Collapse of Air Bubbles as Oxygen Provider in Wastewater Aeration Tank

Abstract

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.