Phase transitions, crystal growth

Homogeneous nucleation and diffusion-driven growth of a nanoparticle under ultrasonic excitation

S. Sh. Rekhviashvili

Institute of Applied Mathematics and Automation, Nalchik

Abstract: A theoretical model is proposed for the homogeneous nucleation and growth of an individual nucleus (nanoparticle) in a liquid-phase medium under ultrasonic excitation. The model combines a thermodynamic approach, which enables calculation of the nucleation work and the critical radius of the nucleus in a non-stationary pressure field, with a kinetic description of diffusion-driven mass transfer and the growth of an individual nanoparticle under acoustic oscillations. The proposed approach establishes a relationship between the intensity of ultrasonic exposure and the characteristics of nanoparticle formation and can also serve as a basis for constructing the statistical size distribution of nanoparticles.

Keywords: homogeneous nucleation, ultrasonic treatment, critical nucleus radius, diffusion growth, acoustic oscillations, nanoparticle, thermodynamic model, kinetic mode.

Received: 19.09.2025
Revised: 28.09.2025
Accepted: 29.09.2025

DOI: 10.61011/FTT.2025.09.61625.258-25

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