On the autonomous motion of active drops or bubbles

Abstract

Thermo-capillary stresses on the surface of a drop can be the result of a non-isothermal surface chemical conversion of a reactant dissolved in the host fluid. The strength of heat production (with e.g. absorption) on the surface is ruled by the diffusion of the reactant and depends on the state of motion of the drop. Such thermo-capillary stresses can provoke the motion of the drop or its motionless state in the presence of an external body force. If in the balance of forces, including indeed viscous drag, the net resultant force vanishes there is the possibility of autonomous motion with constant velocity of the drop. Focusing on drops with radii in the millimeter range provided here is a quantitative study of the possibility of such autonomous motion when the drop, considered as active unit, is seat of endo- or exo-thermic reactive processes that dominate its motion. The framework is restricted to Stokes flows in the hydrodynamics, negligible heat Peclet number while the solute Peclet number is considered very high. A boundary layer approximation is used in the description of reactant diffusion. Those processes eventually end up in the action being expressed by surface tension gradients and the Marangoni effect. Explicit expressions of the force acting on the drop and the velocity fields inside and outside the drop are provided. Some significant particular cases are discussed to illustrate the usefulness of the theory.