Mixing of a confined two-layer stratified liquid by a bubble plume

Bubble plumes are often encountered in numerous industrial applications where the gas-liquid two phase interaction is used to promote the mixing of the liquid phase. The current work is focused on the investigation of the mixing behavior of bubble plumes produced by a circular source in confined two-layer stratified fluids. In analogy to the study of linear stratification, two non-dimensional parameters PN_EQ (=NEQ3H4/QBg\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {N}_{EQ}^3{H}^4/{Q}_Bg $$\end{document}, where NEQ is the equivalent linear buoyancy frequency, H is the water depth, QB is the gas flow rate, and g is the gravity acceleration) and MH (=QBg/4πα2us3H\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ {Q}_Bg/\left(4\pi {\alpha}^2{u}_s^3H\right) $$\end{document}, where α is the entrainment coefficient and us is the slip velocity) are selected to investigate the flow patterns and mixing efficiency in two-layer stratified fluids. The equivalent linear buoyancy frequency NEQ of the two-layer stratification is proposed to calculate the non-dimensional parameter PN_EQ. The flow structure of a bubble plume in two-layer stratified fluids is introduced in detail. The correlations of the non-dimensional parameters with the bubble plume properties, such as the flow patterns, initial destratification height and mixing efficiency, are obtained. The results show that correlations with the non-dimensional parameter PN_EQ can be successfully used to predict the bubble plume behavior in a confined two-layer stratified fluids.