Turbulent Poiseuille flow of two immiscible liquid layers inside a channel

We use pseudo-spectral Direct Numerical Simulation (DNS), coupled with a Phase Field Method (PFM), to investigate the turbulent Poiseuille flow of two immiscible liquid layers inside a channel. The two liquid layers, which have the same thickness (h₁=h₂=h), are characterized by the same density (ρ₁=ρ₂=ρ) but different viscosities (μ₁ ≠ μ₂). The full problem is described in terms of the following flow parameters: the shear Reynolds number (Re_τ, which quantifies the importance of inertia compared to viscous effects), the Weber number (We, which quantifies surface tension effects compared to inertia) and the viscosity ratio, λ between the two fluids. In particular, we fix Re_τ=300, We=1, and we consider viscosity ratios in the range 0.1≤ λ=μ₁/μ₂ ≤ 1. We focus on the role of turbulence in initially deforming the interface and on the subsequent growth of capillary waves. Compared to a single phase flow at the same shear Reynolds number (Re_τ=300), in the two-layers case we observe a strong interaction between the turbulent flow and the deformable liquid-liquid interface. A full characterization of the interface deformation, in terms of spatiotemporal specta of wave elevation will be presented and discussed.