| Student Name | Malini Mukherji |
| School Name/Tchr | Indus Center for Academic Excellence -HS - Rahul Mital |
| Project Title | Solving minimality problems using soap bubbles |
| Category: | EN - Engineering |
| Grade: | 9 |
| Exhibit Location: | 1-SEN-025(37089) |
Category Award: 4 (Blue - Outstanding)
Research Plan:
Abstract:
BACKGROUND
Surface tension manifests when the molecules at the top of a liquid have less liquid molecules to bond with, unlike the rest of the molecules in the liquid. This causes them to have stronger bonds with each other, creating a thin film on top of the liquid. Surface tension and surfactant interactions (as in soap bubbles), are capable of forming many different 2d and 3d shapes, which are produced to create the optimal surface area. The optimal surface area has the least surface area to volume ratio, and is formed because it requires the least energy. This is why water forms spherical beads .
Motivation
In school we were reading a chapter about the chemical basis of life. That is where is first learned about surface tension. Later on we did an activity on calculating the surface area and volumes of certain 3d shapes and finding which shape had the least surface area to volume ratio. We did this to find out what the desirable shape for a cell would be. We found out that a sphere was the desirable shape. As I stated before, the sphere requires the least energy to be formed. Now I wanted to find out what other applications surface tension had in the real world. I encountered a problem about how to find the shortest path connecting a number of points and how to design the roof of a stadium with the smallest area. The first problem is called the Steiner tree Problem, which only deals with 2d structures, and the second one is an application of the plateau problem, which deals with 3d structures. These problems are very hard to solve theoretically, but very easy to solve with soap bubbles as shown by Joseph Plateau and Jakob Steiner in the 19th century.
OBJECTIVE
I want to use plateau and Steiner's methods, which uses soap bubbles, to demonstrate how to find the shortest path connecting some number of points, and how to design the roof of a stadium with the smallest area.
EXPERIMENTS
Paperclip floating on water
Pepper spreading in water
Alveoli in lungs
Boat propelled by surface tension
Frame experiment
3D – cube
Two Plates
N number of towns/points
Shortest paths between them
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