1. The Study of Self Assembly of Flexible Bodies
Van T. Lam
Faculty Advisor: John Pelesko

2. Original Goals: Understanding the Cheerio Effect
Capillary Surface between Two Vertical Plates
Capillary Surface between a Rigid Rod and a Moving Rod
Capillary Surface between a Rigid Rod and a Flexible Chain
Fully Understanding of the Motion of Flexible Bodies in Liquid

3. Cheerio Effect

4. Cheerio Effect (cont.) Schematic of a Single Bubble close to a wall
θ ≡ contact angle
Fg ≡ gravitational force

5. Capillary Surface Between Two Vertical Plate
Ordinary Differential Equation Approach: x’ d
Initial Condition:

6. Capillary Surface Between Two Vertical Plate (cont.)
Calculating Equation of Interface:
For small interfacial deformation, we have:
From (a), (b) and (c), we have the equation of the interface as followed:

7. Capillary Surface Between Two Vertical Plate (cont.)
Calculating the Equation of the Force:

8. Capillary Surface Between Two Vertical Plate (cont.)
Energy Approach:
 We got the same equations for the interface and the attractive force

9. Capillary Surface Between a Rigid Rod and a Moving Rod
Calculating the Contact Angle: θ
 θ = 540

10. Capillary Surface Between a Rigid Rod and a Moving Rod
Experiment Set Up:
Liquid: Distill water
Temperature: 200C
Material: Plastic Straw
One long and stable horizontal Straw
A single straw of same material with one head sticking to the stable straw
Length: 80mm
Diameter: 6mm
The data were collected, measured, and plotted in a graph of distance (mm) vs. time (second)

11. Capillary Surface Between a Rigid Rod and a Moving Rod (cont.)

12. Capillary Surface Between a Rigid Rod and a Moving Rod (cont.)

13. Capillary Surface Between a Rigid Rod and a Moving Rod (cont.)

14. Capillary Surface Between a Rigid Rod and a Flexible Chain
Experiment Set Up:
Liquid: Distill water
Temperature: 200C
Material: Plastic Straw
One long and stable horizontal Straw
A chain of 4 straw of same material connected to each other using a thin thread. The first straw has one head sticking to the long straw
Length: mm
Diameter: 6mm
We collected the distance between each end of each straw and the long stable straw. The data were plotted in a graph of distance (mm) vs. time (second)

15. Capillary Surface Between a Rigid Rod and a Flexible Chain

16. Capillary Surface Between a Rigid Rod and a Flexible Chain (cont.)

17. Capillary Surface Between a Rigid Rod and a Flexible Chain (cont.)

18. Conclusions
Our Results came out just as expected, although many of the experiments failed due to many reasons.
Attractive force between the experimental objects at certain criteria.
The experiment with hair failed.

19. Future Work
Derive the fitted equations for the plots in the case of one single rod and multiple ones.
Understand the dynamics of these two cases.
Conduct more experiments with more and shorter rods.
Study the case of a fully flexible body and a rigid body.
Study the case of multiple flexible bodies in distill water.

20. Reference
Farlow, Jerry; Hall, J.E.; McDill, J.M.; West, B.H. Differential Equations and Linear Algebra. Second Edition
Isenberg, C., The Science of Soap Films and Soap Bubbles
Vella, Dominic; Mahadevan, L. The “Cheerio Effect” 2005 Harvard University.
Vella, Dominic; Kim, H.; Mahadevan L. The wall-induced motion of a floating flexible train Cambridge University Press. P United Kingdom.
Weinstock, R. Calculus of Variations

21. Special Thanks to Dr. John Pelesko Regan Beckham Lucero Carmona
Anson Carter