Hydrodynamic instabilities in miscible fluids

TL;DR

This review explores the mechanisms behind hydrodynamic instabilities in miscible fluids, focusing on interface dynamics, stabilization mechanisms, and the debate over effective interfacial tension in such systems.

Contribution

It provides a comprehensive overview of the physical mechanisms, stability analysis challenges, and recent research on interfacial tension in miscible fluid flows.

Findings

Interfacial stresses in miscible fluids are debated and may mimic surface tension.

Viscous dissipation can act as a stabilizing mechanism.

The lack of a clear interfacial tension complicates stability analysis.

Abstract

Hydrodynamic instabilities in miscible fluids are ubiquitous, from natural phenomena up to geological scales, to industrial and technological applications, where they represent the only way to control and promote mixing at low Reynolds numbers, well below the transition from laminar to turbulent flow. As for immiscible fluids, the onset of hydrodynamic instabilities in miscible fluids is directly related to the physics of their interfaces. The focus of this review is therefore on the general mechanisms driving the growth of disturbances at the boundary between miscible fluids, under a variety of forcing conditions. In the absence of a regularizing mechanism, these disturbances would grow indefinitely. For immiscible fluids, interfacial tension provides such a regularizing mechanism, because of the energy cost associated to the creation of new interface by a growing disturbance. For miscible fluids, however, the very existence of interfacial stresses that mimic an effective surface tension is debated. Other mechanisms, however, may also be relevant, such as viscous dissipation. We shall review the stabilizing mechanisms that control the most common hydrodynamic instabilities, highlighting those cases for which the lack of an effective interfacial tension poses deep conceptual problems in the mathematical formulation of a linear stability analysis. Finally, we provide a short overview on the ongoing research on the effective, out of equilibrium interfacial tension between miscible fluids.