Turbulent Poiseuille flow of two immiscible liquid layers inside a channel

Abstract

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 (Reτ, 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 Reτ=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 (Reτ=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.