Bubble Trajectory Research Articles

Direct numerical simulation of bubble rising in turbulence

We describe the rising trajectory of bubbles in isotropic turbulence and quantify the slowdown of the mean rise velocity of bubbles with sizes within the inertial subrange. We perform direct numerical simulations of bubbles, for a wide range of turbulence intensity, bubble inertia and deformability, with systematic comparison with the corresponding quiescent case, with Reynolds number at the Taylor microscale from 38 to 77. Turbulent fluctuations randomise the rising trajectory and cause a reduction of the mean rise velocity $\tilde {w}_b$ compared with the rise velocity in quiescent flow $w_b$ . The decrease in mean rise velocity of bubbles $\tilde {w}_b/w_b$ is shown to be primarily a function of the ratio of the turbulence intensity and the buoyancy forces, described by the Froude number $Fr=u'/\sqrt {gd}$ , where $u'$ is the root-mean-square velocity fluctuations, $g$ is gravity and $d$ is the bubble diameter. The bubble inertia, characterised by the ratio of inertial to viscous forces (Galileo number), and the bubble deformability, characterised by the ratio of buoyancy forces to surface tension (Bond number), modulate the rise trajectory and velocity in quiescent fluid. The slowdown of these bubbles in the inertial subrange is not due to preferential sampling, as is the case with sub-Kolmogorov bubbles. Instead, it is caused by the nonlinear drag–velocity relationship, where velocity fluctuations lead to an increased average drag. For $Fr > 0.5$ , we confirm the scaling $\tilde {w}_b / w_b \propto 1 / Fr$ , as proposed previously by Ruth et al. (J. Fluid Mech., vol. 924, 2021, p. A2), over a wide range of bubble inertia and deformability.

A hovering bubble with a spontaneous horizontal oscillation

Active matters, characterized by multi-mode motions, have been emerging for both engineering and biological applications. Generally, active objects rely on the symmetry-broken structures, compositions, or interfacial activities through a physical or chemical approach. Here, we report an active bubble spontaneously hovering with a horizontal oscillation at the solid/liquid interface by impacting a stationary laser beam into a liquid through a transparent solid cover. This spontaneous oscillation mode of the bubble synchronizes with that of the interfacial temperature and hydrodynamical flow. A physical mechanism is proposed, and the scaling analysis of the oscillation frequency agrees well with experiments in various liquids under different laser powers. Additionally, the bubble trajectory rotates azimuthally, arising from the symmetry breaking of the vortex pair accompanying the oscillation. Moreover, the double pendulum of oscillation bubbles has been demonstrated, achieving a preferable oscillation direction in a controllable way. These findings would not only advance our understanding of active matters but also shed light on the bubble-mediated technological applications, such as microrobots and drug deliveries.

Uncertainty study of two-phase flow distribution characteristics measurement based on bubble trajectory tracking method

Bubbles undergo complex motions such as nonlinear trajectories in two-phase flow, where the position, velocity magnitude, and direction of bubble centers continuously change as they evolve under the influence of forces. The complexity of bubble trajectory increases the difficulty in measuring the flow field distribution characteristics, which has been understudied in the previous. The bubble trajectory tracking model based on the Monte Carlo method is constructed to study the uncertainty of two-phase flow distribution characteristics measurement by the conductivity probe. The Monte Carlo method is adopted to randomly generate the bubble velocity at the initial moment and the bubble force characteristics are embedded to simulate the three-dimensional motion of the bubble. The influence of various factors on the distribution of effective bubble numbers and velocity relative error at the local point is quantitatively analyzed. It is found that the lateral spacing of the sensors has the greatest influence on the measurement results of small-sized bubbles, the accuracy is greatly reduced when the space is larger than the radius of the measured bubbles. Moreover, the measurement accuracy of the probe for medium-sized bubbles is high, and the effect of bubble lateral velocity and aspect ratio on the effective bubble ratio and velocity relative error is negligible. In addition, the maximum measurement range of the probe at local points is investigated which is found to be 4 mm in the lateral direction and 2 mm in the longitudinal direction. Finally, uniformly distributed bubbles are generated in a 20 mm × 10 mm transverse plane and the distribution of the effective bubble ratio of the probe is found to be consistent at different measurement points, which verifies the reliability of the probe measurement.

