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On the breakage of drops in a turbulent flow
... In both industrial and natural situations, the knowledge of the bubble size distribution and its temporal evolution is necessary to predict mass transfers across bubble interfaces. As a consequence, the study of bubble breakup in turbulence has received considerable attention since the pioneer works of Kolmogorov (1949) and Hinze (1955). They predicted that, for bubbles of size lying within the inertial range of the turbulent cascade, bubble dynamics and breakup are primarily controlled by the balance between inertial and capillary forces. ...
... As a consequence, as a first guess, they used the Rayleigh natural frequency of mode 2, = 2 , equation (1.1), and the Lamb damping rate = 2 , equation (1.2), even though these values only hold in a quiescent irrotational flow. Then, following the original idea from Kolmogorov (1949) and Hinze (1955), they assumed that the turbulent forcing from turbulence scales as the square of the instantaneous velocity increment at the bubble scale ( , ) 2 , leading to a forcing ( ) = ( , ) 2 from dimensional analysis, where is a numerical constant of order 1. Doing so, they assumed that the presence of the bubble does not strongly affect the flow properties, so that the flow statistics correspond to the single fluid case. ...
... (3.20)) then provides a complete model of a synthetic stochastic effective forcing for bubbles deformations in turbulence. Previous modelling approaches have used two points velocity measurements to model an effective forcing term (Risso & Fabre 1998;Lalanne et al. 2019;Masuk et al. 2021b), following the original idea from Kolmogorov (1949) and Hinze (1955). Here we found that the statistics of the effective forcing differ significantly from two points statistics, in particular due to the volumetric filtering effect at the particle size. ...
We investigate bubble deformations in an homogeneous and isotropic turbulent flow by means of direct numerical simulations of a single bubble in turbulence. We examine interface deformations by decomposing the local radius into the spherical harmonics base. We show that the linear dynamics of each mode, (for low Weber number), can be modeled by a forced stochastic linear oscillator. We measure the coefficients of the model directly from the modes' statistics. We find that the natural frequency corresponds to the Rayleigh frequency, derived in a quiescent flow. However, dissipation increases by a factor 15 compared to the quiescent case, at . This enhanced dissipation originates from a thick boundary layer surrounding the bubble. We demonstrate that the effective forcing, originating from the integration of pressure over the bubble surface, is independent on bubble deformability. Therefore, the interface deformations are only one-way coupled to the flow. Eventually, we investigate the pressure modes' statistics in the absence of bubbles and compare them to the effective forcing statistics. We show that both fields share the same pdf, characterized by exponential tails, and a characteristic timescale corresponding to the eddy turnover time at the mode scale.
... The droplets are modelled using the volume of fluid method, and the soluble surfactant is transported using an advectiondiffusion equation. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, thus allowing us to extend the framework developed by Hinze (1955) and Kolmogorov (1949) for surfactant-free bubbles to surfactant-laden droplets. The Kolmogorov-Hinze scale is indeed found to be a pivotal length scale in the droplets' dynamics, separating the coalescence-dominated (droplets smaller than the Kolmogorov-Hinze scale) and the breakage-dominated (droplets larger than the Kolmogorov-Hinze scale) regimes in the droplet size distribution. ...
... We find that the length scale separating these two regimes is the Kolmogorov-Hinze scale, defined as the maximum size of a droplet that is not broken apart by turbulent fluctuations; droplet breakage becomes prevalent for droplets larger than the Kolmogorov-Hinze scale. The concept of the Kolmogorov-Hinze scale originates from the works of Kolmogorov (1949) and Hinze (1955), who applied Kolmogorov's (1941) assumptions to droplets in turbulence. Some recent studies, however, have disputed the theoretical framework upon which Hinze's theory is based and hence the relevance of the Kolmogorov-Hinze scale: Qi et al. (2022) showed that droplets interact with eddies of a range of length scales, rather than solely with eddies of a size similar to the droplet, and Vela- Martín & Avila (2022) showed that droplet breakup does, in fact, occur below the Kolmogorov-Hinze scale. ...
... Several authors have devoted their attention to the development of models for the unresolved scales to be used in direct numerical simulations and large eddy simulations. In their original works Kolmogorov (1949) and Hinze (1955) identified the maximum size of a non-breaking droplet in turbulence. Experimental measurements (Deane & Stokes 2002;Garrett et al. 2000) later showed that the existence of two different regimes in the droplet size distribution, separated by the Kolmogorov-Hinze scale. ...
