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Interaction of Fine-Dispersed Particles in Ultrasonic Field

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Fibre Chemistry Aims and scope

Aerosols of chemical mineral and organic fibres pose a serious threat to the sanitary air condition in some industries. It is known that to combat suspended particles, it is possible to expose them with ultrasonic oscillations. However, as applied to suspended fibres, the ultrasonic exposure modes, identified for spherical particles, turn out to be inapplicable. It is due to the complex rotational nature of fibrous particles motion in an ultrasonic field. In this study, the frequency and level of ultrasonic exposure, which provide the minimum time for particles to approach each other, depending on their size, have been determined. Mathematical models of the behaviour of a separate suspended particle and the spatial single interaction of two particles in an ultrasonic field have been considered. The influence of the gaseous medium viscosity has been considered, which made it possible to determine the shape of the resulting particle agglomerates for the first time.

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Authors and Affiliations

  1. Biysk Technological Institute: Branch of the Polzunov Altai State Technical University (AltSTU), Biysk, Russia

    A. V. Shalunov, R. N. Golykh, V. A. Nesterov & A. S. Bochenkov

Authors
  1. A. V. Shalunov
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  2. R. N. Golykh
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  3. V. A. Nesterov
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  4. A. S. Bochenkov
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Corresponding author

Correspondence to A. V. Shalunov.

Additional information

Translated from Khimicheskie Volokna, No. 6, pp. 30-32, November-December, 2021.

Appendix

Appendix

$$ {\displaystyle \begin{array}{c}p\left(\mathbf{r}\right)=\sum_{i=1}^3{H}_i^A\frac{\partial }{\partial {x}_i}\left(\frac{1}{X_A}\right)+\sum_{i=1}^3\sum_{j=1}^3{H}_{ij}^A\frac{\partial^2}{\partial {x}_i\partial {x}_j}\left(\frac{1}{X_A}\right)+\sum_{i=1}^3\sum_{j=1}^3\sum_{k=1}^3{H}_{ij k}^A\frac{\partial^3}{\partial {x}_i\partial {x}_j\partial {x}_k}\left(\frac{1}{X_A}\right)+\\ {}+\sum_{i=1}^3\sum_{j=1}^3\sum_{k=1}^3\sum_{h=1}^3{H}_{ij k h}^A\frac{\partial^3}{\partial {x}_i\partial {x}_j\partial {x}_k\partial {x}_h}\left(\frac{1}{X_A}\right)+\cdots +\sum_{i=1}^3{H}_i^B\frac{\partial }{\partial {x}_i}\left(\frac{1}{X_B}\right)+\sum_{i=1}^3\sum_{j=1}^3{H}_{ij}^B\frac{\partial^2}{\partial {x}_i\partial {x}_j}\left(\frac{1}{X_B}\right)+\\ {}+\sum_{i=1}^3\sum_{j=1}^3\sum_{k=1}^3{H}_{ij k}^B\frac{\partial^3}{\partial {x}_i\partial {x}_j\partial {x}_k}\left(\frac{1}{X_B}\right)+\sum_{i=1}^3\sum_{j=1}^3\sum_{k=1}^3\sum_{h=1}^3{H}_{ij k h}^B\frac{\partial^4}{\partial {x}_i\partial {x}_j\partial {x}_k\partial {x}_h}\left(\frac{1}{X_B}\right)+\cdots \end{array}} $$
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Shalunov, A.V., Golykh, R.N., Nesterov, V.A. et al. Interaction of Fine-Dispersed Particles in Ultrasonic Field. Fibre Chem 53, 395–398 (2022). https://doi.org/10.1007/s10692-022-10311-8

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  • DOI: https://doi.org/10.1007/s10692-022-10311-8

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