Nucleation Rates Of Ethanol And Methanol Using SAFT

And PC-SAFT EOSs

Fawaz HrahshehAdvisor ::Dr. Abdalla ObeidatCo-advisor ::Dr. H. Al-Ghanim

Department of PhysicsJUST

Outline

● Metastability and nucleation● Work of formation and versions● Temperature and saturation dependence

of classical theories● Conclusions

• 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

Metastable and unstable regions for the van der Waals

fluid

• 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

Kinds & Definition Of Nucleation

-Homogeneous Nucleation-Hetrogeneous Nucleation

-The process of formation of the critical size cluster (droplet) which has the ability to

grow spontaneously.

The work of formation-The work of Formation is the work

which is needed To form the critical size droplet

-The work of formation consists from two terms: the bulk (volumetric) term

and the surface term.

APPVWvl

)(

The work of formation composite by two terms.

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 Ratio)

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 skTw l

Pressure vs density isotherm

Nucleation rate is given by

/KTWCL eJJ

*

0

where

2

0

2

KTP

mJ

l

SAFT & PC-SAFT Theories

● SAFT…Statistical Associating Fluid Theory

● PC-SAFT….Perturbed-Chain Statistical

Associating Fluid Theory

SAFT and PC-SAFT EOS

RTA

RTA

RTA

RTA

RTA

RTA assocdischainhsideal

●A is the reduced free helmholtz energy●The association term is just for polar

fluids

Binodal points of ethanol And methanolusing SAFT and PC-SAFT

Gibbs’s formula improves classical nucleation rates for METHANOL

based on SAFT EOS.

Gibbs’s formula improves classical nucleation rates for ETHANOL

based on PC-SAFT EOS.

Conclusions

• P-form improves the T and S dependence for methanol and ethanol at high temperature..• Quantitatively, P-form improves the results

by than S-form for methanol and ethanol.

42 1010

Thank You