Coalescence Regime Research Articles

The numerical analysis of complete and partial electrocoalescence in the droplet-layer system employing the sharp interface technique for multiphase-medium simulation

In this paper, the coalescence of a drop of water suspended in oil with a layer of water under the influence of a constant electric field is numerically investigated. Unlike most existing studies, the calculations are based on the application of the arbitrary Lagrangian-Eulerian method (ALEM), also called the moving mesh method, which belongs to the class of methods for modeling two-phase liquids with a sharp interface. Using this approach made it possible to avoid a false "escape" of the surface charge from the interface, which often occurs when using methods involving a diffuse interface. Despite the fact that ALEM does not allow describing topology changes by default, a numerical model was implemented in which the calculation is divided into three parts: the convergence of the drop and the layer before the moment of touch; the manual construction of the bridge at the moment of touch; the union of the drop and the layer. The developed model allowed us to obtain three possible modes of this process: complete coalescence, partial coalescence and a mode of stretching which has not practically been considered yet. The dependence of the volume of the separated secondary droplet on the size of the initial droplet and the average intensity of the applied electric field is obtained. The model showed good quantitative agreement with experimental studies. It has been shown that generally, the spots where the bridge and the neck are formed in case of partial coalescence do not coincide. A map of coalescence modes was obtained, i.e., the dependence of the transition threshold from coalescence to partial coalescence and from partial coalescence to stretching regime in a wide range of radii of initial droplets and electric field strengths. It has been shown that there is a maximum field strength at which droplets of any size merge with the layer. This map makes it possible to predict the coalescence regime in electrocoalescer. The proposed modeling technique can be used to calculate electrocoalescence modes at various values of the main parameters, which will help to optimize electrocoalescers at the design stage.

Collision dynamics of binary equal-size droplets at high pressures: a focus on stretching separation and reflexive separation

ABSTRACT Stretching separation and reflexive separation are two collision regimes that give rise to satellite droplets, significantly impacting the droplet size distribution. However, the influence of high pressure on these regimes remains unclear. This paper investigates the collision dynamics of binary equal-size droplets under varying ambient pressures using the volume of fluid method and adaptive mesh refinement. The results show that vortices, generated during droplet motion changes or ligament ruptures, facilitate mass transport within the droplet–droplet deformation. Additionally, this paper summarizes four phases of droplet deformation in the separation regimes, which are delayed in stretching separation and advanced in reflexive separation with increasing ambient pressure. Elevated ambient pressure restricts droplet movement, resulting in tougher ligament fractures, smaller satellite droplets, and an expanded coalescence regime boundary. Unlike previous works, this paper incorporates gas kinetic and dissipation energies during droplet collisions at high pressures, revealing that at 7 MPa, the gas dissipation energy is comparable to the liquid dissipation energy and cannot be neglected. To account for these effects, a pressure-dependent formula is integrated into the composite collision model under the Lagrangian framework, offering enhanced predictions of droplet size within the stretching separation regime.

Topological Defects in Tactoid Nematic Phase

The purpose research of the work is to illustrate the role of point surface topological defects in nematics in phase transitions using the example of inorganic sols of vanadium pentoxide in water V2O5/H2O.Methods. Basing on the measurements on polarization light microscopy and theoretically, in frames of the Landau-de Gennes model and the Kibble-Zurek model for defects, the influence of point topological defects at the surface of nematic colloid of lyotropic liquid crystals, in particular, in inorganic sols of the V2O5/H2O system, on their critical thermodynamic, electric, optical, elastic and mechanical properties is estimated. For the system V2O5/H2O, we study the developed models of nematic colloid phases with non-trivial topology composed of spindle-shaped particles, in which their topological defects are classified; geometrical parameters of nematic particles in dynamics and evolution depending on physicochemical conditions, phase stability criteria, conditions for coalescence of particles, including, under external magnetic field, and also, experimental observations confirmed the proposed theories and models, are considered.Results. With a glance of coalescence regime, the critical size of a colloid particle of the system V2O5/H2O, ~ 10 nm in the long axis direction, in which the value of magnetic energy equals to the sum of elastic and surface energy of acolloid particle, is estimated.Conclusion. We confirmed, that the prerequisite of sol particle coalescence in the system V2O5/H2O in the magnetic field is annihilation of the point topological defects at their poles, the geometrical criterion of tactoid coalescence in magnetic field is established basing on the different theories of their surface defects.

