Applying Gibbs theory on SAFT and PC-SAFT EOS’s to calculate nucleation rates of Ethanol and Methanol.

Fawaz HrahshehDr. Abdalla Obeidat

Department of PhysicsJUST

EXTENSIONS OF SAFT & PC-SAFT

● SAFT…Statistical Associating Fluid Theory

● PC-SAFT….Perturbed-Chain Statistical

Associating Fluid Theory

SAFT and PC-SAFT EOS

assocdisphc ZZZZ 1

Outline

● Metastability and nucleation● Temperature dependence of

classical theories● Conclusions

• Solid black lines represent points of equilibrium two-phase coexistence

• c is the critical point

• b is the triple point

• When, say, gas is forced to cross lines ab or bc it is no longer the thermodynamically stable phase.

• The transition to the new stable phase is not instantaneous.

SPINODALLINE

Schematic pressure – temperature phase diagram for a pure substance

• The binodal curve (solid dome)separates one-phase and two-phase states

• TC = critical temperature

• The spinodal curve (dashed dome) separates metastable and unstable states

• One true horizontal isotherm is shown

• Adapted from Davis (1996)

gas

liquid

fluid

critical point

binodal spinodal

Metastable and unstable regions for the van der Waals fluid

Classical nucleation rates are too low at low T; too high at high T.

Classical nucleation rates are too low at low T; too high at high T.

5 10 15 20 25106

107

108

109

1010

260 K 250 K

240 K

230 K

H2O Expt

S-form

T=220 K

J (c

m-3 s

-1)

S

Three Versions of Classical Theory

●Gibbs’s exact formula: ● version 1: use bulk surface tension for

● Version 2: liquid droplet is incompressible,– and ● Version 3: the vapor is an ideal gas– and

–S =Pv /Pve (Supersaturation)

W p ( / ) / ( )1 6 3 3 2

p p pre f vap

p l

kT Sln

2

2)/()3/16(

lw

)ln/()3/16(3

skTwl

Pressure vs density isotherm

Nucleation rate is given by

/KTWCL eJJ

*

0

where

2

0

2

KT

P

mJ m

Gibbs’s formula improves classical nucleation rates for H2O based on IAPWS-95.

Conclusions

• Pressure version of W resulted in improvements over the other versions for H2O.

• The first version of classical theory with exact EOS’s used to predict the T dependence.

Thank You