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<p>Results of theoretical analysis of the laws of oxygen mass transfer from the air bubbles floating up in water in different hydrodynamic regimes are presented. It is shown that the currently accepted theoretical models of diffusion of the air oxygen into water, such as the Lewis–Whitman two-film model, the Higbie penetration model, and the Danckwerts surface renewal model, can be used for the definition of the mass transfer from the air bubbles floating up in water in the hydrodynamic Stokes regime, the laminar regime with a slipping boundary layer, and the turbulent regime. On the basis of the thermodynamic approach involving analysis of the energy characteristics of the deformed air bubbles floating up in water in the turbulent regime, equations, allowing one to determine the factor of renewal of the surface of a bubble, used in the Danckwerts theoretical model, have been derived. The results obtained can be used for the assessment of the influence of a change in the geometric and thermodynamic characteristics of the air bubbles, floating up in fine-bubble aeration systems in the turbulent regime, on the technical characteristics of these systems.</p>

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Theoretical Analysis of the Laws of Oxygen Mass Transfer in Dynamic Dispersed Water–Air Systems

  • 期刊论文

  • 发表日期：

    2026年3月1日

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  • S. Yu. Andreev,
  • M. A. Safronov,
  • K. V. Lebedinskii,
  • L. V. Belova

摘要

Results of theoretical analysis of the laws of oxygen mass transfer from the air bubbles floating up in water in different hydrodynamic regimes are presented. It is shown that the currently accepted theoretical models of diffusion of the air oxygen into water, such as the Lewis–Whitman two-film model, the Higbie penetration model, and the Danckwerts surface renewal model, can be used for the definition of the mass transfer from the air bubbles floating up in water in the hydrodynamic Stokes regime, the laminar regime with a slipping boundary layer, and the turbulent regime. On the basis of the thermodynamic approach involving analysis of the energy characteristics of the deformed air bubbles floating up in water in the turbulent regime, equations, allowing one to determine the factor of renewal of the surface of a bubble, used in the Danckwerts theoretical model, have been derived. The results obtained can be used for the assessment of the influence of a change in the geometric and thermodynamic characteristics of the air bubbles, floating up in fine-bubble aeration systems in the turbulent regime, on the technical characteristics of these systems.