TY - CHAP

T1 - Chapter 2

T2 - Mathematical Model and Analyses on Spontaneous Motion of Camphor Particle

AU - Kitahata, H.

AU - Koyano, Y.

AU - Iida, K.

AU - Nagayama, M.

N1 - Funding Information:
We gratefully acknowledge the valuable contributions of Satoshi Nakata, Nobuhiko J. Suematsu, Yutaka Sumino, Natsuhiko Yoshinaga, Kota Ikeda, Tomoyuki Miyaji, Tatsunari Sakurai, Jerzy Gorecki, Shin-ichiro Ei, Alexander S. Mikhailov and Takao Ohta. This work was supported by JSPS KAKENHI Grant Numbers JP25103008, JP15K05199, JP16H03949 and JP17J05270, and the Cooperative Research Program of the ‘Network Joint Research Center for Materials and Devices’ No. 20175002 (to Y.K.) and No. 20173006 (to H.K.).
Publisher Copyright:
© The Royal Society of Chemistry 2019.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

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U2 - 10.1039/9781788013499-00031

DO - 10.1039/9781788013499-00031

M3 - Chapter

AN - SCOPUS:85058894970

T3 - RSC Theoretical and Computational Chemistry Series

SP - 31

EP - 62

BT - Self-organized Motion

A2 - Lagzi, Istvan

A2 - Pimienta, Veronique

A2 - Suematsu, Nobuhiko J.

A2 - Nakata, Satoshi

A2 - Kitahata, Hiroyuki

PB - Royal Society of Chemistry

ER -