Drag Coefficient Prediction of a Single Bubble Rising in Liquids

Abstract

The motion of single bubbles rising in 2-octanol solutions was investigated experimentally. By using a high-speed video system to follow the rising bubble, the sequences of the recorded frames were digitized and analyzed using image analysis software. The periodical fluctuation of the bubble terminal velocity was observed, which is indicative of a nonconstant bubble drag coefficient. Then, the measured drag coefficient was compared with correlations available in the literature. The comparison shows that these correlations cannot give fully satisfactory results in predicting the fluctuated drag coefficient. Using the extensive experimental data, the authors proposed a new correlation to predict the drag coefficient calculated from the fluctuated motion with the added mass force and history force included. In virtue of nonlinear curve fitting, the drag coefficient of the single bubble is correlated as a function of the Re number, Eo number, We number, and Mo number based on the equivalent bubble diameter. This new model successfully predicts the periodical fluctuations of the drag coefficients. For the standard drag prediction (when averaged terminal velocity is used), this model agrees better with our experimental results and has a maximum relative error of 2.2% and an average relative error of 0.87%. This model is also verified by bubble rising in methyl isobutyl carbinol cas (MIBC) and OP-10 (C 32 H 58 O 10 ) aqueous solutions, and the errors are similar to that of 2-octanol solutions. On the basis of a comparison with measurements in other liquids from the literature, this new correlation represents well the experimental data which covers 21 pure liquids and contaminated liquids in a very wide range of parameters as follows: 10 −3 ≤ Re ≤ 10 5 , 10 −2 ≤ Eo ≤ 10 3 , and 10 −14 ≤ Mo ≤ 10 7 . This work is an extension of our previous one (Yan et al. Chem. Eng. J. 2017, 316, 553) in which the old correlation predicts the fluctuated drag coefficient for bubble rising in pure water.

A Review of Drag Coefficient Models in Gas‐Liquid Two‐Phase Flow

“…Neither viscous nor inertial forces can be neglected in this range, so it is almost impossible to obtain the exact C Dp -Re p relationship by solving the N-S equation. The method to determine that relationship in this range is usually by fitting the desired equation from the experimental data which is new experimental data supplemented by existing experimental data in the literature [20,[27][28][29][30]. Clift [31] states that the total drag force on a spherical particle in an infinite fluid medium in any flow pattern is the sum of the laminar component (extended Stokes law) and the turbulent com-ponent (Newton's law).…”

“…They obtain a correlation of the drag coefficient involving the Eo, Re and We with a periodical fluctuation feature. Then Yan et al [30] measure the motion of a single bubble rising in 2-octanol solutions.…”

“…Then Yan et al. 30 measure the motion of a single bubble rising in 2‐octanol solutions. They propose a new correlation that can successfully predict the periodical fluctuations of the drag coefficient, whether in pure liquids or contaminated liquids.…”

Experimental Study on Bubble Dynamics and Mass Transfer Characteristics of Coaxial Bubbles in Petroleum-Based Liquids

“…Shi et al examined the influence of orifice diameter and superficial gas velocity on bubble dynamics and mass transfer in NaOH aqueous solutions. Different literature sources presented the drag model of the bubble in experiments calculated with the Reynolds number ( Re ), Weber number ( We ), and Morton number ( Mo ). − They are defined respectively as italicRe = ρ normall d normale U μ normall italicWe = ρ normall d normale U 2 σ italicMo = g μ normall 4 ( ρ l − ρ g ) ρ normall 2 σ 3 in which ρ l and ρ g are the density of liquid and gas, respectively; μ l and σ are the liquid viscosity and the liquid surface tension, respectively; U is the bubble velocity; and d e is the bubble equivalent diameter. Cai et al investigated with deionized water and glycerol aqueous solution as liquid and improved and extended the work of Jamialahmadi et al They obtained a new drag coefficient model that is applicable to a broad range of system properties.…”

Review of Single Bubble Motion Characteristics Rising in Viscoelastic Liquids

“…While the abovementioned processes encounter bubble swarms, understanding the behavior of the motion of a single bubble can provide important insights for optimally designing the processes involving bubble swarms. Consequently, efforts have been made to explore the velocity, shape, trajectory, drag coefficients, and flow field of a single bubble rising in the liquid phase [7][8][9][10][11]. Nevertheless, most of these studies focus on Newtonian fluids, whereas a viscoelastic fluid is a very important type of non-Newtonian fluid that possesses viscosity as well as elasticity, and the behavior of bubbles in this fluid type is quite different from that in Newtonian fluids.…”