File Name : figure s1.tif Caption : fig.s1 simulation grid models. (a) piezoelectric vibrator. (b) three types of rectification structures: the series rectification structure, crescent bluff body, and nozzle-diffuser. (c) overall structure of the valveless. piezoelectric micropump. File Name : figure s2.tif Caption : fig. s2 the bottom pump body of pdms and the assembled piezoelectric valveless micropump. File Name : figure s3.tif Caption : fig. s3 flow resistance measuring experiment. File Name : figure s4.tif Caption : fig. s4 simulated internal flow fields of the micropump with different heights of the nested rectification structure: (a) 50 μm, (b) 100 μm, (c) 150 μm, (d) 200 μm, (e) 250 μm, and (f) 300 μm. the insets show enlarged views of the local flow field near the nested rectification region. File Name : figure s5.tif Caption : fig. s5 experimental effect of frequency on the net flow rate of the micropump at a fixed driving voltage of 30 v.