Physics
in Fluid Mechanics
Sunghwan (Sunny) Jung 정승환
Applied Mathematics Laboratory
Courant Institute, New York University
Surface waves
on a semi-toroidal ring
Sunghwan (Sunny) Jung
Erica Kim
Michael Shelley
Motivation
 Faraday (1831) - wave formation due to vibration
 Benjamin & Ursell (1954) - stability analysis
Vibrating a pool
Vibrating a bead
Vertically vibrated
Vertically vibrated
 Other geometries of the water surface
 Quasi-one dimensional surface wave
Hydrophobic Materials
4 mm
1 mm
HydrophobicSurface
Surface
Hydrophobic
Contact Angle ~ 150
O
Glass Surface
Hydrophobic
Surface
Experimental Setup
Hydrophobic surfaces
Glass
1 cm
Speaker
3 cm
3 cm
1 cm
3 cm
1 cm
Standing Surface Waves
Coordinate for Water Surface
 (m = 2) mode along
 Neglect the small curvature along the torus ring.
Surface waves in a water ring
 Potential flow
 Balance b/t pressure and surface tension
 pressure, stress and gravitation
Kinematic boundary condition
Mathieu Equation
where
is the external frequency.
 In the presence of viscosity, the dominant
response frequency is
Stability
k : wavenumber along a toroidal tube
a : nondimensionalized vibrating acceleration
Frequency Response
Conclusion
Our novel experimental technique can
extend the study of surface waves on
any geometry.
 We studied a surface wave on a semitoroidal ring.
 Applicable to the industry for a local
spray cooling.

Locomotion of
Micro-organism
Sunghwan (Sunny) Jung
Erika Kim
Michael Shelley
Various Bio-Locomotions
• Flagellar locomotion
• Ciliary locomotion
• Muscle-undulatory
locomotion
C. Elegans (Nematode)
Thickness ~ 60 μm
1 mm
• Length is 1 mm and thickness is 60 μm.
• Consists of 959 cells and 300 neurons
• Swim with sinusoidal body-waves
On the plate
In water
• Bending Energy
• Force
where
is the curvature of the slender body and
is the coordinate along the slender body
In a simulation
In the high viscous fluid
In the low viscous fluid
In a 200 micro meter channel
In a 300 micro meter channel
Swimming C. Elegans
Swimming velocity increases as the
width of walls decreases.
 Amplitude in both cases is similar.

Effect of nearby boundaries
 C. Elegans swim faster with a narrow channel.
Effect of nearby boundaries
Fs
Fn
As the nematode is close to the boundary,
decreases.
(Brennen, 1962)
=> It gains more thrust force in the presence of the boundary.
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.

Periodic Parachutes
in Viscous Fluid
Sunghwan (Sunny) Jung
Karishma Parikh
Michael Shelley
Why do they rotate?
T=0
T=t
Shear Flow
Thanks to
Prof.
Prof.
Prof.
Prof.
Michael Shelley, Steve Childress (Courant Institute)
Jun Zhang (Phy. Dep., NYU)
Albert Libchaber (Rockefeller Univ.)
Lisa Fauci (Tulane Univ.)
Dr. David Hu
Erica Kim, Karishma Parikh
Future works
Interaction among helixes
 Microfluidic pump using Marangoni
stress

Cilia
Why do cells move? Is there any advantage in being
motile?
•Microbial locomotion.
•Flagella and motility.
Energy expenditure
•Different flagellar arrangements.
Peritrichous
Polar
Lophotrichous
Flagellar structure: the hook and the motor.
Wavelength, flagellin.
Flagella
Swimming E. Coli
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.