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Liquid-Liquid Equilibrium

In thermodynamics and chemical engineering, liquid–liquid equilibrium (LLE), also known as phase separation, is a type of phase equilibrium in which two partially miscible liquids are placed in contact with one another and allowed to come to thermal, mechanical, and chemical equilibrium, resulting in two coexisting liquid phases of different chemical composition.

Thermodynamic description of liquid–liquid equilibrium

Thermodynamic equations are useful in describing liquid—liquid equilibrium. The most common way to express LLE conditions is using fugacity:

$f_{i}^{\alpha }=f_{i}^{\beta }$

where $f_{i}^{\alpha }$ and $f_{i}^{\beta }$ are the fugacities of component $i$ in phase α and β, respectively. Eliminating fugacities in favor of activity coefficients gives:

$x_{i}^{\alpha }\gamma _{i}^{\alpha }=x_{i}^{\beta }\gamma _{i}^{\beta }$

where $x_{i}^{\alpha }$ and $x_{i}^{\beta }$ are the mole fractions of component $i$ in phase α and β and $\gamma _{i}^{\alpha }$ and $\gamma _{i}^{\beta }$ are the activity coefficients of component $i$ in phase α and β, respectively.

Liquid-liquid equilibrium diagrams

Binary LLE phase diagrams

See also

• Phase separation
• Liquid–liquid extraction
• Multiphasic liquid