In parallel with recent developments in carbon nanomaterials, there is growing interest in using these nano materials for desalination. To date, many studies have affirmed the potential of using such nanomaterials for constant pressure desalination operation. In this work, the performance of such membrane when subjected to oscillatory pressure at sub-nanosecond is investigated in detail. Using the transverse flow CNT membrane operating at periods ranging from 0.02 to 0.1 ns, we find that oscillatory pressure operation can increase the permeability of the membrane by 16% with a salt rejection close to 100%. Detailed studies on the salt concentration profile, water orientation and water permeance behavior revealed that this increase in permeability is due to the development of resistance to reverse flow at higher periods of oscillation. Further extension of the analysis to periods on the order of 0.1 ns and beyond do not show a positive influence on water permeability. Thus, this work shows that periods on the order of 10(-2) ns are required for improved performance of low dimensional nanomaterials membrane. The results from this work shows that nanomaterials membrane is suitable for oscillatory operation, such as electrodialysis reversal. Due to the nanoscale sized of the membrane channels, sub-nanoseconds pulsations are more effective in introducing instabilities to the system to positively influence the water permeance behavior of the membrane.