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The mathematical model for the secondary breakup of dropping liquid


[ 1 ] Instytut Technologii i Inżynierii Chemicznej, Wydział Technologii Chemicznej, Politechnika Poznańska | [ 2 ] Instytut Inżynierii Środowiska i Instalacji Budowlanych, Wydział Inżynierii Środowiska i Energetyki, Politechnika Poznańska | [ P ] employee

Scientific discipline (Law 2.0)

[2.10] Environmental engineering, mining and energy
[7.6] Chemical sciences

Year of publication


Published in


Journal year: 2020 | Journal volume: vol. 13 | Journal number: no. 22

Article type

scientific article

Publication language


  • oscillatory wall
  • vibrational impact
  • Weber number
  • critical value
  • nonstable droplet

EN Investigating characteristics for the secondary breakup of dropping liquid is a fundamental scientific and practical problem in multiphase flow. For its solving, it is necessary to consider the features of both the main hydrodynamic and secondary processes during spray granulation and vibration separation of heterogeneous systems. A significant difficulty in modeling the secondary breakup process is that in most technological processes, the breakup of droplets and bubbles occurs through the simultaneous action of several dispersion mechanisms. In this case, the existing mathematical models based on criterion equations do not allow establishing the change over time of the process’s main characteristics. Therefore, the present article aims to solve an urgent scientific and practical problem of studying the nonstationary process of the secondary breakup of liquid droplets under the condition of the vibrational impact of oscillatory elements. Methods of mathematical modeling were used to achieve this goal. This modeling allows obtaining analytical expressions to describe the breakup characteristics. As a result of modeling, the droplet size’s critical value was evaluated depending on the oscillation frequency. Additionally, the analytical expression for the critical frequency was obtained. The proposed methodology was derived for a range of droplet diameters of 1.6–2.6 mm. The critical value of the diameter for unstable droplets was also determined, and the dependence for breakup time was established. Notably, for the critical diameter in a range of 1.90–2.05 mm, the breakup time was about 0.017 s. The reliability of the proposed methodology was confirmed experimentally by the dependencies between the Ohnesorge and Reynolds numbers for different prilling process modes.

Date of online publication


Pages (from - to)

6078-1 - 6078-17





Article number: 6078

License type

CC BY (attribution alone)

Open Access Mode

open journal

Open Access Text Version

final published version

Date of Open Access to the publication

at the time of publication

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