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 Capillary Surface between a Rigid Rod and a Flexible Chain Fully Understanding of the Motion of Flexible Bodies in Liquid

Cheerio Effect

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

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

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:

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

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

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

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)

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

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

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

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)

Capillary Surface Between a Rigid Rod and a Flexible Chain

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

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

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.

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.

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.

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