž41.
0.158Ž43.
a
U
Values in brackets represent the uncertainty in the last digit.
Ž T U s kTr´ ., energy Ž EU s Er´ . and pressure Ž P U s Ps 3r´ . . To check that material equilibrium
had been achieved, the chemical potential Ž not recorded in Tables 1 and 2. was determined from the
equation proposed by Smit and Frenkel w21x. In Tables 1 and 2, the different mixtures are identified
by different values of ´ 33.
The vapour–liquid equilibria exhibited by dilute ternary Lennard–Jones mixtures at T U s 0.9 are
compared with the vapour–liquid equilibria reported w16x for the binary Lennard–Jones mixture in
Fig. 1. Dilute mixtures Ž typically 5 mol% of component 3. were chosen to specifically observe the
effect of a third component on binary phase equilibria. In all cases s 33 s 1, consequently all three
component molecules are of identical size. A variety of values of ´ 33 were used ranging from 0.1 to
1.25. The value of ´ 33 also partly determines the values of ´ 13 and ´ 23 obtained from the combining
rule ŽEq. Ž 2... When ´ 33 s 0.95 or 1.25, the liquid and vapour coexistence curves of the ternary
mixture are shifted to compositions lower in component 1 than is apparent in the binary mixture. The
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
174
Fig. 1. Comparison of the vapour–liquid phase envelope of a binary Lennard–Jones mixture Žv . w16x at T U s 0.9 with the
vapour–liquid resulting from the addition of a third component with ´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že. and 0.1 Ž`.. The
lines are for guidance only.
critical pressure of these mixtures is probably substantially lower than the critical temperature of the
binary mixture. The remaining ternary mixtures have values of ´ 33 Ž0.25 and 0.1. that are
substantially smaller than either ´ 11 or ´ 22 . In these cases vapour–liquid equilibria is observed for a
larger range of x 1 at the expense of x 2 . Vapour–liquid equilibria for the ternary mixtures is also
observed at higher pressures than in the binary mixture.
The effect of the third component on the energy of the coexisting liquid and vapour phases is
illustrated in Fig. 2. The comparison with binary mixture data presented in Fig. 2 indicates that the
addition of a third component slightly increases the energy of the vapour phase while lowering
substantially the energy of the liquid phase. This change in energy is particularly significant at higher
pressures.
It is of interest to consider the relative distribution of the third component in the vapour and liquid
phases ŽFig. 3.. When ´ 33 s 0.95, the third component favours the liquid phase whereas in all other
cases it is found overwhelmingly in the vapour phase. It is evident from Fig. 3 that the distribution of
the third component between the vapour and liquid phases is very sensitive to the value of ´ 33.
The coexistence composition data obtained from molecular simulation enables us to determine the
mixture values of ´ and s using the one-fluid mixture prescriptions, i.e.,
N
´ mix smix s
N
Ý Ý x i x j ´ i j si j
Ž4.
js1 is1
N
smix s
N
Ý Ý x i x j si j
Ž5.
js1 is1
These mixture values are of interest because they take account of all the pair interactions in the
mixture. The value of ´ mix for the various ternary mixtures is compared with values obtained for the
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
175
Fig. 2. Comparison of the energy associated with the vapour–liquid phase envelope of a binary Lennard–Jones mixture Žv .
w16x at T U s 0.9 with the energy resulting from the addition of a third component with ´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že.
and 0.1 Ž`.. The lines are for guidance only.
binary mixture in Fig. 4. The comparison shows that the addition of third component results in a
substantial reduction of ´ mix in the vapour phase whereas the effect on liquid phase values is
considerably less.
Fig. 3. The relative distribution of component 3 in the vapour and liquid phases as a function of pressure when ´ 33 s1.25
Ž=., 0.95 Ž^., 0.25 Že. and 0.1 Ž`.. The lines are for guidance only.
176
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
Fig. 4. Comparison of ´ mix along the vapour–liquid coexistence curve for the binary mixture and ternary mixtures with
´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že. and 0.1 Ž`.. The lines are for guidance only.
