Extended Thermodynamic and Mechanical Evolution Criterion for Fluids

TL;DR

This paper extends the classical thermodynamic evolution criterion to include surface effects in fluid flows with time-dependent boundaries, validated through analytical and numerical methods in complex geometries.

Contribution

It introduces a more comprehensive evolution criterion that accounts for surface contributions, applicable to time-dependent viscous flows with dynamic boundary conditions.

Findings

The extended criterion reduces to the GEC when surface terms are zero.

Analytical solutions confirm the validity of the extended criterion.

Numerical validation in complex geometries supports practical applicability.

Abstract

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 timeindependent 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 flow with time-dependent boundary conditions. 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 use the closed-form analytical solution of the starting flow problem in straight cylindrical pipes to confirm this extended general evolution criterion. We next validate the starting flow problem and evolution criterion numerically. Numerical methods are used to validate the extended evolution criterion in non-fully developed flows inside complex geometries with curvature and torsion, such as encountered in sections of helical pipes. Knowledge of only the algebraic sign of the surface contribution is sufficient for predicting how the volume thermodynamic forces evolve in time and how the system approaches its non-equilibrium stationary state consistent with the boundary conditions.