1. Applying Gibbs theory on SAFT and PC-SAFT EOS’s to calculate nucleation rates of Ethanol and Methanol. Fawaz Hrahsheh Dr. Abdalla Obeidat Department of Physics JUST

2. EXTENSIONS OF SAFT & PC-SAFT ● SAFT …Statistical Associating Fluid Theory ● PC-SAFT …. Perturbed-Chain Statistical Associating Fluid Theory

3. SAFT and PC-SAFT EOS

4. Outline ● Metastability and nucleation ● Temperature dependence of classical theories ● Conclusions

5. 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. SPINODAL LINE Schematic pressure – temperature phase diagram for a pure substance

6. The binodal curve (solid dome)separates one-phase and two- phase states T C = 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

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

9. 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 =P v /P ve (Supersaturation)

10. Pressure vs density isotherm

11. Nucleation rate is given by where

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

13. Conclusions Pressure version of W resulted in improvements over the other versions for H 2 O. The first version of classical theory with exact EOS’s used to predict the T dependence.

14. Thank You