1. Self-Assembly of Hollow Cylinders at Liquid Interfaces
Laura Ostar (Undergraduate Researcher) and Robert Weir (MS Student)
Advisor: Dr. Shahab Shojaei-Zadeh
Complex Fluids and Soft Matter Laboratory
Mechanical and Aerospace Engineering – Rutgers, The State University of New Jersey
References
[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), 209-240.
Acknowledgements
New Jersey Space Grant Consortium
Hossein Rezvantalab
Ken Brakke
A. Background and Motivation
1. 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.
2. 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 
E. Numerical ApproachB. Experimental Approach
 A hollow cylinder deforms the interface which induces capillary attractions between a 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.
Calculating the Pair Potential
1. The equation governing the motion of the
object of mass m is[1]:
2. This scale is large enough to neglect thermal
forces.
3. The inertial term on the left side of the equation
is neglected.
4. Therefore, the interaction force can be
calculated from the drag force:
thermalterindrag FFFam


5. 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.
6. Knowing the interaction forces, the pair
potential can be calculated as follows:

r
r
ddragnteri
contact
vdrcUU 
 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.
 Complementary experimental and numerical investigation is performed to better understand the nature of such interactions.
 Such knowledge enables the bottom-up fabrication of 1D (chains) and 2D (membranes) useful for a range of advanced applications. Side ViewFront View Top View
Experimental Procedure
1. Two 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 as well as front 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 calculated.
5. From this data, the distance between the centroids, as well as the
velocity of approach is extracted.
Hollow Cylinder
Length (L) = 25mm
Radius (R) = 5mm
Wall thickness = 0.3mm
Contact Angle = 80o
deformed interface
1 cm deformed interface
(a) (b) (c)
Capillary attraction between a pair of hollow cylinders
C. Analysis
Inter-particle Separation and Velocity of Approach
-30
-25
-20
-15
-10
-5
0
0 0.5 1 1.5 2 2.5 3
Time (s)
D. Results and Discussion
nteridrag FF


E. Numerical Approach
1. Simulations are done using Surface Evolver
2. The total surface energy is minimized based on the constraints applied
Single Hollow Cylinder
Capillary Interactions between Two Cylinders
Capillary Energy vs. Spacing
1. Normalized capillary energy is plotted vs normalized center-to-center distance.
2. Total surface energy:
3. Capillary energy:
Far-Field means when particles are not interacting.
sgsgslsllglgTot AAAE  
FieldFarTotCapillary EEE 
-14
-12
-10
-8
-6
-4
-2
0
12 14 16 18 20 22 24 26 28
r (mm)
14
16
18
20
22
24
26
28
30
0 1 2 3 4 5
Time (s)
tmax
10
20
30
40
50
0.1 1 10
y = 24.2 + 7.45log(x) R2
= 0.994
log(tmax
-t)
F. Conclusions
Side view
Formation of capillary bridge as cylinders attract/approach one another
-0.07
-0.06
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
0 2 4 6 8 10 12
r/R
r = 10 mm r = 20 mm
Isometric view