GENERIC framework for reactive fluid flows

Abstract

We describe reactive fluid flows in terms of the formalism General Equation forNon-Equilibrium Reversible-Irreversible Coupling also known as GENERIC. We present the thermodynamical and mechanical foundations for the treatment of fluid flows using GENERIC and present a framework for noninvertible transformations, that is in particular applied to transformations of variational approaches between Lagrangian and Eulerian coordinates. We bring the abstract framework to life by providing many physically relevant examples for reactive compressible fluid flows.

Steering droplets on substrates using moving steps in wettability

“…where G is a friction operator [30,31]. Since the Stokes equations are linear in the fluid velocity field v, G is a linear operator that does not depend on v. After discretizing the droplet surface, G becomes a friction matrix and R and K are vectors.…”

Steering droplets on substrates with plane-wave wettability patterns and deformations

“…As a result, for any point on the droplet surface we can write a force balancewhere the friction force K = − GṘ ,is linear in the surface velocity field Ṙ and G is a linear operator that does not depend on v , since the Stokes equations are linear in the fluid velocity field v . 32,33 The force derives from the droplet free energy, as we explain in Section 2.2, and provides the Laplace pressure, Young's force at the contact line, and constraint forces. Finally, F governs the dynamics induced by deforming substrates.…”

A porous-media model for reactive fluid–rock interaction in a dehydrating rock

“…First, based on our findings in Ref. 17, we investigate the thermodynamical structure of models (1) and (2) in the framework GENERIC (General Equations of Non-Equilibrium Reversible-Irreversible Coupling). For this, we briefly review the modeling concept of GENERIC in Sec.…”

“…We further assume that the conservative contribution to dynamics is represented by the operator J from (16). In analogy to (17), we introduce the general structure of the Onsager operator for the two-phase reaction-diffusion system as follows:…”