Multicomponent Lattice Boltzmann Research Articles

Lattice Boltzmann modeling for enhanced membrane separation of geothermal energy utilization

Reducing carbon emissions and utilizing geothermal energy via supercritical carbon dioxide extraction from reservoirs for direct power generation necessitates the removal of mixed vapor. A shell-tube hollow fiber membrane contactor, utilizing differential pressure and absorption fluid, is devised for vapor absorption. This membrane-based separation process encompasses a multicomponent multiphase system of supercritical carbon dioxide and water, water-salt transport, and mass transfer across the porous membrane. To investigate pore-scale mass transfer, a multicomponent multiphase pseudopotential lattice Boltzmann model is established, simulating carbon dioxide-water two-phase flow, coupled with a continuous species transfer model for salt behavior in the absorbent. Flow direction analysis reveals countercurrent flow as superior to cocurrent for vapor absorption. Augmenting the original membrane with equal macropore counts enhances mass transfer, with increasing size amplifying the effect. Macropore arrangements at constant porosity suggest minimizing resistance in the propagation path as crucial for mass transport improvement. A left-small-right-large macropore size gradient distribution outperforms its reverse counterpart, enhancing performance by approximately 20%. This is attributed to larger macropores in high-concentration regions facilitating localized vapor transport.

A Thread-Safe Lattice Boltzmann Model for Multicomponent Turbulent Jet Simulations

In this work an optimized multicomponent lattice Boltzmann (LB) model is deployed to simulate axisymmetric turbulent jets of a fluid evolving in a quiescent, immiscible environment over a wide range of dynamic regimes. The implementation of the multicomponent LB code achieves peak performance on graphic processing units (GPUs) with a significant reduction of the memory footprint, retains the algorithmic simplicity inherent to standard LB computing, and, being based on a high-order extension of the thread-safe LB algorithm, allows us to perform stable simulations at vanishingly low viscosities. The proposed approach opens attractive prospects for high-performance computing simulations of realistic turbulent flows with interfaces on GPU-based architectures.

Pore-scale modeling of wettability alteration coupled two-phase flow in carbonate porous media

The Middle East marine carbonate reservoirs are the primary targets for global crude oil exploration and production. In contrast to the clastic rock reservoirs, the marine carbonate reservoirs have undergone more complicated deposition, diagenesis and transformation, and the rock surface tends to be oil-wet or mixed-wet. One of the most effective methods for enhancing oil recovery in marine carbonate reservoirs is the use of an ion matched (IM)-surfactant (S) system to alter the wettability of rock surfaces. In this paper, we propose a microscale mathematical model of wettability alteration-coupled fluid flow by considering oil–water two-phase flow, wettability alteration, solute advection- diffusion and surfactant adsorption. The proposed microscale mathematical model is solved using the multi-component lattice Boltzmann model, and its accuracy is further verified. Finally, the effects of displacing fluid, ion-matched water concentration and surfactant concentration on oil mobilization at pore-scale are studied. Results show that, ion-matched water has a positive effect on wettability alteration, and typically shifts the cross-point of oil–water relative permeability curve to the right. The concentration of ion-matched water primarily affects fluid morphology of the wetting-phase and has little effect on phase permeability. After adding surfactant to the ion-matched water, the Euler coefficient of oil-phase gradually increases as the displacement continues, a large amount of remaining oil is gradually dispersed into scattered oil droplets and the oil-phase relative permeability is further improved.

Lattice Boltzmann modeling of forced imbibition dynamics in dual-wetted porous media

Forced imbibition dynamics are critical for enhancing recovery rates in reservoirs, as efficient fluid displacement directly impacts resource extraction. This study employs the Zou-He velocity boundary condition and a modified convective boundary condition (mCBC) within the multi-component Shan-Chen lattice Boltzmann method (LBM), thus facilitating unobstructed flow of multi-component fluids at the outlet while maintaining constant outlet pressure. The model's validity was established through outflow tests of immiscible droplets in channels. Its accuracy was further confirmed by comparing results from forced imbibition dynamics tests in dual-wetted pores with theoretical predictions. A symmetrical porous medium was constructed using the stacking method, achieving dual wettability by fixing the contact angle in the upper region and varying it in the lower region. We performed 20 simulation sets under unfavorable viscosity ratios and varying capillary numbers, focusing on overall displacement efficiency before and after breakthrough, and employing energy balance equations to evaluate the dominant forces. Results reveal that capillary forces predominantly dictate forced imbibition dynamics in low capillary number scenarios. In strongly wetted regions, the invading fluid fully occupies pore spaces; however, in weakly wetted regions, displacement efficiency significantly declines as wettability approaches neutrality, even nearing zero. As capillary numbers increase, viscous forces become more prominent, controlling dynamics and leading to fingering and trapping of defending fluids. In weakly wetted areas, the increasing influence of viscous forces enhances fluid displacement, resulting in significant improvements in overall displacement efficiency compared to conditions dominated by capillary forces.

