Pattern formation revisited within nonequilibrium thermodynamics: Burgers'-type equation

Area of Science:

• Physical Chemistry
• Nonlinear Dynamics
• Thermodynamics

Background:

• Reaction-diffusion systems are fundamental in various scientific fields.
• Non-equilibrium thermodynamics provides a framework for analyzing these systems.
• A nonstandard entropy balance splitting reveals new insights.

Purpose of the Study:

• To investigate the impact of a diffusion kinetic energy term on reaction-diffusion phenomena.
• To derive and analyze governing equations within a modified thermodynamic framework.
• To explore pattern formation and stability in reaction-diffusion systems.

Main Methods:

• Utilizing a nonstandard splitting of the entropy balance.
• Applying standard constitutive relations from linear non-equilibrium thermodynamics.
• Deriving governing equations for a two-species reaction-diffusion system.
• Analyzing the connection to Burgers' equation with a source term.

Main Results:

• A new thermodynamic force derived from diffusion kinetic energy drives reaction kinetics.
• Governing equations are linked to Burgers' equation, allowing for non-periodic pattern emergence.
• Transients resembling saw-tooth solutions to Burgers' equation are predicted.
• Turing's reaction-diffusion model shows robustness to this new term when small.

Conclusions:

• The inclusion of diffusion kinetic energy can lead to richer pattern formation in reaction-diffusion systems.
• Non-standard reaction kinetics, beyond the law of mass action, can significantly alter system behavior.
• This approach offers a pathway to explore novel phenomena in classical reaction-diffusion models.