1. 14
16
18
20
22
24
26
28
30
0 1 2 3 4 5
Time (s)
Inter-particle Separation and Velocity of Approach
tmax
Data Analysis
10
20
30
40
50
0.1 1 10
y = 24.2 + 7.45log(x) R2
= 0.994
log(tmax
-t)
Self-Assembly of Hollow Cylinders at the Water-Air Interface
Laura Ostar (Undergraduate Research Fellow)
Advisor: Dr. Shahab Shojaei-Zadeh
Complex Fluids and Soft Matter Laboratory
Mechanical and Aerospace Engineering – Rutgers, The State University of New Jersey
The distance between the centers of the cylinders follows
a power law over time, where tmax is the time at contact
and 0<α<1.
For the experiments performed, the exponent α was found
to be 0.2, in agreement with the range proposed in other
experiments. [2]

)( max ttr 
1. Cylinders are released simultaneously at the flat DI water/air interface formed in a large container.
2. Interface deformation is recorded using a grid at the bottom of the container and side images.
3. The inter-particle interaction is captured using a CCD camera looking down at the setup.
4. Using image processing techniques, the video is disassembled into frames and the position data of
each cylinder is extracted.
5. From this data, the distance between the centroids and the velocity of approach is calculated.
Hollow Cylinder
Length (L) = 25mm
Radius (R) = 5mm
Wall thickness = 0.3mm
Contact Angle = 80o
(a) (b) (c)
Experimental Procedure
Calculating the Pair Potential
1. The equation governing the motion of the object of
mass m is[1]:
2. This scale is enough to neglect thermal forces and
inertial terms. Therefore, the interaction force can
be calculated from the drag force.
3. The viscous drag force is calculated from
Fdrag = - η cd v, where η is the viscosity of water
(1 mPa.s), cd is the drag coefficient of a cylinder
(1.38)[3] and v is the instantaneous velocity of the
particle, as shown in the plot above.
4. Knowing the interaction forces, the pair potential
can be calculated as follows:
thermalterindrag FFFam



r
r
ddragnteri
contact
vdrcUU 
nteridrag FF


-14
-12
-10
-8
-6
-4
-2
0
12 14 16 18 20 22 24 26 28
r (mm)
Results and Discussion
Background and Motivation
Front View
deformed interface
1 cm Side View
deformed interface
Top View
[1]Rezventalab, H., Shojaei-Zadeh, S. (2013). Soft Matter, 9: 3640-3650.
[2]Loudet, J. C., Alsayed, A. M., Zhang, J., Yodh, A. G. (2005). Physical review letters, 94(1), 018301.
[3]Ye, T., Mittal, R., Udaykumar, H., Shyy, W. (1999). Journal of Computational Physics, 156(2).
References
Conclusions
 Hollow cylinders deform the interface which induces capillary attractions between the pair.
Side-by-side alignment seems to be energetically favorable over tip-to-tip alignment.
The center-to-center distance between the approaching cylinders follows a power-law, with an
exponent of α = 0.2.
The measured pair-potential and calculated capillary energy both confirm the attraction between the
two cylinders.
 Objects can deform liquid/fluid interfaces due to shape, gravity, surface roughness, electrical
charges, and surface chemistry.[1]
 Capillary-induced interactions take place when two neighboring objects with deformed interfaces
interact (to minimize the interfacial energy.)
 Such interactions result in specific arrangement leading to self-assembly of such objects.
 We would like to explore interface deformation and resulting capillary-induced interactions
between a pair of hollow cylinders.
Such knowledge enables the bottom-up fabrication of 1D (chains) and 2D (membranes) useful for a
range of advanced applications.