Dynamics of liquid bridges between patterned surfaces

We have simulated the motion of a single vertical, two-dimensional liquid bridge spanning the gap between two flat, horizontal solid substrates consisting of alternating hydrophilic and hydrophobic stripes, using a multicomponent pseudopotential lattice Boltzmann method. This extends our earlier work where the substrates were uniformly hydrophilic or hydrophobic. In steady-state conditions, we calculate the following, as functions of pattern wavelength: (i) the velocity fields of moving bridges, in particular their (time-averaged) terminal velocities; (ii) the deformation of moving bridges, as measured by the deviation of bridge contact angles from their equilibrium values; (iii) the minimum applied force that breaks a moving bridge. In addition, we found that a bridge moving between patterned substrates cannot be mapped onto a bridge moving between uniform substrates endowed with some effective contact angle, even in the limit of very small pattern wavelength compared to bridge width.

Lattice Boltzmann Model Investigation of Simultaneous Imbibition/Evaporation in PEMFC Cathodic Catalyst Layer Using Reconstructed 3D Image Data from Transmission Electron Microscopy

Proton Exchange Membrane Fuel Cells (PEMFCs) are widely used and significant attention is directed towards optimizing of the cathode catalyst layer. The critical focus revolves around refining the multi-phase boundary of the electrically conducting carbon support, the ion-conducting ionomer, the catalyst particles as well as the pore space that can be either occupied by oxygen (feedstock) or water (product). Challenges related to mass transport limitations of oxygen towards these multiple-phase boundaries, also denoted as active sites, persist, especially when liquid water increasingly saturates the pore space (Fig. 1). Furthermore, the evaporated water additionally hinders oxygen transport in the gas phase1,2. This study focuses on the investigation of pore-scale transport mechanisms inside of the cathodic catalyst layer, taking into account the counter-current diffusion of oxygen and water vapor in the gas phase as well as the generation of liquid water that increasingly saturates the void space. For this purpose, a multi-phase and multi-component pore scale Lattice Boltzmann model (LBM), coupled to two-phase reaction, was implemented. The LBM is tailored based on previous works3,4, including the localized generation of water at constant current densities, the imbibition of the pore structure with water counter-currently to the diffusion of oxygen, and the simultaneous evaporation of water. An actual 3D cathode catalyst layer from a commercial membrane electrode assembly, reconstructed from transmission electron microscopy (TEM) image data, was employed. It was imaged using a source voltage of 200kV and a current of 2 nA. The scanned sample had an approximate total volume of 500 × 500 × 100 nm3. From this, a 3D domain of 138 × 138 × 58 nm3 was reconstructed for this study. A 2D cross-section of the reconstructed image is exemplarily shown in Fig. 1. The in-silico study of water and oxygen transport through the catalyst layer elaborates the relationship between the rates of water invasion and evaporation in dependence of current density and catalyst layer structure. The critical conditions for water flooding are evaluated for different process conditions. Fig. 1 Schematic representation of the cathode catalyst layer: The ionomer is represented in white; the carbon for electron connectivity is represented in gray; pore space for oxygen and water transport in yellow; the black circles represent the active sites, i.e., Pt-particles located at the multi-phase boundary of ionomer, carbon and oxygen-filled pores; the red circles represent the inactive sites, that have no connection to ion and/or oxygen transport pathways. References A. Suzuki et al., Int. J. Hydrogen Energy, 36, 2221–2229 (2011) https://www.sciencedirect.com/science/article/pii/S0360319910022913.M. El Hannach, M. Prat, and J. Pauchet, Int. J. Hydrogen Energy, 37, 18996–19006 (2012) https://www.sciencedirect.com/science/article/pii/S0360319912022069.S. Bhaskaran et al., Dry. Technol., 40, 735–747 (2022) https://doi.org/10.1080/07373937.2021.1898417.S. Bhaskaran et al., Int. J. Hydrogen Energy, 47, 31551–31565 (2022) https://www.sciencedirect.com/science/article/pii/S0360319922030932. Figure 1

