On the autonomous motion of active drops or bubbles

Area of Science:

• Fluid dynamics
• Chemical kinetics
• Surface phenomena

Background:

• Non-isothermal surface chemical reactions in drops generate thermo-capillary stresses.
• These stresses are influenced by reactant diffusion and drop motion.
• Such stresses can induce or prevent drop movement under external forces.

Purpose of the Study:

• To quantitatively investigate autonomous motion of millimeter-sized drops driven by internal endo- or exothermic reactions.
• To analyze the interplay between reaction kinetics, fluid dynamics, and surface tension gradients.

Main Methods:

• The study employs Stokes flow hydrodynamics and a boundary layer approximation for high solute Peclet numbers.
• Analysis focuses on the Marangoni effect driven by surface tension gradients.
• Mathematical expressions for forces and velocity fields are derived.

Main Results:

• Conditions for autonomous, constant-velocity motion of reactive drops are established.
• The balance of forces, including viscous drag, determines the drop's motion.
• Explicit formulas for the force on the drop and internal/external velocity fields are presented.

Conclusions:

• Thermo-capillary stresses from surface reactions can lead to self-propulsion in drops.
• The Marangoni effect plays a crucial role in mediating this motion.
• The derived theoretical framework provides a quantitative tool for understanding reactive drop dynamics.