We perform direct numerical simulations of surfactant-laden droplets in homogeneous-isotropic turbulence with Taylor Reynolds number . Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, allowing us to extend the framework developed by Kolmogorov (1949) and Hinze (1955) for surfactant-free bubbles to surfactant-laden droplets. We find the Kolmogorov-Hinze scale () is indeed a pivotal length scale in the droplets' dynamics, separating the coalescence-dominated and the breakage-dominated regimes in the droplet size distribution. We see that droplets smaller than have spheroid-like shapes, whereas larger droplets have long convoluted filamentous shapes with diameters equal to . As a result, droplets smaller than have areas that scale as , while larger droplets have areas that scale as , where d is the droplet equivalent diameter. We further characterise the filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier phase enclosed by the dispersed phase) on each droplet. The number of handles per unit length of filament () scales inversely with surface tension, while the number of voids is independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely inside the droplets.
... La deformaciuon y la rotura determinan el area de la entrefase entre las dos fases, y por tanto las velocidades de transferencia de calor, masa y cantidad de movimiento. Kolomogorov [8] fue el primero en investigar la rotura de gotas (fase dispersa) en un flujo turbulento homogeneo e isctropo (fase continua), bajo la simplificacicn de igual densidad para ambas fases. En funcion de la relacicn entre la escala viscosa del flujo, el tamano de la particula -gota o burbuja-y la relation de viscosidades de los fluidos de cada fase, distinguio diferentes regimenes. ...
... De acuerdo con la teoria de Kolmogorov-Hinze [4,8], el proceso de rotura de una burbuja en un flujo turbulento, es el resultado de una competition entre las tensiones debidas a las fluctuaciones de presion del flujo que tienden a deformar la burbuja, y las debidas a la tension superficial que tienden a que la burbuja mantenga su forma esferica. La relation entre ambas fuerzas es el numero de Weber turbulento, parumetro adimensional clave del problema. ...
... Las imagenes de la morfologia de la burbuja a lo largo del proceso de rotura, muestran como la forma casi esferica inicial de la burbuja, se estira segun una direction preferente, hasta romper, tal y como se puede observar en la figura 2. Por lo tanto, el tipo de rotura observado en los trabajos experimental^, corresponde, de acuerdo con el trabajo clasico de Hinze [4], con un tipo de rotura en forma de cigarro. La observaciun de las imagenes experimental^, permite deducir que la burbuja rompe debido a la interaccicn con vertices turbulentos de tamano similar, que la estiran antes de romper, como era ya postulado por la teoria de Kolmogorov-Hinze [4,8]. El estiramiento observado implica la existencia de una direcciuon preferencial a lo largo de la cual se produce la deformacion, por lo que el proceso de rotura puede considerarse en una primera aproximacicn como axisimetrico. ...
CIEMAT Technical Report in Spanish. Content partially in the paper 'Bubble break-up in a straining flow at finite Reynolds numbers', J. Fluid Mech. (2006), vol. 551, pp. 175–184.
... However, there is also a more fundamental scientific interest in understanding how the details of turbulent flows interact with interfacial dynamics to give rise to deformation and breakup [3][4][5][6]. Although, turbulent drop breakup phenomena have been studied and discussed at least since the 1940s and 1950s [7,8], there is not yet a commonly accepted procedure for making valid and reliable predictions under industrially relevant conditions [2]. ...
... Three main frameworks for predicting drop breakup under turbulent emulsification can be seen in the literature: (i) the extended Kolmogorov-Hinze framework for estimating the largest drop surviving prolonged exposure to a turbulent field [7][8][9][10][11], (ii) the population balance equation (PBE) framework for predicting the dynamic evolution of the drop sizedistribution [12][13][14][15][16] and (iii) the oscillatory resonance mechanism framework for predicting critical drop diameters [5,17,18]. ...
... Whereas originally proposed as a scaling law, the Kolmogorov-Hinze framework (i) is essentially a stress balance where the largest drop surviving prolonged exposure is predicted by equating disruptive and restoring stress [7][8][9]19]. The PBE framework (ii) is a set of conservation laws describing the transport of drop volume between size classes, closed by specifying a breakup frequency function (together with its fragment size distribution and, if present, by a coalescence frequency function) [12]. ...
