Odd capillarity in two-phase flows, Generalized Navier-Stokes equation and asymmetric two-phase flows

Abstract: Odd capillarity in two-phase flows
Fluid interfaces are remarkably rich. A broad range of two-phase and multiphase phenomena can be described within the Cahn–Hilliard–Navier–Stokes (CHNS) framework, where the Navier–Stokes equations are coupled to the Cahn–Hilliard dynamics through the Korteweg stress associated with interfacial tension. Active two-phase flows, described for example by active CHNS models, extend this picture by allowing the mechanical interfacial tension to differ from its passive counterpart and even become negative, leading to phenomena such as interrupted coarsening and self-generated flows. In both passive and active formulations, however, the interfacial stress preserves parity symmetry. This leads us to ask a simple question: what changes when parity symmetry is broken at a fluid interface? We address this question by introducing an odd contribution to the Korteweg stress. In the sharp-interface limit, this generalizes the classical Young-Laplace law: in addition to the familiar normal capillary traction, curvature generates a transverse traction along the interface. We refer to this effect as odd capillarity. We then study the resulting dynamics numerically within a diffuse-interface formulation. Odd capillarity generates circulating flows around droplets, strongly modifies interfacial morphology and phase separation, and, at sufficiently large strength, produces turbulence even at low Reynolds number. These results illustrate how unconventional stresses can qualitatively reshape the dynamics and morphology of two-phase flows.

Generalized Navier-Stokes equation and asymmetric two-phase flows
One way to consider activity in flow is realized by the Generalized Navier-Stokes equation. It is used as a model for bacterial suspensions and provides a higher order equation. We introduce the model and solve it numerically. We characterize the turbulent flow field and identify similarities and difference with classical inertial turbulence. Characterizing the vorticity with respect to its hyperuniform properties allows for a new measure to distinguish both. In the second part of the talk we extend this model towards a two-phase system, coupling it with a classical Navier-Stokes equation using a Cahn-Hilliard equation. The model now describes a coupled active-passive system and could be called Cahn-Hilliard-Generalized-Navier-Stokes (CHGNS) equation. We again solve these equations numerically and explore the emerging morphologies. They turn out to be asymmetric. We explain this behaviour and relate it to other active CHNS models.

Computer scienceMathematics

Audience: researchers in the topic

Modelling of materials - theory, model reduction and efficient numerical methods (UNCE MathMAC)