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This study presents a new theoretical framework for microbubble size variation, crucial for industrial applications. We demonstrate that microbubble size distribution scales with height, not time, offering novel insights into Ostwald ripening.

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Area of Science:

  • Fluid dynamics
  • Colloid science
  • Materials science

Background:

  • Microbubble solutions are vital in heat transfer, agriculture, and water treatment.
  • Controlling microbubble size is critical for optimizing industrial processes.
  • Ostwald ripening significantly influences microbubble size distribution over time.

Purpose of the Study:

  • To develop a theoretical framework for Ostwald ripening of buoyancy-driven microbubbles.
  • To introduce a height-dependent size distribution function for microbubbles.
  • To analyze the steady-state population balance equation within the Lifshitz-Slyozov-Wagner theory.

Main Methods:

  • Development of a theoretical framework for buoyancy-driven microbubble Ostwald ripening.
  • Introduction of a height-dependent size distribution function.
  • Redefinition of the distribution function as the density distribution of buoyancy-induced flux.

Main Results:

  • The steady-state population balance equation is interpretable within the Lifshitz-Slyozov-Wagner theory.
  • The microbubble size distribution function approaches a scaled universal distribution as a function of height.
  • The fifth power of the mean bubble radius grows linearly with height.

Conclusions:

  • A novel theoretical framework for microbubble Ostwald ripening based on height-dependent distribution is established.
  • The findings offer new perspectives on Ostwald ripening dynamics, independent of time.
  • The linear growth of mean bubble radius with height provides a predictable model for industrial applications.