Influence of guide groove structure on in-flow drag reduction in spiral axial gas-liquid mixing pumps

Abstract With the onset of the fossil energy crisis, demand for oil has skyrocketed, and the spiral axial flow gas-liquid mixing pump has emerged as the primary piece of equipment for deep-sea oil extraction. However, at high gas content, the problems of separation of mixed media from hydraulic components, gas-liquid separation and gas phase aggregation are faced. The difficulties of gas-phase aggregation and bubble trajectory in the impeller channel have received much attention, while the problem of increased medium flow resistance induced by flow separation has received less attention. The spiral axial gas-liquid mixing pump is numerically calculated using the Eulerian multiphase flow model and the SST k- turbulence model in this work. The pump is designed with the design flow rate Q = 100 m3/h, rotational speed n = 4500 rmin, and head H = 30m by arranging guide slots with different relative depths and different number of slots to reduce the dissipative vortices, thus reducing the flow resistance in the 1/5 region behind the suction surface. The findings reveal that when the relative depth of the slots is 1/7 and the number of guide slots arranged is 5, the highest drag reduction rate in this location is 69.6% under the design flow condition. When the relative depth of the guide channel is1/7 and the number of guide channels is 3, the performance of the mixing pump is improved most, with an efficiency increment of 1.9% and a head increment of 4.2%, which can provide technical support for the flow resistance reduction of gas-liquid mixing pumps.

Mathematical Modeling on the Multiphase Flow during Top–Bottom Combined Blowing Basic Oxygen Furnace Steelmaking Process

A 3D mathematical model on the multiphase flow and splashing phenomenon in a 210 t Basic oxygen furnace converter is established. The turbulent multiphase flow of the molten steel, slag, and oxygen is simulated by the combined realizable k−ε model and volume of fluid model. The trajectory of argon bubbles and the interaction between the molten steel and argon is simulated by the two‐way coupled Lagrangian discrete phase model. Effects of the lance height and bottom‐blowing gas flow rate on the multiphase flow and splashing phenomenon are investigated. The results indicated that the cavity depth is decreased from 0.45 to 0.36 m when the lance height increases from 1700 to 2300 mm. The cavity depth is not significantly affected by the bottom‐blowing argon flow rate with the 44 000 m3 h−1 top‐blowing oxygen flow rate and 1700 mm lance height. The increased lance height resulted in a decrease in splashing. When the oxygen lance height increases from 1700 to 2300 mm, the amount of the splashed molten steel decreases from 3774.3 to 1953.0 kg.

Uncertainties in measurements of bubbly flows using phase-detection probes

The analysis of bubbly two-phase flows is challenging due to their turbulent nature and the need for intrusive phase-detection probes. However, accurately characterizing these flows is crucial for safely designing critical infrastructure such as dams and their appurtenant structures. The combination of dual-tip intrusive phase-detection probes with advanced signal processing algorithms enables the assessment of pseudo-instantaneous 1-D velocity time series; for which the limitations are not fully fathomed. In this investigation, we theoretically define four major sources of error, which we quantify using synthetically generated turbulent time series, coupled with the simulated response of a phase-detection probe. Based on the analysis of 1010 simulated bubble trajectories, our findings show that typical high-velocity flows in hydraulic structures hold up to 15% error in the mean velocity estimations and up to 35% error in the turbulence intensity estimations for the most critical conditions, typically occurring in the proximity of the wall. Based on thousands of simulations, our study provides a novel data-driven tool for the estimation of these baseline errors (bias and uncertainties) in real-word phase-detection probe measurements of bubbly flows (air concentrations c<40%).

Modeling of dynamic bubble deformation and breakup in T-junction channel flow

Bubble deformation and breakup due to strain-rate-induced stress is investigated for a laminar flow configuration. The bubble shape is assumed to be a prolate ellipsoid. A new model for bubble deformation under dynamic load is introduced in the form of an ordinary differential equation for the deformation energy. Breakup is identified with a critical value of the deformation. As an application case, the flow in a joining T-junction is considered with the ratio of the volume flow rate being unity and the outflow Reynolds number being 1800. Dilute, dispersed bubbles with a diameter of 0.5 mm are injected. High-speed shadowgraphy is used and bubble parameters are evaluated via image processing. The capillary number is obtained from a single-phase flow simulation providing the instantaneous shear rate at the position of the bubble. The deformation resulting from the proposed model is then compared with the measured deformation for an exemplary bubble trajectory.

