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On the importance of modified continuum mechanics to predict the vibration of an embedded nanosphere in fluid

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Abstract

In this paper, a novel analytical approach based on nonlocal strain gradient theory is proposed to investigate small-scale effects on the radial vibration of isotropic spherical nanoparticles interacting with a viscoelastic fluid. The viscoelastic fluid is assumed to be compressible and takes into account both compressional and shear relaxation processes. The frequency equation is derived by imposing the fluid-nanosphere interface continuity conditions. To demonstrate the validity and accuracy of the approach, a comparison is made with the literature results in some particular cases, which shows a good agreement. Numerical examples are finally conducted to reveal the significance of small-scale effects in the radial vibrations, which need to be included in the nonlocal strain gradient model of submerged spherical nanoparticles. It is found that the vibration behavior greatly depends on the nanosphere size, nonlocal parameter, strain gradient parameter and glycerol-water mixture. Particularly, the small-scale effects play a very pronounced role when the spherical gold nanoparticle radius is smaller than 3 nm. Thus, the obtained frequency equation is very useful to interpret the experimental measurements of vibrational characteristics of nanospheres submerged in a viscoelastic fluid.

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Data Availability

The datasets generated and/or analyzed during the current study are not publicly available but are available from the authors on reasonable request.

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  1. LAMPA, Arts et Metiers Institute of Technology, 2 bd du Ronceray, 49035, Angers, France

    Xin Huang, Adil El Baroudi, Jean Yves Le Pommellec & Amine Ammar

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  1. Xin Huang
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Huang, X., El Baroudi, A., Le Pommellec, J.Y. et al. On the importance of modified continuum mechanics to predict the vibration of an embedded nanosphere in fluid. Z. Angew. Math. Phys. 75, 48 (2024). https://doi.org/10.1007/s00033-024-02193-z

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