Persistence exponents in a 3D symmetric binary fluid mixture

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.