Experimental and numerical simulation research on the transport process of bubble clusters in aeration system

Improving gas-liquid mass transfer efficiency in aeration systems contributes to energy savings, cost reduction, and enhanced efficiency in wastewater treatment. However, due to the complex nonlinear interactions among bubbles in turbulence, understanding the transport mechanisms of non-uniform bubble clusters in turbulence remains unclear. This study employs a combined approach of experimental research and numerical simulations to investigate the shape, diameter distribution, trajectory, and velocity of bubbles under different aeration port sizes and flow rates. The diameter distribution of bubble clusters exhibits a bimodal distribution. Bubble trajectories during ascent mainly exhibit two types of motion patterns: “Z” shaped and linear. Increasing aeration port size and flow rate both lead to an increase in the maximum bubble diameter. Higher initial flow rates and smaller port sizes induce greater lateral velocity fluctuations in bubbles. The proposed numerical simulation method serves as a reference for simulating the transport of non-uniform bubble clusters.

On the radial interface profile of the non-circular hydraulic jump

The radial interface profile of the non-circular hydraulic jump is analyzed based on the time-averaged film thickness profile of the liquid film formed by a round jet obliquely impinging on a horizontal plate. The influence of many factors, including the jet velocity, impingement angle, azimuthal angle, liquid viscosity, and surface tension, on the radial interface profile is considered. The interface profile is like a quasi-spherical crown when the azimuthal angle is small but is like a sewing needle when the azimuthal angle is larger than 100°. Six parameters, including the inner and outer tangential angles, width, maximum thickness, radial position of maximum thickness, and area are defined to describe the interface profile. Then, six empirical equations are developed to fit the variation of the six parameters. As the azimuthal angle increases, the inner tangential angle decreases, but the outer tangential angle increases. As the jet velocity increases to 20.3 m/s, both the maximum thickness and the area increase suddenly. All empirical equations have a prediction accuracy of about 10%, except for the empirical equation of the radial position of maximum thickness. The bubble trajectory indicates that the liquid flows radially in the thin-layer zone, deflects the flow direction within a relatively short distance in the inner half of the non-circular hydraulic jump, and then flows tangentially. The normal bulk velocity in the radial section of the non-circular hydraulic jump increases from zero at first and then decreases as the azimuthal angle increases.

Experimental Study of the Rising Behavior of a Single Bubble in Shearshinning Fluids

Background: Non-Newtonian gas-liquid two-phase flows are often seen in industrial processes such as petroleum, chemical, and food engineering. The efficiency of mass and heat transfer between phases is significantly impacted by bubble rise motion in liquids. Therefore, it is crucial to deeply study the hydrodynamic characteristics of a bubble rising in non-Newtonian fluids to improve the transfer efficiency between phases and to enhance the operational efficiency of bubbling equipment. Methods: To understand the rising characteristics of a bubble in non-Newtonian fluids, a single bubble rising in shear-thinning fluids was experimentally studied using a high-speed camera. The effects of xanthan gum (XG) concentration and bubble diameter on bubble shape, trajectory, and terminal velocity were investigated. Results: Bubble terminal velocity increased with an increase in the bubble diameter and a decrease in XG concentrations. The increase rate of bubble terminal velocity varied with an increase in bubble diameter for the bubbles with different diameters and XG concentrations for the solutions with varying XG concentrations. For solutions with the same XG concentration, the Galilei and Eötvös numbers for a small bubble were relatively small but relatively large for a large bubble. Thus, the rise motion of a bubble in XG solutions becomes unsteady with an increase in bubble diameter and a decrease in XG concentrations. The unsteady characteristics of bubble motion decrease with an increase in the XG concentration of solutions. Conclusion: It was found that the influence of XG concentrations on bubble motion depends on bubble diameter since the magnitude of bubble diameter has an essential effect on the shear-thinning effect of solutions. An increase in bubble terminal velocity is mainly caused by an increase in buoyancy (i.e., bubble diameter) rather than a decrease in the apparent viscosity of solutions.

Numerical simulation and model development of drag coefficient of bubbles in gas-liquid metal two-phase flow

The occurrence of a steam generator tube rupture (SGTR) accident in a lead-bismuth cooled fast reactor results in the formation of steam bubbles in the liquid lead-bismuth eutectic (LBE). This may degrade heat transfer and power transients in the reactor core due to the migration and accumulation of steam bubbles. To investigate the dynamics of steam bubbles flowing in liquid LBE, it is essential to develop an accurate model for the bubble drag coefficient. In this paper, a three-dimensional numerical model is first established to simulate the injection of high-pressure steam bubbles into a high-temperature LBE molten pool. The model is based on the CLSVOF method. By analyzing the trajectory, velocity, and diameter of bubbles, and combining them with the force equilibrium equation for bubbles, the values of the drag coefficient for bubbles are determined. On this basis, the suitability of current empirical drag models for bubble migration in LBE is evaluated. Finally, the optimal drag coefficient model is selected and further improved. Results reveal that the prediction error of the optimized model for the bubble drag coefficient in liquid LBE is within ±15 %.