A study on the distribution and movement of water in unsaturated cement paste by a multi-component multi-phase lattice Boltzmann simulation

The distribution of water inside concrete is a crucial factor that determines its mechanical performance and durability. In contrast to experimental investigation, numerical models provide a new way to visualize and characterize the actual situation of water in unsaturated cementitious materials. However, the interactions between different components are quite complex and they are rarely considered so far. In this work, a multi-component multi-phase (MCMP) lattice Boltzmann model is developed to distribute moisture in partially saturated cement paste, in which the interactions between water and air are fully taken into account. The transport of water flow in unsaturated cement paste is modelled and the permeability is thus computed. The simulation results show a satisfactory agreement with experimental data, validating the proposed approach. The obtained permeability is found to decline at a decreased water saturation degree and this is attributed to a reduced number of transport paths for water flow. Moreover, as the contact angle increases from 80° to 100°, large pores become the preferred place for water to accumulate and the formed clusters are observed. According to the results, a strong correlation between pore structure (i.e., pore size and pore connectivity) and water permeability is found and discussed.

Effect of the angle of wedge-shaped hydrophilic patterns on drop evaporation and contact line behaviour: A lattice Boltzmann study

Hypothesis:Angular hydrophilic patterns can manipulate the drop morphology for applications like inkjet-printing. It is hypothesized that such patterns can also affect the contact line behaviour and evaporation rate of drops in a dynamic way, further affecting the quality of depositions. Here, the effect of the angular region is quantified using a wedge-shaped pattern. Experiments:The pseudo-potential multicomponent lattice Boltzmann (LB) model is used for the diffusion-limited (isothermal) evaporation of pinned liquid drops from wedge-shaped hydrophilic patterns. Findings:The contact line unpins the earliest at the apex region of the smallest wedge angles due to a pronounced difference between the local and overall contact angles. The difference reduces linearly with increasing wedge angles, leading to their delayed unpinning. The evaporative flux along the contact line is initially independent of the contact angle but reduces sharply near the unpinning angle. The variation of flux across wedge angles depends more on unpinning timings, as maximum flux values did not differ significantly. The evaporation rate is dynamic, with the smaller wedge angles initially exhibiting a higher evaporation rate because of larger drop surface areas, while the larger wedge angles dominate later owing to the delayed unpinning and retaining larger drop surface areas.

Enhancing flow boiling using a microchannel with pillar–cavity mixed structures: A lattice Boltzmann study

Enhancement of flow boiling in microchannels through adjusting surface structures has attracted much attention in recent years. However, most of the existing studies focus on homogeneous surface structures. In the present study, a novel vertical microchannel with pillar–cavity mixed structures is conceived to enhance flow boiling heat transfer. In the mixed microchannel, cavities and pillars are distributed on the vertical sidewalls of the upstream and downstream flow channel, respectively. A multicomponent phase-change lattice Boltzmann model is employed to investigate the flow boiling performance of the mixed microchannel. Numerical results show that the cavities in the mixed microchannel can supply effective nucleation sites for timely departure of bubbles, while the pillars in the mixed microchannel can suppress the expansion of the vapor film from the outlet toward the inlet. Moreover, the bubbles from the upstream cavities can entrain the cold liquid to disrupt the vapor film covering the downstream pillars for the rewetting of the heated surface. As a result, the flow boiling performance can be significantly enhanced by the synergistic effect of the pillar and cavity structures, and the best flow boiling performance can be achieved by controlling the ratio of the number of cavities to the total number of structures in the mixed microchannel to optimize the synergistic effect. The influences of the structural parameters of pillars and cavities on the flow boiling performance have also been studied. It is found that the height of the pillars and the depth of the cavities have important influences on the flow boiling performance, while the boiling performance is not sensitive to the width of the pillars.

