1. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. (a) Schematic of printhead (Picojet) and (b) its computational domain. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

2. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. (a) Temporally dependent function of wall displacement and (b) temporal profile of the voltage signal and displacement of the wall beside the piezoelectric transducer. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

3. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Numerical grids of a printhead (Picojet). Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

4. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Comparison between experiment and numerical simulation. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

5. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Key stages observed in our numerical experiment 4: (a) ejection, (b) stretching, (c) necking, (d) pinching off, (e) recoil, and (f) breaking up. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

6. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Evolution of the liquid thread shape and velocity vector at the liquid side in experiments (a) 2, (b) 1, and (c) 3. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

7. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of (a) the volume of the primary drop and (b) the velocity of the primary drop in experiments; the volume is in units of Rnoz3=5.044pL and the velocity in units of Rnoz∕tca=2.056ms−1. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

8. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal variation of the rate of volume flow at the plane of the nozzle entrance in (a) experiments 3 and 6 and (b) experiments 4 and 7. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

9. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation with experiments of pinch-off time of liquid thread from nozzle exit; the time is in units of tca=8.341μs. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

10. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of the volume of the primary drop and velocity of the primary drop in experiments; the volume is in units of Rnoz3=5.044pL and the velocity in units of Rnoz∕tca=2.056ms−1. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

11. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Evolution of the shape of the liquid thread during the backward stroke. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

12. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal variation of the rate of volume flow. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

13. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation with experiments of pinch-off time of liquid thread from nozzle exit; the time is in units of tca=8.341μs. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

14. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal evolution of the liquid thread shape in experiments (a) 1 and (b) 12. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

15. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal evolution of the liquid thread shape in experiments (a) 8 and (b) 15. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

16. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of the volume of the primary drop and velocity of the primary drop in experiments; the volume is in units of Rnoz3=5.044pL and the velocity in units of Rnoz∕tca=2.056ms−1. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

17. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of duration of the liquid thread pinching off from nozzle exit; the time is in units of tca=8.341μs. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

18. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal evolution of the free surface contour of the liquid thread crossing the period of actuation of the backward stroke. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

19. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Satellite formation by multiple breaking up observed in numerical experiment 6. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

20. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of length of the liquid thread at pinching off with varied conditions in (a) the forward and backward stages and (b) the pause stage. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

21. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of length of liquid thread at pinching off in various conditions. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

22. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of c2 with experiments shown in Tables (a) 4 and (b) 7. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

23. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Schematic diagram of representative points during the evolution of an ejected liquid thread. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

24. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Variation of the primary drop volume and velocity with firing frequency. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

25. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal variation of the rate of volume flow rate at the plane of the nozzle entrance. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201

26. Date of download: 5/31/2016 Copyright © 2016 SPIE. All rights reserved. Temporal variation of the position of the free surface along the center line of the nozzle. Figure Legend: From: Numerical investigation of the effect of a transducer pulse on the microfluidic control of a piezoelectric printhead J. Micro/Nanolith. MEMS MOEMS. 2010;9(3):033010-033010-20. doi:10.1117/1.3486201