The liquid–liquid equilibria at P U s 1 exhibited by ternary mixtures characterised by various ´ 33
values and s 33 s 1 is compared with data w17x for the binary mixture in Fig. 5. Irrespective of the
Fig. 5. Comparison of the liquid–liquid phase envelope of a binary Lennard–Jones mixture Žv . w17x at P U s 0.9 with the
liquid–liquid equilibria resulting from the addition of a third component with ´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že., and 0.1
Ž`..
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
177
Fig. 6. Comparison of the energy associated with the liquid–liquid phase equilibria of a binary Lennard–Jones mixture Žv .
w17x at P U s1 with the energy resulting from the addition of a third component with ´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že.
and 0.1 Ž`.. The lines are for guidance only.
value of ´ 33 , the ternary coexistence curves are found inside the coexistence curve of the binary
mixture. The addition of a third component does not significantly alter either the density or the
composition of the coexisting phases.
Fig. 7. The relative distribution of component 3 in liquid phases A and B as a function of temperature when ´ 33 s1.25 Ž=.,
0.95 Ž^., 0.25 Že., and 0.1 Ž`.. The lines are for guidance only.
178
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
Fig. 8. Comparison of ´mix along the liquid–liquid coexistence curve for the binary mixture and ternary mixtures with
´ 33 s1.25 Ž=., 0.95 Ž^., 0.25 Že., and 0.1 Ž`.. The lines are for guidance only.
Fig. 6 illustrates the effect of the third component of the energy of the liquid phases. When
´ 33 s 0.1 or 0.25, the energy of the lighter, x 1-poor phase Žphase A. is increased while the energy of
the heavier, x 1-rich phase Žphase B. is increased by the addition of the third component. However,
when ´ 33 s 0.95 or 1.25, the addition of the third component decreases slightly the energy of both
phase A and phase B. This is in contrast to the situation for vapour–liquid equilibria ŽFig. 2. for
which the energy of the liquid phase decreases and the energy of the vapour phase increases
irrespective of the nature of the third component.
The distribution of the third component in the two liquid phases is illustrated in Fig. 7. It should be
noted that the difference in the distribution is considerably less pronounced than in the case of
vapour–liquid equilibria. This is probably a consequence of the similarity of both energy and density
in the two liquid phases compared with the large differences in these properties between vapour and
liquid phases. When ´ 33 s 0.95 or 1.25 the third component is almost distributed equally between the
liquid phase irrespective of temperature. In contrast, there is a considerably higher concentration of
the third component in phase A when ´ 33 s 0.1 or 0.25.
The value of ´ mix calculated for binary and ternary mixtures along the liquid–liquid coexistence
curve is illustrated in Fig. 8. There is a systematic change in ´ mix with respect to ´ 33. Values of
´ 33 s 1.25 or 0.95 result in an increase in ´mix whereas the remaining values of ´ 33 are associated
with ternary mixtures of lower ´ mix at all compositions along the liquid–liquid coexistence curve.
4. Conclusions
The calculations reported here serve to quantify the effect of the addition on a third component on
both the vapour–liquid and liquid–liquid equilibria of fluid mixtures. It is apparent that a small
R.J. Sadusr Fluid Phase Equilibria 157 (1999) 169–180
179
quantity of a third component with dissimilar properties to either of the other components can have a
substantial influence on the observed phase behaviour. Comparison with binary mixture data indicates
that the choice of energy parameters of the third component affects the composition range of
vapour–liquid substantially. The addition of a third component lowers the energy of liquid phase
while slightly increasing the energy of the vapour phase.
5. List of symbols
E
k
P
r
T
u
xi
Configurational energy
Boltzmann’s constant
Pressure
Intermolecular distance
Temperature
Intermolecular potential
Mole fraction of component i
Greek letters
´
Lennard–Jones energy parameter
s
Lennard–Jones distance parameter
r
Number density
Subscripts and superscripts
Reduced property
i, j
Molecule i or j
U
Acknowledgements
The simulations were performed on the Swinburne University of Technology’s Cray YMP-EL
computer and the Australian National University Supercomputer Centre’s Fujitsu VPP300 supercomputer.
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