The interaction of a droplet with an immiscible deep liquid pool for density ratio greater than unity

Droplet interaction with liquid pools has been widely studied. The focus of these studies has primarily been on like-fluids, the droplet being miscible with the pool. Such miscible droplet–pool interactions have been extensively studied for their regimes of Rayleigh jet formation, crater formation, splashing, and coalescence. However, the case of immiscible droplet fluid has received considerably less attention from researchers. The immiscible case is relatively complex to understand owing to the involvement of three interfacial tensions. In the current study, we investigate the regimes of droplet–pool interaction for the case of immiscible droplet fluid having higher density and surface tension than pool fluid. Droplet properties are characterized through Weber number while Ohnesorge number is used to characterize pool fluid. Weber number is controlled through velocity of droplet and viscosity of pool is used to predict Ohnesorge number. Validating the numerical methods with experimental data, extensive numerical simulations are performed to gain insight into droplet–pool interaction. Current investigation reveals that for the case of immiscible fluids, regime formation is observed due to Rayleigh–Plateau instability as well as droplet fluid interacting with the pool fluid. This enables the pool fluid jet separation at high Ohnesorge numbers too, in contrast to miscible fluids case. The regimes of droplet–pool interaction for current case are described in detail and classified over wide range of Weber and Ohnesorge numbers.

Scaling dynamics and universality of fission-gas-bubble growth in amorphous systems

ABSTRACT We present a generalised approach for describing the universal dynamics and statistical properties of fission gas bubble growth in amorphous systems, using as an example. We examine the scaling properties of both the growth and coalescence regimes of bubble growth, and find that the scaling exponents in these regimes are controlled by the fission rate and temperature. The nucleation regime is characterised by a growth exponent close to 1/2, while the coalescence regime is characterised by a growth exponent around 1/3. We show that the statistical distribution over bubble size is of a universal character. Analytical results are verified by numerical simulations and clarified with experimental data. This study provides insight into the kinetics of fission gas bubble growth in amorphous systems.

Direct aqueous mineral carbonation of carbide slag in a bubble column reactor under ambient conditions

The accelerated carbonation technology utilizing the alkaline minerals or alkaline wastes incurs high operation and investment costs low conversion efficiency and high energy consumption. Due to the strong alkalinity of the carbide slag, good feedstock availability and great performance of the bubble column reactor, the direct aqueous mineral carbonation of the carbide slag in a bubble column at ambient conditions is evaluated. The impact mechanism of the liquid to solid ratio (5 mL/g−50 mL/g) and gas velocity (0.0041 m/s−0.205 m/s) on the reactions are investigated. The flow patterns are identified by empirical mode decomposition (EMD) energy entropy, and carbonation efficiencies at different flow regimes are compared and illustrated. It is found that this route has a high carbonation efficiency and short reaction time. The maximum carbonation efficiency is 100% and the capture capacity is 214.05 g CO2 / kg carbide slag. The discrete bubble regime (DBR) and bubble coalescence regime (BCR) are observed, and the increase of the L/S ratio can promote the bubble coalescence. The hydrodynamics can influence the processes of the CO2 mass transfer from gas to liquid phase, Ca(OH)2 dissolution, reactant diffusion, collision and ionic reactions. At small L/S ratio, the greater carbonation efficiency is achieved in discrete bubble regime attributing to the longer gas residence time, larger gas–liquid interfacial area and better CO2 mass transfer than that in BCR. At large L/S ratio, the greater carbonation efficiencies are achieved both in DBR and BCR. It has good CO2 mass transfer in DBR and has the strong liquid turbulence intensity in BCR which is good for the reactant diffusion and collision. The enhancement factor increases when enhancing the L/S ratio in DBR. The 30 mL/g and the gas velocity operated in the discrete bubble regime are recommended considering the better three-phase contact, good carbonation conversion and low energy consumption.

