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The Einstein-Stokes equation accurately predicts nanoparticle diffusion but deviates for nanobubbles larger than 3 nm. This deviation in ultrafine bubble size analysis is due to nanobubble deformability, impacting Brownian motion calculations.

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Area of Science:

  • Physical Chemistry
  • Nanotechnology
  • Fluid Dynamics

Background:

  • Physicochemical properties of ultrafine bubbles depend on their size, necessitating accurate size determination.
  • Current methods like dynamic light scattering and nanoparticle tracking analysis rely on the Einstein-Stokes equation for nanometer-sized bubbles.
  • The applicability of the Einstein-Stokes equation to ultrafine bubbles remains unclear.

Purpose of the Study:

  • To evaluate the applicability of the Einstein-Stokes equation for gas nanobubbles (diameter < 10 nm).
  • To compare the diffusion behavior of nanobubbles with rigid nanoparticles and vacuum nanobubbles.
  • To identify factors causing deviations from the Einstein-Stokes equation for nanobubbles.

Main Methods:

  • Atomic molecular dynamics simulations were employed.
  • Simulations included methane nanobubbles, vacuum nanobubbles, and copper nanoparticles in water.
  • Diffusion coefficients were calculated and compared against the Einstein-Stokes equation predictions.

Main Results:

  • The Einstein-Stokes equation accurately predicted the diffusion coefficient for rigid nanoparticles, with minor deviations for radii < 1 nm.
  • Significant deviations from the Einstein-Stokes equation were observed for nanobubbles with radii > 3 nm.
  • Nanobubble deformability was identified as the cause of deviation, creating a cushioning effect during diffusion.

Conclusions:

  • The Einstein-Stokes equation is not universally applicable for determining the size of nanobubbles.
  • Nanobubble deformability significantly influences their diffusion dynamics, challenging standard measurement techniques.
  • Further research is needed to refine models for ultrafine bubble characterization.