Shear instability of two-fluid parallel flow in a Hele–Shaw cell

Philippe Gondret (1) , Marc Rabaud (1)

1 FAST - Fluides, automatique, systèmes thermiques

We study experimentally the parallel flow in a Hele–Shaw cell of two immiscible fluids, a gas and a viscous liquid, driven by a given pressure gradient. We observe that the interface is destabilized above a critical value of the gas flow and that waves grow and propagate along the cell. The experimental threshold corresponds to a velocity difference of the two fluids in good agreement with the inviscid Kelvin–Helmholtz instability, while the wave velocity corresponds to a pure viscous theory deriving from Darcy’s law. We report our experimental results and analyze this instability by the study of a new equation where the viscous effects are added to the Euler equation through a unique drag term. The predictions made from the linear stability analysis of this equation agree with the experimental measurements.

Domaines: Mécanique des fluides [physics.class-ph]

Philippe Gondret, Marc Rabaud. Shear instability of two-fluid parallel flow in a Hele–Shaw cell. Physics of Fluids, 1997, 9 (11), pp.3267-3274. ⟨10.1063/1.869441⟩. ⟨hal-03865297⟩