Mass transfer enhancement by a pulsatile laminar flow in an axisymmetric wavy channel has been investigated numerically for the range of 50 less than or equal to Re less than or equal to 250 and 0.1 less than or equal to St less than or equal to 10. The optimal Strouhal number has been determined as a function of the Reynolds number and the wavelength of the channel. It is found that the optimal Strouhal number increases weakly as the Reynolds number decreases. It is also found that the optimal Strouhal number is almost inversely proportional to the channel wavelength. For better understanding of the enhancement mechanism, the Lagrangian flow analysis has also been performed. For an efficient computation, the Eulerian velocity field is represented by the Fourier series, Particle trajectories show chaotic behaviors when the Strouhal number is close to the optimal value. It is observed that there is a very strong correlation between the mass transfer enhancement factor and the average Lagrangian Lyapunov exponent.