Developing a Three-Dimensional Bubble Dynamics Model for Centrifugal Nuclear Thermal Propulsion

Nuclear thermal propulsion (NTP) is a highly efficient type of propulsion system that could yield a specific impulse up to 800 s. High-performance NTP allows for possibilities of various mission types from flyby to interplanetary flight, manned or unmanned. Centrifugal nuclear thermal propulsion (CNTP) is a type of NTP that uses liquid fissile material instead of a solid core in a standard reactor configuration. CNTP requires an interaction between liquid fissile fuel and gaseous propellant to perform heat transfer and generate thrust in a spinning enclosure. Because of the liquid state of the fissile fuel, it is essential to monitor bubble behavior and trajectory. For example, the bubble dwell time within the liquid and hydrogen flow rates can influence the liquid volume fraction and volume, which in turn can affect reactivity. A model is developed and presented that, as it matures, will predict the bubbles’ behavior based on the various types of liquid and gas and their corresponding properties as well as assist in cross-validation with the concurring experiment. The model primarily utilizes the smooth particle hydrodynamics (SPH) approach to simulate the liquid and gas interaction within the design space. The physics include buoyancy and drag on the bubbles. The pressure field within the liquid is modeled using hydrostatics, in which centrifugal motion introduces a radial gradient. Boundary conditions are devised to confine the liquid and gas within the enclosure. In this paper, we present the progress to date in two centrifugal fuel element–relevant subscale devices, the so-called “Antfarm” and “Blender II.” Antfarm is a static stage in a rectangular enclosure where buoyancy is purely gravity driven. Blender II refers to a rectangular enclosure that spins at up to 7000 rpm. Both Antfarm and Blender II are experiments that provide important data for validation against our SPH model. Two liquid and gas combinations are modeled in the present study using the Antfarm setup: water-air, and Galinstan-Nitrogen. The bubbles’ behavior was comparable to the experiment, and the velocity was at the same order of magnitude. The liquid simulation performed for the Blender II model shows that the pressure gradient within the liquid in the radial direction matches that predicted analytically from the centrifugal acceleration. The Blender II liquid model awaits experimental data for validation and verification.

Advancements in the Understanding of Single‐Bubble Dynamics: Integrated Experimental and Simulation Studies

Because of wake instability, bubbles always ascend along an unstable path, which is not considered when simulating their movement in steel refining and continuous casting systems. Utilizing the 3D shadow image method, a quantitative characterization of the bubble trajectories is conducted to establish a bubble path oscillation model considering the zigzag lateral movement of bubbles due to asymmetric wake shedding. This model is incorporated into a rectilinear bubble motion model within the Lagrangian framework and then used to simulate the free ascent of single bubbles within the 2.15–2.55 mm range. The predicted bubble ascent velocities and trajectories agree well with the experimental. The spatial position, velocity, acceleration, forces, volume swept by bubbles, and bubble residence time are discussed. The results shown that the dominant force in the horizontal direction is the lateral force, followed by the drag and virtual mass force. Compared to the rectilinear path model, the volume swept by bubbles with initial diameters of 2.15, 2.25, 2.34, 2.45, and 2.55 mm in this model increases by 30.8%, 32.0%, 34.0%, 31.5%, and 29.6%, respectively. These findings help accurately predict the path of bubbles and also may contribute to a better understanding of bubble dynamics in bubble metallurgy and clean steel production.

