Physics in Fluid Mechanics

Sunghwan (Sunny) Jung 정승환

Applied Mathematics LaboratoryCourant Institute, New York University

Surface waves on a semi-toroidal ring

Sunghwan (Sunny) JungErica Kim Michael Shelley

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

Hydrophobic Materials

Hydrophobic Surface

4 mm1 mm

Hydrophobic Surface

Hydrophobic Surface

Glass SurfaceContact Angle ~ 150O

Experimental Setup

Hydrophobic surfaces

3 cm

1 cm

Speaker

Glass

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

Balance b/t pressure and surface tension

Potential flow

Kinematic boundary condition

pressure, stress and gravitation

Mathieu Equation

In the presence of viscosity, the dominant response frequency is

where is the external frequency.

Stability

k : wavenumber along a toroidal tubea : 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 semi-toroidal ring.

Applicable to the industry for a local spray cooling.

Locomotion of Micro-organism

Sunghwan (Sunny) JungErika KimMichael Shelley

Various Bio-Locomotions

• Flagellar locomotion

• Ciliary locomotion

• Muscle-undulatory locomotion

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

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

As the nematode is close to the boundary, decreases.

Fs Fn

=> It gains more thrust force in the presence of the boundary.(Brennen, 1962)

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) JungKarishma ParikhMichael Shelley

Why do they rotate?

Shear Flow

T = 0 T = t

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.)

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.

•Different flagellar arrangements.

Energy expenditure

Peritrichous

Polar

Lophotrichous

Wavelength, flagellin.

Flagellar structure: the hook and the motor.

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.