Continuum Thermodynamics of Constrained Reactive Mixtures

Area of Science:

• Thermodynamics
• Continuum Mechanics
• Biophysics

Background:

• Constrained reactive mixtures model biological tissue growth and remodeling.
• Existing models are limited to isothermal conditions.
• Extends classical damage mechanics and viscoelasticity.

Purpose of the Study:

• Establish thermodynamic foundations for constrained reactive mixtures under general conditions.
• Incorporate arbitrary reactive processes with spatiotemporal temperature variations.
• Develop novel formulas for reactive heat supply and energy of formation.

Main Methods:

• Incorporating general expressions for reaction kinetics.
• Applying the Clausius-Duhem inequality and axiom of energy balance.
• Deriving new formulas for energy of formation and heat of reaction.

Main Results:

• Residual dissipation must include reactive power density.
• Energy balance must include reactive heat supply density.
• Novel formulas link heat supply to free energy and reaction rate.

Conclusions:

• The framework accommodates reactive processes with temperature variations.
• Facilitates analysis of reactive tissue biomechanics.
• Applicable to physiological and biomedical engineering where temperature changes are significant.