Buoyancy-driven attraction of active droplets

Area of Science:

• Soft Matter Physics
• Fluid Dynamics
• Chemical Engineering

Background:

• Active oil droplets in ambient liquids typically exhibit repulsive interactions due to the Marangoni effect.
• Buoyancy effects arising from density differences are often neglected in studies of active droplet interactions.
• Recent experiments suggest buoyancy-driven convection can lead to active droplet clustering.

Purpose of the Study:

• To numerically investigate the role of buoyancy effects on the interaction and behavior of active oil droplets.
• To analyze how buoyancy, in addition to Marangoni flow, influences droplet attraction and repulsion.
• To determine the dependence of droplet interactions on key control parameters: Péclet number (Pe), Galileo number (Ga), and solutal Rayleigh number (Ra).

Main Methods:

• Numerical simulations were employed to model active oil droplet dynamics.
• The study incorporated both Marangoni-driven propulsion (Pe) and buoyancy effects (Ga, Ra).
• Analysis focused on the attractive and repulsive behaviors of neighboring droplets under varying parameter conditions.

Main Results:

• Marangoni effect causes droplet repulsion, while buoyancy of the reaction product induces attraction.
• Sufficiently high solutal Rayleigh number (Ra) can lead to droplet collisions.
• Increasing Galileo number (Ga) delays droplet collisions.
• Attractive velocity (Red) is proportional to Ra^(1/4)/(ℓ/R), and repulsive velocity (Rerep) is proportional to Pe*Ra^(-0.38).

Conclusions:

• Buoyancy effects, particularly from the diffusing product, are crucial in governing active droplet interactions and can overcome Marangoni repulsion.
• The interplay between attractive (buoyancy) and repulsive (Marangoni) forces dictates droplet aggregation and collision dynamics.
• A balance condition (Pe ~ Ra^0.63) accurately predicts the transition between non-colliding and colliding regimes.