Particle transport and mixing in modulated traveling waves in a binary-fluid mixture heated from below is studied numerically. The fluid divides into three regions separated by Kolmogorov-Arnol’d-Moser curves: a core region where particles are carried along with the wave (trapped), an outer region where particles are left behind by the wave (untrapped), and a separatrix layer between the two where particles chaotically alternate between being trapped and untrapped. The probability distributions for the lengths of individual trapped and untrapped events are sharply peaked at small times, have a power-law decay, and exhibit similar complex structure. The core and outer regions are responsible for long-range transport with no diffusion. The chaotic separatrix layer gives rise to long-range transport with enhanced mixing and anomalous diffusion, where, for long times< x 2 (t)>-< x (t)> 2∼ t ν, 1< ν< 2.