Generalized Lorentz reciprocal theorem in complex fluids and in non-isothermal systems

Area of Science:

• Fluid Dynamics
• Thermodynamics
• Non-equilibrium Statistical Mechanics

Background:

• The classical Lorentz reciprocal theorem (LRT) applies to simple Newtonian fluids under isothermal conditions.
• Complex fluids exhibit coupled hydrodynamics and internal degree-of-freedom evolution.
• Non-equilibrium stationary states and moving boundaries pose challenges for classical theorems.

Purpose of the Study:

• To generalize the Lorentz reciprocal theorem (LRT) for complex fluids.
• To establish a connection between local Onsager's reciprocal relations (ORR) and global Onsager's reciprocal relations (GORR).
• To extend the LRT to non-isothermal systems.

Main Methods:

• Derivation of generalized LRT and GORR for quasi-stationary states near equilibrium.
• Analysis of complex fluids with coupled hydrodynamics and internal variable evolution (e.g., solute concentration, spin).
• Consideration of systems with open or moving boundaries.

Main Results:

• A generalized LRT is derived for complex fluids in quasi-stationary states.
• The study establishes a link between local ORR and boundary GORR.
• The LRT is shown to be extendable to non-isothermal systems, including thermal conduction.

Conclusions:

• The generalized LRT provides a powerful tool for analyzing complex fluid behavior.
• The findings bridge the gap between microscopic Onsager relations and macroscopic boundary conditions.
• The work opens avenues for studying non-isothermal complex fluid dynamics.