Chapter 2: Mathematical Model and Analyses on Spontaneous Motion of Camphor Particle

H. Kitahata, Y. Koyano, K. Iida, M. Nagayama

Research output: Chapter in Book/Report/Conference proceedingChapter

3 Citations (Scopus)


When a camphor particle is placed on a water surface, it supplies camphor molecules to the water surface, which decrease the surface tension. Owing to the difference in surface tension originating from the difference in camphor concentration, the camphor particle starts to move. In this chapter, we introduce a mathematical model for the motion of a single camphor particle, and present the procedures to analyse the model. The original model is composed of a partial differential equation describing the time evolution of the concentration profile of camphor molecules and ordinary differential equations describing the time evolution of position and characteristic angle of the camphor particle. In the analysis, we derive the reduced ordinary differential equation regarding the dynamics of the camphor particle position and characteristic angle and discuss it considering the bifurcation theory of dynamical systems. We also discuss the effects of the particle shape based on the theoretical analysis.

Original languageEnglish
Title of host publicationSelf-organized Motion
Subtitle of host publicationPhysicochemical Design based on Nonlinear Dynamics
EditorsIstvan Lagzi, Veronique Pimienta, Nobuhiko J. Suematsu, Satoshi Nakata, Hiroyuki Kitahata
PublisherRoyal Society of Chemistry
Number of pages32
Publication statusPublished - 2019

Publication series

NameRSC Theoretical and Computational Chemistry Series
ISSN (Print)2041-3181
ISSN (Electronic)2041-319X

ASJC Scopus subject areas

  • Chemistry(all)
  • Computer Science Applications


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