Persistence exponents in a 3D symmetric binary fluid mixture

TL;DR

This study numerically investigates the persistence exponent in a 3D symmetric binary fluid mixture, revealing a power-law decay of no-flip fraction influenced by hydrodynamic transport regimes.

Contribution

It provides the first numerical analysis of the persistence exponent in a 3D binary fluid system with hydrodynamic coarsening, highlighting its dependence on domain growth regimes.

Findings

Persistence exponent ranges from 1.23 to 1.37.

Power-law decay of no-flip fraction observed.

Exponent varies with hydrodynamic regime.

Abstract

The persistence exponent, theta, is defined by N_F sim t^theta, where t is the time since the start of the coarsening process and the "no-flip fraction", N_F, is the number of points that have not seen a change of "color" since t=0. Here we investigate numerically the persistence exponent for a binary fluid system where the coarsening is dominated by hydrodynamic transport. We find that N_F follows a power law decay (as opposed to exponential) with the value of theta somewhat dependent on the domain growth rate (L sim t^alpha, where L is the average domain size), in the range theta=1.23 +-0.1 (alpha = 2/3) to theta=1.37 +-0.2 (alpha=1). These alpha values correspond to the inertial and viscous hydrodynamic regimes respectively.