Interfaces as transport barriers in two-dimensional Cahn-Hilliard-Navier-Stokes turbulence

TL;DR

This study uses numerical simulations to show that interfaces in 2D binary-fluid turbulence act as effective transport barriers, trapping tracers and significantly affecting their dispersal times.

Contribution

It demonstrates that interfaces serve as transport barriers in 2D CHNS turbulence, quantifies trapping times, and analyzes the role of interface fluctuations and flow parameters.

Findings

Tracers remain within droplets for long times before escaping.

The decay time of tracer retention scales as R_0^{3/2}.

First-passage times inside droplets are much larger than in equivalent circles.

Abstract

We investigate the role of interfaces as transport barriers in binary-fluid turbulence by employing Lagrangian tracer particles. The Cahn-Hilliard-Navier-Stokes (CHNS) system of partial differential equations provides a natural theoretical framework for our investigations. For specificity, we utilize the two-dimensional (2D) CHNS system. We capture efficiently interfaces and their fluctuations in 2D binary-fluid turbulence by using extensive pseudospectral direct numerical simulations (DNSs) of the 2D CHNS equations. We begin with $n$ tracers within a droplet of one phase and examine their dispersal into the second phase. The tracers remain within the droplet for a long time before emerging from it, so interfaces act as transport barriers in binary-fluid turbulence. We show that the fraction of the number of particles inside the droplet decays exponentially and is characterized by a decay time $\tau_{\xi}\sim R_0^{3/2}$ that increases with $R_0$, the radius of the initially circular droplet. Furthermore, we demonstrate that the average first-passage time $\langle \tau \rangle$ for tracers inside a droplet is orders of magnitude larger than it is for transport out of a hypothetical circle with the same radius as the initially circular droplet. We examine the roles of the Okubo-Weiss parameter $\Lambda$, the fluctuations of the droplet perimeter, and the probability distribution function of $\cos(\theta)$, with $\theta$ the angle between the fluid velocity and the normal to a droplet interface, in trapping tracers inside droplets. We mention possible generalisations of our study.