Probability density functions for bubble size distribution in air–water systems in stirred tanks

ABSTRACT

Bubble size distribution (BSD) is relevant to the design of gas–liquid systems, as it determines the interfacial area available in heat and mass transfer processes. Although data on BSD in stirred aerated tanks are available, a systematic comparison of alternative modeling functions for these data is lacking. In this work, BSDs obtained in air–water dispersions in a stirred aerated tank with a Rushton turbine and BSDs available in the literature for similar systems were modeled by 14 empirical probability density functions (PDFs). It was found that both the distribution of Nukiyama–Tanasawa with three adjustable parameters and the Rosin–Rammler distribution with two adjustable parameters reasonably fit original and literature BSDs. It is also concluded that it is possible to correlate the PDF parameters with the power dissipated by the agitator in the liquid phase, allowing the BSD to be modeled with only two parameters in a range of dissipated power from 0.5 to 2.3 kW/m³. BSDs thus modeled provide good predictions of average bubble size.

KEYWORDS:

• Nukiyama–Tanasawa distribution
• particle size distribution
• probability density function
• Rosin–Rammler distribution
• Sauter mean diameter
• two-phase flow

Abbreviations:

• BE, bi-exponential distribution
• BS, Birnbaum–Saunders distribution
• BSD, bubble size distribution
• CDF, cumulative distribution function
• CFD, computational fluid dynamics
• F, Frechet distribution
• G, gamma distribution
• G–L, gas–liquid
• IG, inverse Gaussian distribution
• J, Johnson distribution
• LH4, four parameter log-hyperbolic distribution
• LL, log-logistic distribution
• LN, log-normal distribution
• N, normal distribution
• NT, two-parameter Nukiyama–Tanasawa distribution
• NT3, three-parameter Nukiyama–Tanasawa distribution
• PDF, probability density function
• PSD, particle size distribution
• RR, Rosin–Rammler distribution
• UL3, upper limit distribution