Note on the early thermoelastic stage preceding Rayleigh-Bénard convection in soft materials

Rachid Rahouadj (1) , Chérif Nouar (2) , Antonio Pereira (2)

1 LEM3 - Laboratoire d'Etude des Microstructures et de Mécanique des Matériaux
2 LEMTA - Laboratoire d'Energétique et Mécanique Théorique et Appliquée

In this paper, we focus on the first stage of transition to Rayleigh-Bénard convection in softjammed systems (yield stress fluids) confined in a parallelepiped box heated from the bottom. Up to yielding, the material is at solid-state with constant elastic modulus. By means of a linear thermoelastic model, an analytical solution for stresses and strains induced by the gravity and the temperature gradient is derived. The analytical solution allows to emphasize the appropriate dimensionless parameters. The onset of plastic deformation is then investigated using the classical yield criteria (Tresca, von Mises, Drucker-Prager). This analysis is subsequently applied to experimental data of the literature dealing with Rayleigh-Bénard convection in Carbopol micro gels.

Mots clés: Rayleigh–Bénard convection; yield stress fluids; linear thermoelasticity

Domaines: Mécanique des matériaux [physics.class-ph]; Matière Molle [cond-mat.soft]

Rachid Rahouadj, Chérif Nouar, Antonio Pereira. Note on the early thermoelastic stage preceding Rayleigh-Bénard convection in soft materials. Fluids, 2022, 7 (7), pp.231. ⟨10.3390/fluids7070231⟩. ⟨hal-03767211⟩