Macroscopic Internal Variables and Mesoscopic Theory: A Comparison Considering Liquid Crystals.

Area of Science:

• Continuum Mechanics
• Statistical Mechanics
• Materials Science

Background:

• Internal and mesoscopic variables are both state space variables.
• Mesoscopic variables include a distribution function, introducing statistical elements.
• Internal variables lack this statistical component.

Purpose of the Study:

• To fundamentally differentiate internal and mesoscopic variables.
• To demonstrate the application of mesoscopic variables in various physical systems.
• To highlight the statistical nature introduced by mesoscopic variables.

Main Methods:

• Formulating mesoscopic balance equations.
• Introducing an evolution equation for the mesoscopic distribution function.
• Applying the mesoscopic concept to liquid crystals, dipolar media, and flexible fibers.

Main Results:

• The alignment tensor in liquid crystal theory can be treated as either an internal variable or derived from a mesoscopic background.
• Mesoscopic variables, being part of the state space, transform balance equations into mesoscopic balances.
• The mesoscopic framework introduces an evolution equation for the distribution function.

Conclusions:

• The mesoscopic concept offers a flexible approach to modeling physical systems.
• This framework enhances the analysis of systems with statistical distributions.
• The study validates the mesoscopic approach across diverse materials like liquid crystals, dipolar media, and flexible fibers.