Electrocoalescence dynamics of two unequal-sized droplets

The present study investigates the electrocoalescence dynamics of two unequal-sized water droplets surrounded by a different fluid (typically considered oil). Finite element method-based level-set formalism has been adopted to solve the governing transport equations for a two-dimensional framework, and the accuracy of the solver is ascertained by validating with previously reported experimental results. The study extensively explores the characteristics of the droplet-to-droplet coalescence phenomenon, which is governed by key determinants like electric field strength , diameter ratio of the coalescing droplets, and viscosity of the fluids. It reveals that the electric field application shifts the coalescence regime from complete to partial beyond a limiting field strength for a corresponding diameter ratio. For a larger diameter ratio, the electric field strength required to get partial coalescence is relatively smaller than that needed for a smaller diameter ratio. In the context of partial coalescence, increasing electric field generates larger satellite droplets. With significantly higher electric field strength application, the satellite droplet goes under the second stage pinch-off phenomenon without coalescence. The partial coalescence gets suppressed with the increase in viscosity of the surrounding fluid; however, with the application of a larger voltage, partial coalescence can be achieved even for higher viscous fluid, and the same becomes more susceptible at a higher diameter ratio of the droplets. Finally, it is also established with an extensive comparison of how the present work is fundamentally remarkable and holds the utmost significance in the community of droplet dynamics research.

Optical Breakdown on Clusters of Gas Nanobubbles in Water; Possible Applications in Laser Ophthalmology

Here we studied the regimes of optical breakdown in water, stimulated by nanosecond and picosecond laser pulses at a wavelength of 1064 nm. A distinctive feature of our theoretical model, confirmed in experiment, is that in our case the optical breakdown develops on heterogeneous centers-clusters of gas nanobubbles. To the best of our knowledge, this is the first study of the role of clusters of gas nanobubbles in the optical breakdown of liquids that are transparent to pump radiation. In the experiment described in this paper, it was found that when initially degassed water is saturated with dissolved air, the breakdown threshold decreases. A theoretical model describing this phenomenon is suggested. This model includes the development of an electron avalanche inside individual nanobubbles, followed by the stimulated optical coalescence of a nanobubble cluster. According to our estimates, this regime occurs at laser radiation intensities of about 106–107 W/cm2. It is important that at such low intensities the breakdown flash (the basic endpoint of optical breakdown) does not appear due to the deficit of input laser energy. We provide an experimental proof of the coalescence regime, stimulated by a laser pulse in nanosecond range. The experimental threshold of stimulated coalescence is in good agreement with the theoretical estimates. Since the stimulated optical coalescence mode occurs at very low laser intensities, its excitation does not result in mechanical side effects in eye tissues, i.e., a shock wave should not be excited. Note that shock wave always occurs during optical breakdown, which is traditionally excited at intensities of 1012 W/cm2. In our experiment, the generation of a shock wave at such pump intensities was also observed. Since, according to the estimates given in the article, the volume number density of nanobubble clusters in the intraocular fluid can reach 108 cm−3, the excitation of the stimulated optical coalescence mode of nanobubble clusters can be used in ophthalmic surgery, such as laser iridotomy.

Investigation of regimes and associated flow structures during impingement of a liquid drop on a liquid pool

We study the impingement of a liquid drop on a liquid pool and find four new flow structures: (i) blob, (ii) blob and secondary ring, (iii) primary ring, secondary ring and jet, and (iv) primary ring and jet. We have delineated comprehensive pictures of coalescence and splashing regimes and their associated flow structures as a function of the controlling dimensionless numbers in a series of phase diagrams. These findings may not only provide physical insight into phenomena associated with the drop impact dynamics but also assist researchers to identify the specific impact conditions under which each phenomenon occurs, so that it can be avoided or allowed depending on the application.

Polarization motion of bubbles in a non-uniform electric field

In this study, the polarization motion of bubbles in a determined dielectric liquid medium (n-heptane) under a direct current (DC) non-uniform electric field were experimentally studied, using high-speed photography and with a focus on the effect of applied voltage and gas flow rate on bubble dispersion characteristics. The results show that increasing the electric field strength leads to a shortening of the bubble growth period, a significant reduction in bubble size and a rapid generation frequency. At low electric field strength, the bubble motion mainly exhibits hydrodynamic characteristics, and the height of the bubble chain shortens with the increase of BoE as a result of wake effect. In contrast, at high electric field strength, the bubble motion is first governed by polarization force and manifests electrohydrodynamic (EHD) characteristics, and the height of the bubble chain extends upward with increasing electrical Bond number (BoE). Nevertheless, once the bubbles leave the region dominated by the polarization force, their motion again displays hydrodynamic characteristics, and then the bubbles spread out the liquid phase, subject to bubble wakes and bubble-to-bubble interaction behaviors. In addition, two typical regimes of bubble coalescence are divided depending on the coalescence positions, including the coalescence near the tube orifice and the coalescence at the end of the bubble chain. The bubble size distribution at different heights corresponds to the bubble coalescence regimes.