Quantum transitions, detailed balance, black holes, and nothingness

We consider vacuum transitions by bubble nucleation among 4D vacua with different values and signs of the cosmological constant Λ, including both up and down tunnelings. Following the Hamiltonian formalism, we explicitly compute the transition probabilities for all possible combinations of initial and final values of Λ and find that up tunneling is allowed starting not only from dS spacetime but also from AdS and Minkowski spacetimes. We trace the difference with the Euclidean approach, where these transitions are found to be forbidden, to the difference of treating the latter spacetimes as pure (vacuum) states rather than mixed states with correspondingly vanishing or infinite entropy. We point out that these transitions are best understood as limits of the corresponding transitions with black holes in the zero mass limit M→0. We find that detailed balance is satisfied provided we use the Hartle-Hawking sign of the wave function for nucleating spacetimes. In the formal limit Λ→−∞, the transition rates for anti–de Sitter (AdS) to dS agree with both the Hartle-Hawking and Vilenkin amplitudes for the creation of dS from nothing. This is consistent with a proposal of Brown and Dahlen to define “nothing” as AdS in this limit. For M≠0, the detailed balance is satisfied only in a range of mass values. We compute the bubble trajectory after nucleation and find that, contrary to the M=0 case, the trajectory does not correspond to the open universe slicing of dS. We briefly discuss the relevance of our results to the string landscape. Published by the American Physical Society 2024

Effect of surfactant on dynamics and gas-liquid mass transfer for single carbon dioxide bubbles

In carbonation reaction, the impact of surfactants on the movement and mass transfer behavior of carbon dioxide bubbles were crucial for the production of high-quality silicon dioxide products. The study employed the Matlab image processing system to investigate the shapes, motion velocities, and rise path of single carbon dioxide bubbles within varying concentrations of cetyltrimethyl ammonium bromide (CTAB) solutions. This exploration aimed to elucidate the effect of CTAB on the movement and mass transfer coefficient (MTRC) of single carbon dioxide bubbles. Alterations in the CTAB solution concentration and bubble sizes significantly influenced the mass transfer and movement characteristics of single carbon dioxide bubbles. The conclusion was drawn through the computation of the MTRC of single carbon dioxide bubbles in deionized water and CTAB solutions: the addition of CTAB significantly reduced the mass transfer efficiency of carbon dioxide in deionized water, with the MTRC of CTAB solutions decreasing as the solution concentration increased. Utilizing the stagnant cap model, it can be concluded that CTAB's reduction of the MTRC of carbon dioxide was attributed to the high viscosity of the medium, low bubble velocity, stable flow conditions, and intensified adsorption degree of CTAB molecules at the gas-liquid interface. According to the significant periodic trajectories of single carbon dioxide bubbles in the stable range, the correlation between the trajectories of compressible bubbles in surfactant solution and mass transfer in liquid phase was established, and the previous method based on rigid sphere model was modified. The paper proposed the mechanism of CTAB's influence on single carbon dioxide bubbles, offering crucial theoretical insights into the industrial application of surfactants in the carbonation process for producing silicon dioxide.

Flow visualization experiments of argon injection in a molten salt natural circulation loop

Off-gas systems are implemented in molten salt reactor designs to control the release of gaseous fission products. Two-phase flow in molten salt must be studied to understand how the system will behave in comparison to traditional working fluids like water. Flow visualization experiments and particle image velocimetry measurements were performed for three argon bubble sizes injected into a co-current stream of molten salt in a natural circulation loop facility. Similar bubble sizes were injected in experiments with water to compare the bubble shape, trajectory, and wake flow behavior of the fluids. The bubble region of interest was used to calculate the equivalent diameter and terminal velocity. Results for water showed a wobbling bubble surface and less stable bubble trajectory due to lower surface tension and viscosity compared with molten salt. Particle image velocimetry results demonstrated the increased viscosity of salt dampens turbulent fluctuations for the smaller bubble size. For a cap bubble, turbulent fluctuations were larger and longer lasting than in results for the wake flow of an argon cap bubble in water.

Bubble tracking method based on Kuhn-Munkres algorithm for boiling two-phase flow study

The study of bubble dynamics is important in various engineering applications as it can provide a fundamental understanding of the bubbly flow behavior. This paper presents a novel method for tracking bubble trajectories and classifying bubble behaviors, including formation, extinction, continuous movement, fragmentation, and coalescence. The method is based on the theory of perfect matching in bipartite graphs. By establishing the perfect matching between bubbles identified at adjacent time instants, judging the continuity of bubble motion, and simply calculating the number of bubbles in the neighbor of matching bubbles at adjacent time instants, the method can deal with the challenging situation where the bubble position and volume significantly change between two adjacent time instants. The method is validated in a simulated vertical pipe boiling flow, showing that the tracking accuracy is 100% and classification accuracies for continuous movement, fragmentation, and coalescence events are estimated to be larger than 90% in a wide range of time steps between two adjacent time instants.

