### Solutal convection and draw resonance

Orateur : **Julien Philippi** / TIPS, Université Libre de Bruxelles

**Abstract** : In this talk I will present two instabilities occurring in very different situations.

In the first part of my presentation I will talk about a hydrodynamic instability responsible of the formation of erosion patterns. Indeed the dissolution of minerals into water becomes significant in geomorphology when the erosion rate is controlled by the hydrodynamics transport of the solute. Even in absence of an external flow, dissolution itself can induce a convection flow due to the action of gravity. Here we perform a study of the physics of solutal convection induced by dissolution. We simulate numerically the hydrodynamics and the solute transport, in a 2D geometry, corresponding to the case where a soluble body is suddenly immersed in a quiescent solvent. We identify three regimes. At short timescale, a concentrated boundary layer grows by diffusion at the interface. After a finite onset time, the thickness and the density reach critical values which starts the destabilization of the boundary layer. Finally, the destabilization is such as we observe the emission of intermittent plumes. This last regime is quasi-stationnary : the structure of the boundary layer as well as the erosion rate fluctuate around constant values. Assuming that the destabilization of the boundary layer occurs at a specific value of the solutal Rayleigh number, we derive scaling laws both for fast and slow dissolution kinetics. Our simulations confirm this scenario by validating the scaling laws both for onset, and the quasi-stationary regime. We find a constant value of the Rayleigh number during the quasi-stationary regime showing that the structure of the boundary layer is well controlled by the solutal convection. Finally, we apply the scaling laws previously established to the case of real dissolving minerals. We predicts the typical dissolution rate in presence of solutal convection. Our results suggest that solutal convection could occur in more natural situations than expected. Even for minerals with a quite low saturation concentration, the erosion rate would increase as the dissolution would be controlled by the hydrodynamics.

The second part of my talk is dedicated to the presentation of an instability occurring in an industrial context. Indeed the draw resonance effect appears in fiber drawing processes when the draw ratio, defined as the ratio between the take-up and the inlet velocity, exceeds a critical value. This instability is characterized by steady oscillations of flow velocity and fiber diameter. In many cases, inertia, gravity and surface tension could not be neglected and a model combining all these effects is necessary in order to correctly describe the physics of the phenomenon. By performing a linear stability analysis which take into account all these effects, M. Bechert and B. Scheid [Phys. Rev. Fluids 2, 113905 (2017)] evidenced that the stability of the system exhibit a strong sensitivity on surface tension and that some regions of the parameters space are unconditionally instable. Additionally, it is also known that cooling have a highly stabilizing effect on the draw resonance instability. However, a nonisothermal model encompassing the effect of inertia, gravity and surface tension which could explain the stability of the system while the draw ratio is of order of 10 000 as in industrial applications is still lacking. By introducing a new scaling, we show that the existence of such regimes is explained if we consider that the heat transfer coefficient is not constant but depends on the velocity and on the section of the fiber. Our model takes also into account radiative heat transfer and its influence on the stability is also investigated. Within this framework, it finally appears that the stability of the system is mainly governed by the temperature at the inlet (which is in fact a control parameter), the aspect ratio of the fiber and the heat transfer.

**Date et lieu** : vendredi 11 octobre 2019 à 11h dans la salle de séminaire IRPHE