Multiple vapor cavitation bubble interactions with a thermal lattice Boltzmann method

The double distribution function thermal lattice Boltzmann method is applied to investigate the thermodynamics of bubble interactions. The complete growth and collapse processes during an interaction are successfully reproduced, and interaction regimes of double cavitation bubbles are systematically studied, including strong and weak interactions. The critical distances to distinguish different interaction modes between two equal-sized bubbles are also proposed. For the weak interaction regime of two unequal-sized bubbles, the pressure wave generated by the smaller cavitation bubble leads to less distortion of the larger bubble in the final collapse stage. Moreover, a modified inertia model is proposed, which can be used to predict the liquid film thickness evolution of the unequal-sized bubbles under strong interaction regimes. Unbalanced forces act on the liquid film for two unequal-sized bubbles, making the film more difficult to rupture than for equal-sized bubbles, and the coalescence regime needs a smaller initial distance between them. Finally, the “shield effect” of the outer layer cavitation bubble and the “wall effect” of inner layer cavitation bubbles have been accurately reproduced in a cavitation bubble cluster, and the toroidal bubble shape in the final collapse stage is successfully simulated.

Binary droplet interactions in shear water-in-oil emulsion: A molecular dynamics study

The shear field and binary droplet interaction regimes of water-in-oil emulsions between parallel gold plates were investigated by molecular dynamics (MD) methods. The developed MD model was subjected to dimensional analysis and the dimensionless numbers that guarantee the similarity between the model and the actual system were identified as the capillary number (Ca), Reynolds number (Re), Weber number (We), and dimensionless time (τ). The effects of different pressures were compared by applying different forces perpendicular to the shear direction to the parallel plates. The heptane formed adsorbed layers on the gold plates, exhibited a shear thinning characteristic, and formed a no-slip uniform shear field driven by the parallel plates. The interactions between gold atoms and a heptane molecule have been investigated in depth by quantum chemical methods and it has been found that the nature of the adsorption is a van der Waals interaction. Three main binary droplet interaction regimes are produced in the presence of shear fields: coalescence, a temporary bridge formation, and sliding. The effects of capillary forces and shear effects on liquid bridges were discussed. Droplet trajectories and deformations under different pressure were analyzed. Finally, the effect of initial offset (ΔYin/2R) and Ca on the droplet interaction regime was investigated through regime maps. It was found that the coalescence regime has upper critical points for ΔYin/2R and Ca; droplet slipping occurs mainly at higher ΔYin/2R; the temporary bridge formation regime appears mainly at higher Ca. This study provides a new idea for understanding binary droplet interactions in shear emulsions.

Coalescence of bubbles in a high Reynolds number confined swarm

We investigate experimentally the coalescence cascade process for a confined swarm of deformable bubbles immersed in a bidimensional vertical cell filled with water. For different gas volume fractions, air bubbles of size $D_0$ larger than the cell thickness are injected at the bottom of the cell. The bubbles swarms transformation is explored using high-speed visualizations. The time evolution of each bubble in the swarm is determined using a specifically developed algorithm, enabling bubble tracking and coalescence detection. We determine the evolution of the bubble size distribution downstream from the injection point, and show that the stages of the coalescence cascade are characterized by the diameter, $D_{V90}$ , representative of the largest bubbles. The collision frequency of pairs of bubbles of sizes $D_k$ and $D_{k'}$ , $h(D_k, D_{k'})$ , and their coalescence efficiency, $\lambda$ , are obtained from the experiments. The efficiency is nearly constant, independently of the bubble sizes and of the gas volume fraction. Concerning collision frequency, our results reveal the existence of two different coalescence regimes depending on the capability of the bubbles to deform. Models describing $h(D_k, D_{k'})$ for both regimes are provided. They take into account the specific response of the bubble pair, which depends on the reduced diameter $D_p = 2 D_k D_{k'} / (D_k + D_{k'})$ , to the global swarm-induced agitation governed by $D_{V90}$ and the gas volume fraction. In the first regime, occurring for smaller $D_p$ , bubbles are brought together by agitation and rapidly coalesce, while for sufficiently large $D_p$ , both bubbles are able to deform and spend more time adapting mutually their shapes before coalescing.

