Hard Spheres, Soap Bubbles, and Hydrogels in Research and Education

Abstract

This thesis concerns various experiments using hard spheres, soap bubbles, hydrogel spheres, and soap films in which we will show these are suitable candidates for research and can be easily performed in universities, classrooms, or even at home to express physical concepts such as instability, symmetry breaking, buckling, dense packing, and failure. Initially, we briefly present examples of using hard spheres and soap film that are used to demonstrate science. For example, we describe how soap films can be used to help with minimization problems such as the Motorway Problem. We then discuss the buckling behavior of a linear chain of hard spheres confined in a transverse harmonic potential that displays instability and buckling under compression and tilt. We will discuss different arrangements of such chains under low and high compressions and under tilt. At low compression, a modulated zig-zag arrangement is observed which is followed by a localized buckling at higher compression and will end with a doublet structure at higher compressions. In addition, we will demonstrate there is a critical tilt for the buckling of the system. Friction plays a critical role in our buckling experiments using hard spheres. To eliminate friction, we will discuss an alternative for buckling experiments using soap bubbles. So, a linear chain of soap bubbles is investigated under compression. Due to the deformability of soap bubbles, we show the onset of buckling occurs at a critical value of compression. Also, our findings are in good agreement with the simulation. In addition, we present how the transverse bubble width changes as a function of compression. Packing experiments using hydrogel spheres will be introduced. First, we will demonstrate how a line of hydrogel spheres lying at the bottom of a cylindrical tube can show a zigzag pattern as observed using a chain of hard spheres and soap bubbles. Then I will show various types of packing problems using hydrogel spheres. The experiments are easy to set up and thus suitable for use in the classroom or in the undergraduate teaching laboratory. As bubbles are a relatively easy system to experiment with, we will introduce another field of research where soap films/bubbles can be used to obtain experimental data related to studies of failure/mortality. We introduce controlled experiments using individual soap films confined in the middle of Perspex tubes as a simple physical system to model the failure and mortality. Our examination of soap film lifetime statistics has yielded valuable insights and showed that individual soap films displayed a common pattern of mortality/failure called the bath-tub curve. Our findings show a linear relationship between film lifetime and tube length and introduce a relationship between defects in the system and soap film lifetime. Finally, we conclude our results and introduce suggestions for further research. First, we suggest another buckling experiment using slanted stoppers instead of flat stoppers to investigate the effect of changing the boundary conditions in buckled structures. We show that instead of using flat stoppers if one uses slanted stoppers that leads to a double-peak structure, and rather than a localized buckling at high compression, a modulated zigzag can be observed. In addition, we suggest further exploration of soap film lifetime to investigate the effect of external factors on the ageing and failure of soap films that can be used as a simple system to see how mortality curves look like for people that always lived under poor conditions.