Multi-component multiphase lattice Boltzmann modeling of water purging during supercritical carbon dioxide extraction from geothermal reservoir pores

Carbon dioxide becomes supercritical and purges subcritical liquid water in the rock channels as extracted from geothermal reservoir pores. A pseudopotential multi-component multiphase lattice Boltzmann method is presented to simulate the dynamic behavior of the water droplets under the purge of the supercritical carbon dioxide. The model is verified by thermodynamic consistency, surface tension independence regulation, the coexistence of the two components at different viscosities, and surface contact angle distribution laws. The results show that the stronger the hydrophobicity of the wall with uniform adhesion, the faster the motion of the droplet, and when the wall adhesion is not uniform, the stronger the hydrophobicity of the upstream, the faster the purge. When there are two droplets, the volume of the first one rapidly becomes larger because of the absorption of moisture and encounters enhanced shear force to obtain greater velocity. The second droplet receives the shear force weakened by the first, so its growth rate and movement do not change significantly and will gradually be caught up, leading to the coalescence of the two droplets. As the droplets move and grow, the obstruction to flow increases and the pressure drop will increase.

Thermodynamic effects of gas adiabatic index on cavitation bubble collapse

In this paper, an improved multicomponent lattice Boltzmann model is employed to investigate the impact of the gas properties, specifically the gas adiabatic index, on the thermodynamic effects of cavitation bubble collapse. The study focuses on analyzing the temperature evolution in the flow field and the resulting thermal effects on the surrounding wall. The accuracy of the developed model is verified through comparisons with analytical solutions of the Rayleigh-Plesset equation and the validation of the adiabatic law. Then, a thermodynamic model of cavitation bubble composed of two-mixed gases collapsing near a wall is established to explore the influence of the gas adiabatic index γ on the temperature behavior. Key findings include the observation that the γ affects the temperature of the first collapse significantly, while its influence on the second collapse is minimal. Additionally, the presence of low-temperature regions near the bubble surface during collapse impacts both bubble and wall temperatures. The study also demonstrates that the γ affects maximum and minimum wall temperatures. The results have implications for selecting specific non-condensable gas properties within cavitation bubbles for targeted cooling or heating purposes, including potential applications in electronic component cooling and environmental refrigeration.

Pore-Scale Investigation of Mass Transport in Compressed Cathode Gas Diffusion Layer of Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs) are considered a promising energy source in the field of transport and distributed power generation. Fundamental research into their key components is needed to improve PEMFC performance and accelerate commercialization. Binder addition and compression induced by assembly pressure can significantly change the microstructure of the gas diffusion layer and affect mass transport. A two-dimensional multicomponent lattice Boltzmann (LB) model considering the cathode electrochemical reaction was developed, and a GDL was reconstructed numerically and considering a binder structure. The effects of the binder and compression on mass transport and electrochemical performance within the GDL were investigated. The results showed that an increase in binder volume fraction led to more chain-like structures and closed pores that were unfavorable for mass transport. Compression increased the mass transfer resistance of the GDL in the region under the rib, leading to a decrease in oxygen concentration and local current density.

Lattice Boltzmann modelling of salt precipitation during brine evaporation

Salt precipitation during brine evaporation in porous media is an important phenomenon in a variety of natural and engineering scenarios. This work establishes a multiphase multicomponent lattice Boltzmann (LB) method with phase change for simulating salt precipitation during brine evaporation. In the proposed LB models, the gas–brine multiphase flow, brine evaporation, salt concentration evolution, salt precipitate nucleation and growth are simultaneously considered. Simulations of the Stefan problem are first conducted to verify the proposed numerical models and determine the diffusion coefficient of brine vapour. Once the lattice Boltzmann models have been validated, salt precipitation during brine evaporation is simulated to investigate the competition mechanisms between salt precipitate nucleation and growth reaction. The results show that the typical salt precipitation patterns in existing experimental observation can be successfully reproduced, including the ring-like and pancake-like patterns. The difference in the salt precipitation patterns is explained by the competition mechanism between precipitate growth and nucleation according to the present study. Furthermore, the salt precipitation during gas injection into a microfluidic chip is investigated. The evolution of salt and brine saturation shows similar patterns to existing experimental results, and the effects of the gas injection rate on salt precipitation performance are clarified. The LB models in the present work can simulate salt precipitation with comprehensive consideration of multiphase brine evaporation, salt species mass transport, precipitate nucleation and growth, which have not been realized in previous studies. The numerical showcases demonstrate the excellent performance of the proposed models for the simulation of salt precipitation in porous media, which promise to guide practical engineering applications like CO2 sequestration.

