Einstein-Stokes relation for small bubbles at the nanoscale

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.