A systematic investigation of the expansion dynamics of plasma plumes generated by two Q-switched Nd:YAG lasers at 1064 nm wavelength operating on a silicon target was undertaken for the inter-pulse delay times of 0, 100, 200, and 400 ns using a technique involving fast-gated intensified charge-coupled device imaging. Our results indicate that the plasmas exhibit free expansion in a vacuum environment at an inter-pulse delay time of 0 ns. With increasing inter-pulse delay time, the plasma front becomes sharpened and an interaction boundary is formed. Moreover, using the radiation intensity distribution along the plasma axis of symmetry, the formation and evolution mechanism of the plasmas generated by the double pulses was analyzed at different inter-pulse delay times. Finally, the experimental results of the expansion of the plasma core and front were compared with a radiation hydrodynamics model and a drag model, and were found to be generally in good agreement.