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The Study of Self Assembly of Flexible Bodies

The Study of Self Assembly of Flexible Bodies. Van T. Lam Faculty Advisor: John Pelesko. Original Goals:. Understanding the Cheerio Effect Capillary Surface between Two Vertical Plates Capillary Surface between a Rigid Rod and a Moving Rod

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The Study of Self Assembly of Flexible Bodies

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  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. d Capillary Surface Between Two Vertical Plate y’ • Ordinary Differential Equation Approach: x’ 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. θ Capillary Surface Between a Rigid Rod and a Moving Rod • Calculating the Contact Angle:  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: 30-30-30-30mm • 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. 2007. • Isenberg, C., The Science of Soap Films and Soap Bubbles. 1992. • 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. 2004 Cambridge University Press. P. 89-98. United Kingdom. • Weinstock, R. Calculus of Variations. 1974.

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

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