Collapse of Air Bubbles as Oxygen Provider in Wastewater Aeration Tank

This paper aims to investigate the role of surrounding parameters on the collapsing of convective air bubbles in the biological stage of wastewater treatment. The diffusion field is assumed to be quasi-static. The mathematical model describing the current problem consists of diffusion, Fick's, and Laplace equations. The system is solved analytically to obtain the evolution formulae of both the collapsing bubble radius and concentration distribution around the collapsing bubble in terms of surrounding parameters. The validity of this model is examined by applying the resultant evolution equation to fit earlier experimental data of the collapsing of an air bubble in water, and good agreement with this experimental data is achieved. The results show that increasing values of the diffusion coefficient, initial concentration difference, wastewater temperature, and initial void fraction result in a decrease in the collapsing time of the air bubble in wastewater whereas increasing values of the surface tension result in an increase of collapsing time. In addition, the collapsing of the air bubble is sensitive to small changes in the values of the diffusivity coefficient and initial concentration difference which is affected by the rate of oxygen consumption by the microorganisms during the biological stage of wastewater treatment. On the contrary, the collapsing process is slightly affected by changes in the surface tension values.


Introduction
To protect the environment, water resources, and the general public's Wastewater treatment is an important application of bubble dynamics.
Wastewater treatment is carried out in

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At a great distance from the bubble Polluted water comes in various types, and how it is treated depends on the type and features of the wastewater.For instance: Black water and grey water are two categories for domestically polluted water.Toilets or ewage are the sources of black water.Showers, sinks, and floor washing all produce gray water (FAO, 2003).Any water that has been impacted by human activity is considered to be polluted.Water that has been used for household, mechanical, commercial, or agricultural purposes, surface runoff or storm water, and any sewer input or sewer penetration is considered polluted water.Due to global water shortage challenges, it is essential to consider non-conventional water sources to meet the growing demand for freshwater.Polluted water is seen as a potential alternative to deal with the shortage of water supply that results from a variety of factors, such as population growth (Noori et al., 2014).Because of there is a wide variety of wastewater sources, which can include both organic and inorganic materials, it is necessary to periodically monitor the water's state in order to assess any potential risks to the environment as a whole (FAO, 2003).
, which is the sludge and air.In other words, the oxygen provided by gas bubbles, combined with the food source, sewage, allows the bacteria to produce enzymes which help break down the waste so that it can settle in the secondary clarifiers or be filtered by membranes.The aeration system in a wastewater or sewage treatment plant consumes an average of 50 to 70 percent of the energy of the entire plant (Spellman, 2013), which maximizes the needs to exert more efforts to find optimal bubble sizes and understanding dynamics as oxygen provider in aeration tanks to increase the efficiency and reduce the cost which represents the main goal of this study and our future studies in this field.This paper is devoted to depicting the role of bubble collapse as oxygencarrier to microorganisms used in the biological treatment of wastewater.The obtained results are presented to the specialists as helpful knowledge in designing biological treatment tanks for wastewater treatment.The formulation of this study consists of representing the problem of collapsing of an air bubble in aeration tank by a system of differential equations, which is solved analytically for the given boundary, initial and final values to obtain equations of evolution of bubble radius and concentration distribution of oxygen around the collapsing bubble.The validity of the model results is checked by applying the equation representing the bubble radius evolution to fit the experimental data of Shimiya and Yano (Shimiya and Yano, 1987) that conducted to express the collapse of an air bubble in waterthe bubble at complete collapse.We devote our efforts to represent a mathematical relation that correlates the evolution of the bubble radius to the elapsed collapse time in combination with the effect of surrounding physical parameters such as surface tension, ambient pressure, By using the Mathematica program, the following series of graphs are obtained which depict the effect of surrounding parameters on the bubble collapse in wastewater treatment.

Fig. ( 2 Figure
Fig. (2): The collapse behaviour of air bubble in aeration tank at different values of the diffusivity coefficient