Many industrially relevant emulsification devices are of the high-energy type, where drop deformation and subsequent breakup, take place due to intense turbulent fluid–drop interactions. This includes high-pressure homogenizers as well as rotor-stator mixers (also known as high-shear mixers) of various designs. The stress acting on a drop in a turbulent flow field varies over time, occasionally reaching values far exceeding its time-averaged value, but only during limited stretches of time, after which it decreases down to low values again. This it is one factor separating turbulent from laminar emulsification. This contribution reviews attempts to take this intermittently time-varying stress into account in models predicting the characteristic drop diameter resulting from emulsification experiments, focusing on industrially applicable emulsification devices. Two main frameworks are discussed: the Kolmogorov–Hinze framework and the oscillatory resonance framework. Modelling suggestions are critically discussed and compared, with the intention to answer how critical it is to correctly capture this time-varying stress in emulsification modelling. The review is concluded by a list of suggestions for future investigations.
... Since the late 2000s, investigators have started to move from using CFD to mainly discuss velocity fields, pressures and turbulence levels, to using the CFD results to model, predict or test emulsification efficiency between designs and operating conditions, either by using Kolmogorov-Hinze theory (Arai et al., 1977;Calabrese et al., 1986;Davies, 1985;Hinze, 1955;Kolmogorov, 1949;Vankova, et al., 2007) or a population balance equation (PBE) formulation (Liao and Lucas, 2009;Ramkrishna, 2000;Solsvik et al., 2013). Köhler et al. (2008) studied a microstructured simultaneous homogenizing and mixing valve using RANS CFD based on RNG k -e model to investigate the effect of the operating parameters on the predicted fat globules size distribution. ...
... The maximum drop diameter resulting from prolonged exposure of an emulsion to a turbulent field characterized by a dissipation rate of e* can be accurately predicted by the drop-viscosity corrected Kolmogorov-Hinze theory (Arai et al., 1977;Calabrese et al., 1986;Davies, 1985;Hinze, 1955;Kolmogorov, 1949;Vankova et al., 2007). When the resulting drop diameter is larger than the Kolmogorov length-scale, the relationship is: ...
... As mentioned in the introduction, most investigators suggest drop breakup in HPH valves to be caused mainly by turbulent interactions, and that the stress on the drop (or the rate of drop breakup) can be predicted using the dissipation rate of TKE (Arai et al., 1977;Calabrese et al., 1986;Davies, 1985;Hinze, 1955;Kolmogorov, 1949;Vankova et al., 2007). At the same time, dissipation rate of TKE is generally understood as difficult to estimate, especially using two-equation RANS modelling approaches (Pope, 2000). ...
There is a large interest in predicting high-pressure homogenizer (HPH) valve hydrodynamics using CFD, in academic research and industrial R&D. Most of these studies still use two-equation RANS turbulence models, whereas only a few have used LES formulations. From a theoretical perspective, LES is known to be more accurate than RANS, especially in terms of estimating the dissipation rate of turbulent kinetic energy, which is the most important parameter needed for predicting efficiency using a population balance equation (PBE). However, LES also comes at a considerably higher computational cost. To choose the appropriate modelling approach, it is important to understand how much the accuracy and the computational cost increase between RANS and LES.
This study provides the first validation of high-pressure homogenizer hydrodynamics, comparing RANS and a well-resolved LES to numerical experimental validation data of direct numerical simulation (DNS), on a model of the gap outlet jet. The LES does result in a higher accuracy throughout, but the differences are relatively small, when focusing on the flow inside the jet. When using the CFD results to predict maximum surviving drop diameter, the LES results in a relative error of 4.8 % whereas the RANS leads to a relative error of 18 %. Both errors are substantially smaller than those from a traditional scale-based equation instead of a CFD-PBE. When seen in the substantial reduction of computational time (a factor of 970), results illustrate how RANS could remain a viable supplementary technique for CFD modelling of HPHs, despite its many limitations. Best practice recommendations for obtaining this RANS performance is discussed.
... to the targeted bubble size based on the critical Weber number as proposed in the classic Kolmogorov-Hinze framework (Kolmogorov 1949;Hinze 1955). The time scale, however, was not discussed until it was first brought up in the seminal work by Levich (1962). ...
