Chapter 14: Theory of Active Particles and Drops Driven by Chemical Reactions: The Role of Hydrodynamics on Self-propulsion and Collective Behaviours

In this chapter, we discuss the mechanism of self-propulsion using simple theoretical models. Particular focus is placed on the roles of hydrodynamic flow on self-propelled particles and drops. We also theoretically investigate self-propelled motion of chemically driven drops. The motion is driven by hydrodynamic flow resulting from the Marangoni effect and occurs for drops under an isotropic chemical reaction rather than under an anisotropic temperature and/or concentration gradient. This occurs even under the low Reynolds number in which fluid flow is described by the linear equations. We propose the mechanism of spontaneous symmetry breaking where hydrodynamics plays a significant role when coupled with nonlinear effects. We summarize the basic theoretical aspects of this phenomena including the reaction-diffusion equations and the hydrodynamic equation. We also discuss the collective behaviours of the drops by analysing the interaction between the self-propelled drops.