Functional constraints on phenomenological coefficients.

Area of Science:

• Non-equilibrium thermodynamics
• Transport phenomena
• Physical chemistry

Background:

• Thermodynamic fluxes are typically proportional to thermodynamic forces, linked by phenomenological coefficients.
• Onsager's relations establish symmetry in the phenomenological coefficient matrix, simplifying models.
• Existing models do not fully constrain the functional dependence of these coefficients on thermodynamic state variables.

Purpose of the Study:

• To demonstrate a new functional constraint on phenomenological coefficients in non-equilibrium thermodynamics.
• To show that coefficients must share functional dependence on local thermodynamic state variables.
• To reduce experimental effort by identifying these additional constraints.

Main Methods:

• Analysis of a class of non-equilibrium thermodynamic models.
• Derivation of functional relationships for phenomenological coefficients.
• Application to coupled heat and mass transport (thermodiffusion) and coupled charge and mass transport (electro-osmotic drag).

Main Results:

• Identified a novel functional constraint on phenomenological coefficients.
• Demonstrated that coefficients must exhibit identical functional dependence on state variables.
• Validated the constraint with examples of thermodiffusion and electro-osmotic drag.

Conclusions:

• The functional dependence of phenomenological coefficients is a critical, previously overlooked constraint.
• Thermodynamic models and experimental data require validation against this functional constraint.
• These constraints significantly reduce the number of experiments needed to characterize transport phenomena.