Interaction of non-radially symmetric camphor particles

Abstract

In this study, the interaction between two non-radially symmetric camphor particles is theoretically investigated and the equation describing the motion is derived as an ordinary differential system for the locations and the rotations. In particular, slightly modified non-radially symmetric cases from radial symmetry are extensively investigated and explicit motions are obtained. For example, it is theoretically shown that elliptically deformed camphor particles interact so as to be parallel with major axes. Such predicted motions are also checked by real experiments and numerical simulations.

A hybrid camphor–camphene wax material for studies on self-propelled motion

“…3,12 For non-radially symmetric camphor particles the motion can be very complex and combines translation with rotation. [13][14][15] However, it is not easy to make camphor pieces of defined shape at room temperature, at which experiments are usually performed. Purified camphor is granular in form and a few techniques are available to transform the camphor grains into shaped objects.…”

“…However, such objects contain smaller amounts of camphor than pills and the longevity of experiments with these objects is of the order of minutes. 15 Experiments performed with pills of pure camphor show a longer time window of self-motion. 20 Both abovementioned techniques generate objects with highly inhomogeneous distribution of camphor.…”

A Perfect Plastic Material for Studies on Self-Propelled Motion on the Water Surface

“…The explanation of a relationship between the symmetry and the geometrical shape of a solid, self-propelled object and the character of its motion has stimulated abundant scientific activity [ 12 , 13 , 14 , 15 , 16 , 17 , 18 ]. It can be expected that shape and motion are correlated.…”

“…An inert porous support material, like a paper membrane [ 21 ] or agar gel [ 22 , 23 ], can be impregnated with a camphor solution, but this technique is not ideal because the process is hard to control and may produce a non-homogeneous distribution of camphor. Moreover, the saturated objects contain smaller amounts of camphor than pills, limiting surface activity to the order of minutes [ 16 ].…”

Reflection of a self-propelling rigid disk from a boundary

“…A camphor scrapping floating on water is a concrete example of a self-propelling rigid body, which obtains the driving force by making the surface tension around the camphor scrapping inhomogeneous [27], [23], [19]. In these decades, camphor motions have been studied from both mathematical and experimental viewpoints [20], e.g., the occurrence of camphor motion ( [17], [1]), motions of asymmetry shape ( [19], [18], [7], [3]), and collective motions of many camphor boats [2], [8]. However, motions of a camphor disk are not fully understood from the viewpoint of mathematics.…”