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Energetics-based model for a diffusiophoretic motion of a deformable droplet.

Hiroyuki Kitahata1, Yuki Koyano2, Yasuaki Kobayashi3,4

  • 1Chiba University, Department of Physics, Graduate School of Science, Chiba 263-8522, Japan.

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Summary

This study models deformable droplets undergoing diffusiophoretic motion. Three stable states were identified: immobile circular, immobile elliptical, and mobile elliptical, with transitions between them discussed.

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Area of Science:

  • Physical Chemistry
  • Fluid Dynamics
  • Soft Matter Physics

Background:

  • Diffusiophoresis drives particle motion via chemical gradients.
  • Droplet deformation influences its transport dynamics.
  • Surface tension gradients are key in interfacial phenomena.

Purpose of the Study:

  • To develop a mathematical model for the diffusiophoretic motion of a deformable droplet at a liquid surface.
  • To investigate the role of droplet deformation in diffusiophoretic transport.
  • To identify and analyze the stable states of the droplet system.

Main Methods:

  • Constructed a free energy functional including surface and line energies.
  • Derived time-evolution equations for translational and elliptical deformation.
  • Analyzed droplet behavior by considering second-mode deformation.

Main Results:

  • Identified three distinct stable states for the droplet: immobile circular, immobile elliptical, and mobile elliptical.
  • The mobile state features elliptical deformation with the minor axis aligned with the motion direction.
  • Characterized the transitions between these stable states.

Conclusions:

  • The mathematical model successfully captures the diffusiophoretic motion of deformable droplets.
  • Droplet deformation significantly impacts its stable states and motility.
  • Understanding these states is crucial for controlling droplet behavior in microfluidic and interfacial systems.