Self-Assembly of Hollow Cylinders at Liquid InterfacesLaura Ostar (Undergraduate Researcher) and Robert Weir (MS Student) Advisor: Dr. Shahab Shojaei-ZadehComplex Fluids and Soft Matter LaboratoryMechanical 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.

AcknowledgementsNew Jersey Space Grant ConsortiumHossein RezvantalabKen 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 Potential1. 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

rddragnteri

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 CylinderLength (L) = 25mmRadius (R) = 5mmWall thickness = 0.3mmContact Angle = 80o

deformed interface

1 cm deformed interface

(a) (b) (c)Capillary attraction between a pair of hollow cylinders

C. AnalysisInter-particle Separation and Velocity of Approach

-30

-25

-20

-15

-10

-5

0

0 0.5 1 1.5 2 2.5 3Time (s)

D. Results and Discussion

nteridrag FF

E. Numerical Approach

1. Simulations are done using Surface Evolver2. 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 28r (mm)

14

16

18

20

22

24

26

28

30

0 1 2 3 4 5Time (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 12r/R

r = 10 mm r = 20 mm

Isometric view