Mathematical analysis of the droplet motion and the particle motion with the chemical reaction.

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Through collaborative research with experimental groups, the mathematical modeling and analysis of mechanisms for the self-propelled motion of droplets and particles under chemical reactions were investigated. The target experimental systems regard the motion of surfactant particles with stabilizing and destabilizing reactions driving their motions. By means of mathematical modeling, we clarified that the reaction order plays a central role in the oscillating phenomenon of the stabilizing system, and that the chemical product generated within the destabilizing system strongly influences the oscillation mechanism through chemical reaction. Moreover, by introducing a mathematical model for determining the mechanisms governing the motion of self-propelled grains, which oscillate spontaneously, we were able to explain the corresponding oscillation mechanism. Additionally, we analyzed the case where the particle’s geometry, here taken to be an elliptically shaped camphor disk, influences its motion.