Persistence exponents in a three-dimensional symmetric binary fluid mixture
The persistence exponent, straight theta, is defined by N(F) approximately t(-straight 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 straight theta somewhat dependent on the domain growth rate (L approximately t(alpha), where L is the average domain size), in the range straight theta=1.23+/-0.1 (alpha=2/3) to straight theta=1.37+/-0.2 (alpha=1). These alpha values correspond to the inertial and viscous hydrodynamic regimes, respectively.