A non-uniform magnetic field coupled lattice Boltzmann model and its application on the wetting dynamics of a ferrofluid droplet under gravity effects

To extend the mesoscopic model for simulating the wetting dynamics of ferrofluid droplets, an improved multicomponent multiphase pseudopotential lattice Boltzmann (LB) model coupled with the magnetic field solver is constructed in this work. Through a series of validation studies, the accuracy and reliability of the proposed coupled model are ensured. The ferrofluid droplet is subjected to the effects of non-uniform magnetic field and gravity. The influences of various magnetic Bond numbers (Bom) and gravitational Bond numbers (Bo) on the wetting dynamics of a ferrofluid droplet on a hydrophobic surface are discussed, and the mechanism behind the morphological evolution of the ferrofluid droplet is unveiled. The results show that the curvature of the phase interface is a key factor influencing both the magnetic field intensity distribution around the phase interface and the pressure distribution inside the ferrofluid droplet, thus changing the evolution of the droplet morphology. The variation of Bom has a monotonic impact on the morphological evolution of the ferrofluid droplet and its equilibrium state, while the effect of the Bo depends on the magnitude of Bom. At Bom=49.98 and Bo=4.1, the ferrofluid droplet splits from the central position and into three parts in the end. The amplitude and duration time of the oscillation of the ferrofluid droplet increase with Bom. This study can provide a model reference and some key theoretical understandings for the numerical study of the wetting dynamics of ferrofluid droplets.

Effects of Cassie-Wenzel wetting transition on two-phase flow in porous media

Wettability is one of the most important factors affecting multiphase flow in porous media. In this study, effects of the dynamic wetting process on two-phase flow displacement are investigated at the pore scale. A time-dependent Cassie-Wenzel wetting transition model is improved and incorporated into the pseudopotential multiphase multicomponent lattice Boltzmann model. With the Cassie-Wenzel wetting transition considered, two-phase flow displacement is simulated in Voronoi porous media with structural disorder and layered characteristics under different capillary number and wetting transition characteristic time. The simulation results show that the wetting transition promotes cooperative pore filling and weakens the effect of nonuniformity of capillary resistance. Under different capillary number, increased wetting transition rate improves the wettability of invading fluid, and thus the saturation of invading fluid is increased. The results also show that the layered structure with decreased pore size along the flow direction compacts the displacement pattern and weakens the viscous fingering, leading to higher displacement efficiency. While in this layered structure, effects of the wetting transition are suppressed due to lower interfacial length between the invading fluid and solid surface. The simulation results provide new insights of the influence of the dynamic wetting transition and on fluid displacement in porous media.

Numerical approach to simulate placement of wellbore plugging materials using the Lattice Boltzmann method

An approach is introduced using the multi-component lattice Boltzmann method (LBM) to numerically simulate multi-layered wellbore plug placement and investigate the effects of the rheological and physical properties of cement slurry and bentonite clay gel as plugging materials. As a proof of concept, this approach is applied to simulate the placement of a layer of cement slurry within a layer of bentonite clay gel to form three distinct alternating material layers in a wellbore. Prior to investigating this system, the LBM approach is validated through physical lab-scale plug placement tests. Then, a computational field-scale case study is examined to evaluate how variations in plug material properties and placement processes affect the resulting multi-layered wellbore plug. The analyses show that cement slurry density is the property that most affects the wellbore plugging process. At lower concentrations of bentonite clay gel, more cement slurry is needed to create the three-layer system, since the cement slurry penetrates further into the bentonite clay gel. Alternatively, for high concentrations of bentonite clay gel, higher density cement slurry can be placed as a distinct layer without having a significant increase in the amount of cement slurry needing to be pumped. For the cases considered, variations in yield stress and viscosity of the cement slurry have negligible effects on the plugging process. Lastly, although the pumping velocity controls the rate of cement slurry layer placement, it has a relatively small effect on the placement process. Overall, the LBM approach is shown to be an effective method to evaluate wellbore multi-layered plugging processes.

Effect of droplet deformability on shear thinning in a cylindrical channel.

