Temperature profile in a liquid-vapour interface near the critical point

Area of Science:

• Thermodynamics
• Fluid Dynamics
• Materials Science

Background:

• Existing models for inhomogeneous fluids, like Cahn-Hilliard, primarily consider mass-density gradients.
• Realistic molecular theories indicate entropy and temperature variations at liquid-vapor interfaces differ from bulk phases.
• A need exists for more comprehensive models of thermocapillary fluids accounting for multiple density expansions.

Purpose of the Study:

• To develop a more realistic model for thermocapillary fluids by incorporating energy, mass, and entropy density expansions.
• To modify the non-convex state law for inhomogeneous fluids using density gradient terms.
• To compare the behavior of liquid-vapor interfaces in the new model with the established Cahn-Hilliard model.

Main Methods:

• Expansion of thermodynamic state laws with respect to energy, mass, and entropy densities.
• Inclusion of terms accounting for density gradients in the modified state law.
• Application of a rescaling process near the critical point to analyze interface behavior.

Main Results:

• A modified state law for thermocapillary fluids is proposed, incorporating energy and entropy density gradients.
• The study demonstrates that liquid-vapor interfaces exhibit behavior consistent with the Cahn-Hilliard model near the critical point.
• The proposed model offers a more realistic description of inhomogeneous fluids compared to models based solely on mass-density gradients.

Conclusions:

• The developed thermocapillary fluid model provides a more accurate representation of inhomogeneous systems.
• Despite incorporating additional density terms, the fundamental behavior of liquid-vapor interfaces near critical points remains consistent with prior models.
• This research refines the understanding of fluid behavior at interfaces, particularly in the context of thermodynamic properties.