# Solid-liquid Equilibrium via EOS

#### Farshad

Hi guys
I want to model the adsorption of asphaltenes on nanoparticles from a thermodynamic equilibrium solution ( this is my thesis ). from this way, I want to show how much asphaltene is adsorbed on nanoparticles at different temperatures and pressures (without using of isotherms of adsorption) .
The problem is that asphaltenes from a solution such as toluene want to be adsorbed onto the surface of the nanoparticles. Considering that in the state of equilibrium, the chemical potential of solids and liquid phases , or in other words, the two-phase fugacities are equal. instead of the fugacity of the asphaltene in the liquid phase (asphaltene fugacity in toluene solution) and the solid phase (asphaltene fugacity on nanoparticles), What equations should i embedding that including fugacity coefficient and the asphaltenes mole fraction in two phases?

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#### Bystander

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(without using of isotherms of adsorption) .
You simply can not do that.

#### Farshad

You simply can not do that.
What do you mean by simply can not? what i have to do? Do you know what equations should I make instead of fugacity of asphaltenes on solid and in solution?

#### Chestermiller

Mentor
You want an equation for the fugacity of asphaltine (a) in a solution of toluene and (b) when adsorbed onto the surface of a nanoparticle, correct?

#### Farshad

You want an equation for the fugacity of asphaltine (a) in a solution of toluene and (b) when adsorbed onto the surface of a nanoparticle, correct?
Yes, for a better understanding, these images show what i need

For the fugacity of asphaltenes in the solid and liquid phase, i dont know what equations of state can be used to include fugacity coefficients?
after doing this, i use the equation that encluding Z, instead of fugacity coefficient. and finally from the equality of first and second sides, i can calculate xA ( amount of adsorbed asphaltene on nanoparticles) at constant T,P .

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#### Chestermiller

Mentor
If the solution of asphaltene in toluene can be approximated as an ideal liquid solution, then the fugacity of the alphaltene in the toluene liquid solution is straightforward. Can it be approximated as an ideal solution? The fugacity of the adsorbed asphaltene on the nanoparticles is more complicated. My background in statistical thermodynamics is very limited, but I know that this would be what one would use to develop the required relationship. Have you had a course in statistical thermodynamics? Sorry I can't offer any more help than this.

#### Farshad

If the solution of asphaltene in toluene can be approximated as an ideal liquid solution, then the fugacity of the alphaltene in the toluene liquid solution is straightforward. Can it be approximated as an ideal solution? The fugacity of the adsorbed asphaltene on the nanoparticles is more complicated. My background in statistical thermodynamics is very limited, but I know that this would be what one would use to develop the required relationship. Have you had a course in statistical thermodynamics? Sorry I can't offer any more help than this.
I think yes, solution is ideal. if its ideal,what is the fugacity of asphaltene in solution equal to? ( i mean which equation should I use? ), and why determining fugacity of asphaltene on nanoparticles is complicated?

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