Droplets suspended in fluids flowing through microchannels are often encountered in different contexts and scales, from oil extraction down to microfluidics. They are usually flexible and deform as a product of the interplay between flexibility, hydrodynamics, and interaction with confining walls. Deformability adds distinct characteristics to the nature of the flow of these droplets. We simulate deformable droplets suspended in a fluid at a high volume fraction flowing through a cylindrical wetting channel. We find a discontinuous shear thinning transition, which depends on the droplet deformability. The capillary number is the main dimensionless parameter that controls the transition. Previous results have focused on two-dimensional configurations. Here we show that, in three dimensions, even the velocity profile is different. To perform this study, we improve and extend to three dimensions a multicomponent lattice Boltzmann method which prevents the coalescence between the droplets.

Pore-scale simulation of gas displacement after water flooding using three-phase lattice Boltzmann method

Water flooding is a commonly used technique to improve oil recovery, although the amount of oil left in reservoirs after the procedure is still significant. Gas displacement after water flooding is an effective way to recover residual oil, but the occurrence state and flow principles of multiphase fluid after gas injection are still ambiguous. Therefore, the gas displacement process after water flooding should be studied on the pore scale to provide a basis for formulating a reasonable gas injection program. Most of the current pore-scale studies focus on two-phase flow, while simulations that account for the influence of oil-gas miscibility and injected water are seldom reported. In this work, the multi-component multi-phase Shan-Chen lattice Boltzmann model is used to simulate the gas displacement after water flooding in a porous medium, and the effects of injected water, viscosity ratio, pore structure, and miscibility are analyzed. It is established that the injected water will cause gas flow path variations and lead to premature gas channeling. Under the impact of capillary pressure, the water retained in the porous medium during the water flooding stage further imbibes into the tiny pores during gas injection and displaces the remaining oil. When miscibility is considered, the oil-gas interface disappears, eliminating the influence of the capillary effect on the fluid flow and enabling the recovery of remaining oil at the corner. This study sheds light on the gas displacement mechanisms after water flooding from the pore-scale perspective and provides a potential avenue for improving oil recovery. Cited as: Wang, S., Chen, L., Feng, Q., Chen, L., Fang, C., Cui, R. Pore-scale simulation of gas displacement after water flooding using three-phase lattice Boltzmann method. Capillarity, 2023, 6(2): 19-30. https://doi.org/10.46690/capi.2023.02.01

PORE SCALE INVESTIGATION ON THE EFFECT OF TEMPERATURE ON THREE-PHASE REACTIVE FLOW IN POROUS MEDIA USING THE LATTICE BOLTZMANN METHOD

In this study, the process of carbonate rock acidification with three-phase immiscible fluid [water, oil, and supercritical carbon dioxide (scCO<sub>2</sub>)] reactive flow in nonisothermal condition at pore scale was simulated by the lattice Boltzmann method (LBM). The three immiscible fluids' flow, solute transport, and heat transfer were solved by the Shan-Chen multiphase multicomponent lattice Boltzmann model, mass transport lattice Boltzmann model, and multicomponent thermal lattice Boltzmann model, respectively. The solid phase was updated by the volume-of-pixel method. In addition, the effect of temperature on the multiphase multicomponent reactive flow was numerically investigated. The results show that the dissolution rate is determined by three-phase distribution. The increase of temperature can accelerate the dissolution rate and decrease the inhibition influence of the non-acid phase on dissolution. Furthermore, the influence of temperature decreases with the increase of inlet velocity and oil wettability.

Numerical simulation of methane hydrate dissociation characteristics in microporous media using lattice Boltzmann method: Effect of fluid flow

A multi-phase multi-component lattice Boltzmann model for modeling the gas hydrate dissociation process is proposed, which takes into account the dissociation kinetics, gas-water migration, and heat-mass transfer processes. This model is validated by simulating the xenon hydrate dissociation process. Subsequently, the dissociation mechanism of methane hydrate in microporous media, the gas-water migration, and the effect of fluid flow on the dissociation are investigated by using the present model. The simulation results indicate that methane hydrate dissociation facing the inlet is faster than that away from the direction of inlet flow. Meanwhile, fluid flow promotes methane hydrate dissociation. In addition, the rapid dissociation process within the pore space may lead to a large amount of water production accumulation. Another noteworthy phenomenon is the observation of bubbles formed by liquid curling flows. Liquid curling is one of the reasons for bubble formation near the gas-liquid interface.