Persistence exponents in a three-dimensional symmetric binary fluid mixture

The persistence exponent, theta, is defined by N(F)similar to t(-theta), wh ere t is the lime since the start of the coarsening process and the "no-fli p 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 hydrodynami c transport. We find that N-F follows a power law decay (as opposed to expo nential) with the value of theta somewhat dependent on the domain growth ra te (L similar to t(alpha), where L is the average domain size), in the rang e theta=1.23 +/- 0.1 (alpha=2 /3) to theta=1.37 +/- 0.2 (alpha=1). These al pha values correspond to the inertial and viscous hydrodynamic regimes, res pectively.