Extended thermodynamic and mechanical evolution criterion for fluids

The Glansdorff and Prigogine General Evolution Criterion (GEC) is an inequality that holds for macroscopic physical systems obeying local equilibrium and that are constrained under time-independent boundary conditions. The latter, however, may prove overly restrictive for many applications involving fluid flow in physics, chemistry and biology. We therefore analyze in detail a physically more-encompassing evolution criterion for time-dependent convective viscous flows with time-dependent boundary conditions: The Extended General Evolution Criterion (EGEC). The result is an inequality involving the sum of a bulk volume and a surface contribution, and reduces to the GEC if and only if the surface term is zero. We first use the closed-form analytical solution of the Poiseuille starting flow problem in straight cylindrical pipes to confirm the validity of the EGEC. Next, we validate both the Poiseuille starting flow problem and the EGEC numerically. Numerical methods are employed to test the EGEC in not fully developed flows within complex geometries, including curvature and torsion, such as those encountered in helical pipes. Notably, knowledge of only the algebraic sign of the surface contribution is sufficient to predict how the volume thermodynamic forces evolve over time and how the system approaches its non-equilibrium stationary state, consistent with the boundary conditions.