Temperature Effects in the Initial Stages of Heteroepitaxial Film Growth

Kinetic Monte Carlo simulations of a model of thin film heteroepitaxy are performed to investigate the effects of the deposition temperature in the initial growth stages. Broad ranges of the rates of surface processes are used to model materials with several activation energies and several temperature changes, in conditions of larger diffusivity on the substrate in comparison with other film layers. When films with the same coverage are compared, the roughness increases with the deposition temperature in the regimes of island growth, coalescence, and initial formation of the continuous films. Concomitantly, the position of the minimum of the autocorrelation function is displaced to larger sizes. These apparently universal trends are consequences of the formation of wider and taller islands, and are observed with or without Ehrlich-Schwöebel barriers for adatom diffusion at step edges. The roughness increase with temperature qualitatively matches the observations of recent works on the deposition of inorganic and organic materials. In thicker films, simulations with some parameter sets show the decrease of roughness with temperature. In these cases, a re-entrance of roughness may be observed in the initial formation of the continuous films.

Droplet behavior in overexpanded supersonic two-phase jets

The interaction of liquid droplets generated by spray atomization with high-speed co-flowing gas is of interest in various applications including fuel injection, spray cooling, and surface coating. The underlying processes involve interactions between the droplets themselves, and with the carrier gas. Additionally, they are influenced by shock and expansion waves present in high-speed flows, accompanied by resulting velocity and pressure fluctuations. Non-intrusive diagnostics including Shadowgraphy and Phase Doppler Particle Anemometry, along with flow simulations, are used to study droplet behavior, characterized by size and velocity changes, as a finely atomized spray is propelled by a carrier gas through a supersonic, overexpanded jet structure. Measurements of droplet size and velocity are correlated to the shock train structure of the overexpanded jet and further to gas velocity as obtained from simulation results. While the shock structure is observed to be unaffected by spray injection, periodic increases and decreases are observed in average droplet size. Analysis using gas flow field obtained from simulations, estimated critical Weber numbers for droplet breakup and timescales for droplet dynamics, compared to residence time in the flow, suggests that droplet size changes can be attributed to alternating coalescence and breakup. The two-dimensional flow structure involving converging and diverging sections as well as a spread in droplet sizes likely promote coalescence and breakup processes leading to periodic variation in droplet SMD. The streamwise variations of gas velocity along the centerline caused by the shock train are not noticed in the droplet velocity, which can be explained by the high Stokes number causing droplets at the centerline to behave as ballistic particles moving through the shock structure. Experimental measurements, simulation results, and their subsequent analyses show that droplet collision and coalescence regimes established in previous work for ambient conditions show deviations when subject to high-speed gas flow conditions.

Investigation of regimes during partial/complete coalescence of a liquid drop on a liquid pool

The coalescence dynamics of a liquid drop on a liquid pool are investigated, considering either air or another liquid as a surrounding fluid. Numerical simulations are performed over a wide range of dimensionless parameters to investigate the subtle interplay of different forces on the partial coalescence and complete coalescence regimes. Our comprehensive study reveals that these two regimes can be demarcated into three sub-regimes depending on the coalescence stage: (i) first-stage partial coalescence, (ii) second-stage complete coalescence, and (iii) first-stage complete coalescence. This rarity classification of the coalescence process is illustrated as a function of the controlling dimensionless numbers in the phase diagrams. To gain quantitative insights into the coalescence dynamics, the hydrodynamic variances associated with this parametric analysis are examined in terms of kinetics of the neck radius and the apex height of the drop, ratio of the daughter drop to mother drop diameter, and the pinch-off time.

