Mathematical Modeling of Oxygen Transfer Using a Bubble Generator at a High Reynolds Number: A Partial Differential Equation Approach for Air-to-Water Transfer
Abstract
:1. Introduction
2. Materials and Methods
2.1. The Fine Bubble Generator with the Plate with Orifices in Rotational Motion
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- A high Reynolds number indicates turbulent flow, which enhances mixing and mass transfer rates.
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- The bubbles have a constant size, neglecting variations due to changes in hydrostatic pressure or coalescence/breakup dynamics.
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- The bubbles are uniformly distributed within the fluid.
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- Homogeneity in fluid properties (density, viscosity, diffusivity).
2.2. Solving the Differential Equation of Diffusion with the Term “Source”
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- According to the order of the partial derivatives, they are classified into first-order, second-order, and n-order equations;
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- According to the character of linearity, they are divided into linear, quasi-linear, and nonlinear equations;
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- According to the type of influence of the integration domain on the solution at a point, they are divided into elliptic, parabolic, and hyperbolic equations;
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- According to the general form of a linear differential equation with partial derivatives with two variables [29]
3. Results
4. Discussion
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Characteristic | Notation | Value |
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Initial dissolved oxygen concentration | C0 | 3.12 mg/dm3 |
Dissolved oxygen concentration at saturation | Cs | 8.3 mg/dm3 |
Water temperature | t | 24 °C |
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Constantin, M.; Dobre, C.; Oprea, M. Mathematical Modeling of Oxygen Transfer Using a Bubble Generator at a High Reynolds Number: A Partial Differential Equation Approach for Air-to-Water Transfer. Inventions 2024, 9, 76. https://doi.org/10.3390/inventions9040076
Constantin M, Dobre C, Oprea M. Mathematical Modeling of Oxygen Transfer Using a Bubble Generator at a High Reynolds Number: A Partial Differential Equation Approach for Air-to-Water Transfer. Inventions. 2024; 9(4):76. https://doi.org/10.3390/inventions9040076
Chicago/Turabian StyleConstantin, Mihaela, Cătălina Dobre, and Mugurel Oprea. 2024. "Mathematical Modeling of Oxygen Transfer Using a Bubble Generator at a High Reynolds Number: A Partial Differential Equation Approach for Air-to-Water Transfer" Inventions 9, no. 4: 76. https://doi.org/10.3390/inventions9040076