Interface-induced turbulence in viscous binary fluid mixtures

TL;DR

This paper reveals a novel interface-induced turbulence in binary fluid mixtures at low Reynolds numbers, characterized by a steady state with chaotic properties and strong mixing, studied through direct numerical simulations.

Contribution

It uncovers the existence and properties of interface-induced turbulence in binary fluids, a phenomenon not previously characterized at low Reynolds numbers.

Findings

Energy spectrum exhibits power-law behavior over multiple decades

Lagrangian tracers show diffusive behavior at long times

Interfacial stresses significantly contribute to energy dissipation

Abstract

We demonstrate the existence of interface-induced turbulence, an emergent nonequilibrium statistically steady state (NESS) with spatiotemporal chaos, which is induced by interfacial fluctuations in low-Reynolds-number binary-fluid mixtures. We uncover the properties of this NESS via direct numerical simulations (DNSs) of cellular flows in the Cahn-Hilliard-Navier-Stokes (CHNS) equations for binary fluids. We show that, in this NESS, the shell-averaged energy spectrum $E(k)$ is spread over more than one decade in the wavenumber $k$ and it exhibits a power-law region, indicative of turbulence \textit{but without a conventional inertial cascade}. To characterize the statistical properties of this turbulence, we compute, in addition to $E(k)$, the time series $e(t)$ of the kinetic energy and its power spectrum, scale-by-scale energy transfer as a function of $k$, and the energy dissipation resulting from interfacial stresses. Furthermore, we analyze the mixing properties of this low-Reynolds-number turbulence via the mean-square displacement (MSD) of Lagrangian tracer particles, for which we demonstrate diffusive behavior at long times, a hallmark of strong mixing in turbulent flows.