Learning new physical descriptors from reduced-order analysis of bubble dynamics in boiling heat transfer

Understanding bubble dynamics during boiling is challenging due to the drastic changes in system parameters, such as nucleation, bubble morphology, temperature, and pressure. In this study, principal component analysis (PCA), an unsupervised dimensionality reduction algorithm, is used to extract new physical descriptors of boiling heat transfer from pool boiling experimental images without labeling and training. The dominant frequency and amplitude of the time-series principal components (PCs) are analyzed, where the first few dominant PCs are used to approximate the instantaneous bubble morphologies, drastically reducing the data dimensions. The results show that the dominant frequency and amplitude can be used as new physical descriptors to distinguish different boiling regimes. The dominant frequency of the first PC is found to increase with heat flux in the discrete bubble regime until it reaches a peak and then decreases with heat flux in the bubble interference and coalescence regime, where the former is believed to be associated with the increase in bubble nucleation sites and the latter is associated with the bubble coalescence during pool boiling. The dominant frequency and amplitude extracted from the present unsupervised learning are qualitatively compared to the bubble count and size extracted from a supervised deep-learning algorithm, and the approach appears highly robust over multiple datasets and heater surfaces. To predict future boiling states for mitigating boiling crises, bidirectional long short-term memory (BiLSTM) neural network is used to estimate the future variations of PCs and hence the bubble dynamics, from time-series PCs. The PCA-BiLSTM models predict reduced-order bubble images well and show significantly higher prediction accuracy compared to the Convolutional-LSTM.

Quasi-two-dimensional coalescence of nematic and isotropic droplets and Rayleigh-Plateau instability in flat optical cells.

We investigated the coalescence of nematic droplets in an isotropic environment and that of isotropic droplets in a nematic environment in quasi-two-dimensional geometry of a flat optical cell. Two different regimes of coalescence were found. In the circular meniscus between the nematic and isotropic regions both nematic and isotropic phases exist. As a result, two bridges form at coalescence: a nematic and an isotropic bridge. In this work, we focus on the situation when nematic wets the cell surface. The coalescence of nematic droplets starts near the cell surfaces where the droplet bridge from the nematic phase is formed. An outer bridge connecting the isotropic environment is localized in the middle of the cell. When the outer bridge gets thinner it becomes unstable and breaks up. A series of pinch-offs leads to the formation of satellite droplets. On the contrary, when isotropic droplets coalesce, the coalescence starts in the middle of the cell and breaking of the bridges occurs without instability and without the formation of satellite droplets. Breakup of the outer bridge is a new example of Rayleigh-Plateau instability in addition to actively studied transformation and breaking of filaments and stretched droplets.

Numerical Investigation of Two In‐Line Two‐Dimensional Bubbles Rising in a Two‐Dimensional Quiescent Ambient Liquid by a Conservative Phase‐Field Lattice Boltzmann Method

The coalescence and interaction of two in‐line two‐dimensional bubbles rising in viscous ambient liquids were studied using two‐dimensional simulations. A mass‐conserving lattice Boltzmann model that was combined by the phase‐field lattice Boltzmann equation (LBE) and the pressure‐evolution lattice Boltzmann method (LBM) with a multiple‐relaxation‐time (MRT) collision operator was used to solve the Navier–Stokes equations for multiphase flow. Starting from the circle shape, the interfaces of bubbles during the rising processes are captured by the calculation of the conservative phase‐field LBE. The influence of liquid viscosity and interface tension on the coalescence and interaction of bubbles was studied by varying the Archimedes numbers (Ar) from 1 to 300 and several Bond numbers (Bo) from 5 to 200. It was found that the bubble–bubble interaction is enhanced with the decrease of the liquid viscosity, and the outcome of the coalescence is promoted by the two vortex rings (liquid circulations) around the two bubbles. A comprehensive map of the coalescence regime was obtained. Four distinct coalescence regimes (namely, Central I, Central II, Edge, and Hug) were identified, and three critical Ar that can distinguish the above four regimes were defined. Moreover, the effects of Ar and Bo on the coalescence time and the relative velocity between the two bubbles were also investigated. The current work enhances the understanding of the coalescence and interaction of bubbles.

Impacts of Particle Properties on Gas Holdup under Four Flow Regimes in Three‐Phase Bubble Columns

AbstractThe impacts of the solid volume fraction Vs and particle size dp on the total and local gas holdups in gas‐liquid‐solid bubble columns under different flow regimes were investigated. The flow regimes discussed were the discrete bubble regime (DBR), transition regime (TR), bubble coalescence regime (BCR), and strong turbulent regime (STR). The results demonstrated that the bed average gas holdup εg decreased with higher solid volume fraction in DBR, TR, and BCR. The increment of the solid volume fraction promoted bubble coalescence and also can enhance the particle effect on the average gas holdup. The εg changed slightly when shifting the Vs or dp in STR. A new correlation for εg was developed considering the particle properties and the flow regimes studied.