1. Physics in Fluid Mechanics Sunghwan (Sunny) Jung 정승환 Applied Mathematics Laboratory Courant Institute, New York University

2. Surface waves on a semi-toroidal ring Sunghwan (Sunny) Jung Erica Kim Michael Shelley

3. Motivation Faraday (1831) - wave formation due to vibration Benjamin & Ursell (1954) - stability analysis Vertically vibrated  Other geometries of the water surface  Quasi-one dimensional surface wave Vertically vibrated Vibrating a pool Vibrating a bead

4. Hydrophobic Materials Hydrophobic Surface 4 mm 1 mm Hydrophobic Surface Glass Surface Contact Angle ~ 150 O

5. Experimental Setup Hydrophobic surfaces 3 cm 1 cm Speaker Glass

7. 3 cm 1 cm

8. 3 cm 1 cm

9. Standing Surface Waves

10. Coordinate for Water Surface (m = 2) mode along Neglect the small curvature along the torus ring.

11. Surface waves in a water ring  Balance b/t pressure and surface tension  Potential flow Kinematic boundary condition  pressure, stress and gravitation

12. Mathieu Equation  In the presence of viscosity, the dominant response frequency is where is the external frequency.

13. Stability k : wavenumber along a toroidal tube a : nondimensionalized vibrating acceleration

14. Frequency Response

15. Conclusion Our novel experimental technique can extend the study of surface waves on any geometry. We studied a surface wave on a semi- toroidal ring. Applicable to the industry for a local spray cooling.

16. Locomotion of Micro-organism Sunghwan (Sunny) Jung Erika Kim Michael Shelley

17. Various Bio-Locomotions Flagellar locomotion Ciliary locomotion Muscle-undulatory locomotion

18. C. Elegans (Nematode) 1 mm Length is 1 mm and thickness is 60 μm. Consists of 959 cells and 300 neurons Swim with sinusoidal body-waves Thickness ~ 60 μm

19. On the plate

20. In water

21. Bending Energy Force whereis the curvature of the slender body and is the coordinate along the slender body

22. In a simulation In the high viscous fluid In the low viscous fluid

23. In a 200 micro meter channel

24. In a 300 micro meter channel

25. Swimming C. Elegans Swimming velocity increases as the width of walls decreases. Amplitude in both cases is similar.

26. Effect of nearby boundaries C. Elegans swim faster with a narrow channel.

27. Effect of nearby boundaries As the nematode is close to the boundary, decreases. Fs Fn => It gains more thrust force in the presence of the boundary. (Brennen, 1962)

28. Conclusion Simple argument explains why C. Elegans can not swim efficiently in the low viscous fluid. C. Elegans are more eligible to swim when the boundary exists.

29. Periodic Parachutes in Viscous Fluid Sunghwan (Sunny) Jung Karishma Parikh Michael Shelley

32. Why do they rotate? Shear Flow T = 0 T = t

34. Thanks to Prof. Michael Shelley, Steve Childress (Courant Institute) Prof. Jun Zhang (Phy. Dep., NYU) Dr. David Hu Erica Kim, Karishma Parikh Prof. Albert Libchaber (Rockefeller Univ.) Prof. Lisa Fauci (Tulane Univ.)

35. Future works Interaction among helixes Microfluidic pump using Marangoni stress

36. Cilia

37. Why do cells move? Is there any advantage in being motile? Microbial locomotion. Flagella and motility. Different flagellar arrangements. Energy expenditure Peritrichous Polar Lophotrichous Wavelength, flagellin. Flagellar structure: the hook and the motor.

38. Flagella

39. Swimming E. Coli

40. Manner of movement in peritrichously flagellated prokaryotes. (a) Peritrichous: Forward motion is imparted by all flagella rotating counterclockwise (CCW) in a bundle. Clockwise (CW) rotation causes the cell to tumble, and then a return to counterclockwise rotation leads the cell off in a new direction.