Review of potential flow solutions for velocity and shape of long isolated bubbles in vertical pipes

The motion of elongated gas bubbles in vertical pipes has been studied extensively over the past century. A number of empirical and numerical correlations have emerged out of this curiosity; amongst them, analytical solutions have been proposed. A review of the major results and resolution methods based on a potential flow theory approach is presented in this article. The governing equations of a single elongated gas bubble rising in a stagnant or moving liquid are given in the potential flow formalism. Two different resolution methods (the power series method and the total derivative method) are studied in detail. The results (velocity and shape) are investigated with respect to the surface tension effect. The use of a new multi-objective solver coupled with the total derivative method improves the research of solutions and demonstrates its validity for determining the bubble velocity. This review aims to highlight the power of analytical tools, resolution methods and their associated limitations behind often well-known and wide-spread results in the literature.

Influence of Temperature on Rising Bubble Dynamics in Water and n-pentanol Solutions

Data in the literature on the influence of water temperature on the terminal velocity of a single rising bubble are highly contradictory. Different variations in bubble velocity with temperature are reported even for potentially pure systems. This paper presents a systematic study on the influence of temperature between 5 °C and 45 °C on the motion of a single bubble of practically constant size (equivalent radius 0.74 ± 0.01 mm) rising in a clean water and n-pentanol solution of different concentrations. The bubble velocity was measured by a camera, an ultrasonic sensor reproduced in numerical simulations. Results obtained by image analysis (camera) were compared to the data measured by an ultrasonic sensor to reveal the similar scientific potential of the latter. It is shown that temperature has a significant effect on the velocity of the rising bubble. In pure liquid, this effect is caused only by modifying the physicochemical properties of the water phase, not by changing the hydrodynamic boundary conditions at the bubble surface. In the case of the solutions with surface-active substances, the temperature-change kinetics of the dynamic adsorption layer formation facilitate the immobilization of the liquid/gas interface.

Review of Single Bubble Motion Characteristics Rising in Viscoelastic Liquids

The emphasis of this review is to discuss three peculiar phenomena of bubbles rising in viscoelastic fluids, namely, the formation of a cusp, negative wake, and velocity jump discontinuity, and to highlight the possible future directions of the subject. The mechanism and influencing factors of these three peculiar phenomena have been discussed in detail in this review. The evolution of the bubble shape is mainly related to the viscoelasticity of the fluid. However, the mechanisms of the two-dimensional cusp, tip-streaming, “blade-edge” tip, “fish-bone” tip, and the phenomenon of the tail breaking into two different threads, in some special viscoelastic fluids, are not understood clearly. The origin of the negative wake behind the bubbles rising in a viscoelastic fluid can be attributed to the synergistic effect of the liquid-phase viscoelasticity, and the bubbles are large enough; thus, leading to a very long relaxation time taken by the viscoelastic stresses. For the phenomenon of bubble velocity jump discontinuity, viscoelasticity is the most critical factor, and the cusp of the bubbles and the surface modifications play only ancillary roles. It has also been observed that a negative wake does not cause velocity jump discontinuity.

Bubble wall velocity at strong coupling

Using the holographic correspondence as a tool, we determine the steady-state velocity of expanding vacuum bubbles nucleated within chiral finite temperature first-order phase transitions occurring in strongly coupled large N QCD-like models. We provide general formulae for the friction force exerted by the plasma on the bubbles and for the steady-state velocity. In the top-down holographic description, the phase transitions are related to changes in the embedding of $$ Dq\hbox{-} \overline{D}q $$ Dq ‐ D ¯ q flavor branes probing the black hole background sourced by a stack of N Dp-branes. We first consider the Witten-Sakai-Sugimoto $$ D4\hbox{-} D8\hbox{-} \overline{D}8 $$ D 4 ‐ D 8 ‐ D ¯ 8 setup, compute the friction force and deduce the equilibrium velocity. Then we extend our analysis to more general setups and to different dimensions. Finally, we briefly compare our results, obtained within a fully non-perturbative framework, to other estimates of the bubble velocity in the literature.

Velocity bias in intrusive gas-liquid flow measurements

Gas–liquid flows occur in many natural environments such as breaking waves, river rapids and human-made systems, including nuclear reactors and water treatment or conveyance infrastructure. Such two-phase flows are commonly investigated using phase-detection intrusive probes, yielding velocities that are considered to be directly representative of bubble velocities. Using different state-of-the-art instruments and analysis algorithms, we show that bubble–probe interactions lead to an underestimation of the real bubble velocity due to surface tension. To overcome this velocity bias, a correction method is formulated based on a force balance on the bubble. The proposed methodology allows to assess the bubble–probe interaction bias for various types of gas-liquid flows and to recover the undisturbed real bubble velocity. We show that the velocity bias is strong in laboratory scale investigations and therefore may affect the extrapolation of results to full scale. The correction method increases the accuracy of bubble velocity estimations, thereby enabling a deeper understanding of fundamental gas-liquid flow processes.

Comparison of Two Solvers for Simulation of Single Bubble Rising Dynamics: COMSOL vs. Fluent

Multiphase flows are a part of many industrial processes, where the bubble motion influences the hydrodynamic behavior of the batch. The current trend is to use numerical solvers that can simulate the movement and mutual interactions of bubbles. The aim of this work was to study how two commercial CFD solvers, COMSOL Multiphysics and Ansys Fluent, can simulate the motion of a single rising bubble in a stagnant liquid. Simulations were performed for spherical or slightly deformed bubbles (Db = 0.6, 0.8, and 1.5 mm) rising in water or in propanol. A simple 2D axisymmetric approach was used. Calculated bubble terminal velocities and bubble shape deformations were compared to both experimental data and theoretical estimations. Solver Comsol Multiphysics was able to precisely calculate the movement of smaller and larger bubbles; due to the 2D rotational symmetry, better results were obtained for small spherical bubbles. The deformation of larger bubbles was calculated sufficiently. Solver Ansys Fluent, in the setting used, failed to simulate the motion of small bubbles due to parasitic currents but allowed for modeling of the motion of larger bubbles. However, the description of the bubble velocity and shape was worse in comparison with experimental values.