Effect of swirl flow on the bubble motion and spatial distribution in a venturi tube

In the process of carbon dioxide capture by chemical absorption, swirl flow plays a positive role in enhancing mass transfer. To leverage the advantages of swirl flow in enhancing mass transfer and overcome the drawback of bubbles easily aggregating in swirl flow, a tangential inlet venturi tube is designed. This study utilized dual-perspective high-speed imaging technology to achieve clearer measurements of the spatial positions of individual bubbles and the spatial distribution of bubble clusters. By measuring the three-dimensional motion trajectories of individual bubbles in still water and at low Re, the positive effect of swirl flow in expanding the distribution range of bubbles is observed. By measuring the three-dimensional motion trajectories of bubbles of different sizes at the same Re, it is observed that smaller bubbles are less likely to be captured by the vortices. And the spatial distribution of the bubble cluster in the diffuser section is analyzed by extracting grayscale values and correlating them with the flow field using Computational Fluid Dynamics (CFD) method. Experimental results indicate that as the bubble size decreases, the number of grayscale peaks gradually increases, indicating an expansion of the spatial distribution range of the bubble cluster in the diffuser section. CFD results reveal the presence of two vortices that continuously rotate around the central axis in the diffuser section. However, these vortices attract but did not confine small-sized bubbles. The bubbles are distributed around the vortices and moved along with the rotational motion of the vortices, allowing the bubble cluster to maintain a larger spatial distribution level within the swirl flow.

VOF study of mesoscale bubble flow dynamics in the side-blown gas–liquid two-phase reactor

Understanding the flow and mixing characteristics of mesoscale bubbles within side-blown gas–liquid two-phase systems is paramount for the design and optimization of associated industrial processes. This study elucidates the gas–liquid side-blown two-phase reactor, employing the volume of fluid method coupled with the realizable k-ε turbulence model. Following the model validation through experimental measurements, the mesoscale bubble dynamics, flow characteristics, and multiscale coupling mechanisms inherent to side-blown gas–liquid reactor are explored. The key insights can be obtained: (1) the upward trajectory of bubbles originating from side-injection gas can be categorically divided into four phases with different bubble behaviors. (2) A reduction in the ratio of inertial forces to buoyancy forces during bubble ascent induces a decrease in the bubble shape factor. This transition manifests as a shift from vertical to flattened bubble shapes within the transition and plume regions. (3) Bubbles undergo transitions between states characterized by high buoyancy and low surface tension, accompanied by varying levels of viscous forces during their ascent. These dynamic states render bubbles susceptible to breakup. Under conditions of a constant nozzle diameter, the maximum bubble size within the reactor is inherently restricted. (4) Drawing upon the correlation between bubble Weber and Reynolds numbers, a predictive formula for determining the characteristic velocity of bubbles within side-blown reactors is proposed:uc=σ1-0.456(ρlLC)0.456512μl11.36Overall, this work offers meaningful insights into the fundamental mechanisms governing bubble cluster dynamics within side-blown gas–liquid reactors.

Hydrodynamics and shape reconstruction of single rising air bubbles in water using high-speed tomographic particle tracking velocimetry and 3D geometric reconstruction

Time-resolved tomographic particle tracking velocimetry (TR-3D-PTV), also called 4D-PTV, is used here to obtain the instantaneous 3D liquid flow field information in the wake of a single rising bubble in water. Simultaneously, the bubble shape, size and velocity are determined by tomographic reconstruction of the 3D bubble shape. Both, tracer particles for PTV and bubbles, are imaged in a shadow mode with background illumination. The Lagrangian method used in this paper, especially combined with the shake the box algorithm, has big advantages compared to particle image velocimetry, in situations, where only low particle per pixel values can be obtained. In this research, single air bubbles of different sizes, with diameters of around 2.4 mm, 4.0 mm, 6.0 mm and 9.6 mm, were injected into stagnant de-ionized water. Their shape was reconstructed in 3D, and an equivalent bubble diameter was determined from this reconstruction. Compared to conventionally used 2D shadow imaging, this diameter is about 13% smaller. The 3D bubble trajectory can be analysed and decomposed into a sinusoidal function curve lateral projection and an ellipsoidal shape vertical projection. As the bubble diameter increases, the radius of the spiral trajectory is decreasing as well as the amplitude of vertical sinusoidal oscillation. The wake structure in the liquid behind the bubbles is also changing with bubble size: from simple vortex pairs for smaller bubbles to an intertwined structure of several twisted vortices for the bigger ones.Graphical abstractThree-dimensional bubble reconstruction (grey surface) and liquid stream lines coloured with velocity magnitude around an ascending air bubble in de-ionized water.