... Given the fact that τ e is driven by surrounding turbulence, two simple approaches are available to model τ e . The first approach is the Kolmogorov-Hinze (KH) framework (Kolmogorov 1949;Hinze 1955), based on which the time scale of the inertial deformation process τ e can be estimated using the turn-over time scale of the bubble-sized eddy, i.e. τ D = D/( √ C 2 ( D) 1/3 ), which is shown in figure 5 as purple dashed lines for various . The other approach is to associate τ e with the resonance oscillation of the bubble, which could also lead to breakup (Risso & Fabre 1998). ...
The familiar process of bubbles generated via breaking waves in the ocean is foundational to many natural and industrial applications. In this process, large pockets of entrained gas are successively fragmented by the ambient turbulence into smaller and smaller bubbles. The key question is how long it takes for the bubbles to reach terminal sizes for a given system. Despite decades of effort, the reported breakup time from multiple experiments differs significantly. Here, to reconcile those results, rather than focusing on one scale, we measure multiple time scales associated with the process through a unique experiment that resolves bubbles’ local deformation and curvature. The results emphasize that the scale separation among various time scales is controlled by the Weber number, similar to how the Reynolds number determines the scale separation in single-phase turbulence, but shows a distinct transition at a critical Weber number.
... The Kolmogorov-Hinze (KH) theory (Kolmogorov, 1949;Hinze, 1955) illustrated the stability condition of fluid particles in the view of the particle-turbulence interactions. In the theory, fluid particle was assumed to break when the hydrodynamic stress generated by turbulence velocity fluctuation exceeds the restraining force of interfacial tension, and a particle Weber number was defined to characterize the competition between the disruptive and the restoring forces in a dimensionless form ...
... In turbulence, an eddy bombards a bubble and delivers its kinetic energy to the bubble, leading to an increase in the surface energy. The mean kinetic energy contained in an eddy with size λ is given by the energy spectrum of the inertial subrange (Kolmogorov, 1949;Hinze, 1955), expressed as ...
... Despite the wide range of scales involved, many key concepts crucial to understanding deformation and breakup in turbulence can be traced back to the seminal works by Kolmogorov (1949) and Hinze (1955), i.e. the Kolmogorov-Hinze (KH) framework. The KH framework has gained widespread acceptance in various fields, however, it is crucial to acknowledge that it contains a number of assumptions and hypotheses. ...
... The problem at hand is characterized by a multitude of parameters, and as a result, the relevant dimensionless groups are also vast. However, by making some key assumptions and hypotheses, as outlined in Textbox 1, Kolmogorov (1949) was able to simplify the problem. He proposed that, for the deformation and breakup of large bubbles/droplets (η ≪ D ≪ L), the most important dimensionless number is the Weber number, which is a measure of the ratio between the inertial forces to surface tension forces. ...
Fragmentation of bubbles and droplets in turbulence produces a dispersed phase spanning a broad range of scales, encompassing everything from droplets in nanoemulsions to centimeter-sized bubbles entrained in breaking waves. Along with deformation, fragmentation plays a crucial role in enhancing interfacial area, with far-reaching implications across various industries, including food, pharmaceuticals, and ocean engineering. However, understanding and modeling these processes is challenging due to the complexity of anisotropic and inhomogeneous turbulence typically involved, the unknown residence time in regions with different turbulence intensities, and difficulties arising from the density and viscosity ratios. Despite these challenges, recent advances have provided new insights into the underlying physics of deformation and fragmentation in turbulence. This review summarizes existing works in various fields, highlighting key results and uncertainties, and examining the impact on turbulence modulation, drag reduction, and heat and mass transfer.
... The presence of a deforming/breaking/coalescing interface couples the two phases in a non-trivial way, absorbing and distributing energy over the whole spectrum of scales. The Kolmogorov-Hinze (KH) theory 18,19 is the cornerstone of existing models and applications; this framework is based on the breakup of isolated droplets in turbulence and identifies the scale d H above which a droplet breaks up due to the local environment turbulence and below which surface tension forces are able to resist the action of the turbulent eddies. This picture, based on breakup only, is incomplete and has been recently challenged 20 . ...
... is the time-space average energy dissipation rate, and using dimensional analysis, Kolmogorov and Hinze first derived an estimate for the maximum droplet size for which surface tension is able to resist the pressure fluctuations 7,18,19 : ...
The dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at Rλ ≈ 140, the highest attained up to now. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality. Dynamics of droplet fragmentation in turbulence is described by the Kolmogorov-Hinze theory, but at higher concentrations common in most flows a quantitative theory is required. The authors use direct numerical simulations of turbulent multiphase flows finding that larger droplets break up absorbing energy from the flow, while smaller droplets undergo rapid oscillations and tend to coalesce releasing energy to the flow.
... In the low-volume-fraction regime, droplet fragmentation is generally caused by the turbulent stress, while the presence of droplets hardly affects the continuous phase (Afshar Ghotli et al. 2013). The study of the droplet size in a turbulent flow can be traced back to Kolmogorov (1949) and Hinze (1955), who attributed the droplet breakup to turbulent fluctuations. Although the Kolmogorov-Hinze (K-H) theory has been validated in a variety of experimental and numerical studies on droplets or bubbles in a turbulent flow (Risso & Fabre 1998;Perlekar et al. 2012;Eskin, Taylor & Yang 2017;Rosti et al. 2019), it was found to have limitations, for example, in non-homogeneous turbulent flows (Hinze 1955). ...
... The O/W emulsions at φ o = 1 % without surfactant are considered here. surface (Kolmogorov 1949;Hinze 1955), of which the ratio is usually indicated by the droplet turbulent Weber number We = ρ δu 2 D/γ , where ρ is the density of the continuous phase, δu 2 is the mean-square velocity difference over a distance equal to the droplet diameter D, and γ is the interfacial tension between the two phases (Risso & Fabre 1998). If the droplet diameter D belongs to the inertial turbulent sub-range, then δu 2 could be expressed as a function of the local energy dissipation rate: δu 2 = C 1 (εD) 2/3 , where the constant is C 1 ≈ 2 according to Batchelor (1953). ...
By varying the oil volume fraction, the microscopic droplet size and the macroscopic rheology of emulsions are investigated in a Taylor–Couette turbulent shear flow. Although here oil and water in the emulsions have almost the same physical properties (density and viscosity), unexpectedly, we find that oil-in-water (O/W) and water-in-oil (W/O) emulsions have very distinct hydrodynamic behaviours, i.e. the system is clearly asymmetric. By looking at the micro-scales, the average droplet diameter hardly changes with the oil volume fraction for O/W or for W/O. However, for W/O it is about larger than that of O/W. At the macro-scales, the effective viscosity of O/W is higher when compared to that of W/O. These asymmetric behaviours are expected to be caused by the presence of surface-active contaminants from the walls of the system. By introducing an oil-soluble surfactant at high concentration, remarkably, we recover the symmetry (droplet size and effective viscosity) between O/W and W/O emulsions. Based on this, we suggest a possible mechanism responsible for the initial asymmetry and reach conclusions on emulsions where interfaces are fully covered by the surfactant. Next, we discuss what sets the droplet size in turbulent emulsions. We uncover a scaling dependence of the droplet size on the Reynolds number of the flow. Combining the scaling dependence and the droplet Weber number, we conclude that the droplet fragmentation, which determines the droplet size, occurs within the boundary layer and is controlled by the dynamic pressure caused by the gradient of the mean flow, as proposed by Levich ( Physicochemical Hydrodynamics , Prentice-Hall, 1962), instead of the dynamic pressure due to turbulent fluctuations, as proposed by Kolmogorov ( Dokl. Akad. Nauk. SSSR , vol. 66, 1949, pp. 825–828). The present findings provide an understanding of both the microscopic droplet formation and the macroscopic rheological behaviours in dynamic emulsification, and connects them.
... The presence of a deforming/breaking/coalescing interface couples the two phases in a non-trivial way, absorbing and distributing energy over the whole spectrum of scales. The Kolmogorov-Hinze (KH) theory [18,19] is the cornerstone of existing models and applications; this framework is based on the breakup of isolated droplets in turbulence and identifies the scale d H above which a droplet breaks up due to the local environment turbulence and below which surface tension forces are able to resist the action of the turbulent eddies. This picture, based on breakup only, is incomplete and has been recently challenged [20]. ...
... The disruptive inertial-range velocity fluctuations can initiate fragmentation above a critical threshold W e c [21]. Assuming the local Kolmogorov description of turbulence [7,22], u 2 d ∼ ε 2/3 d 2/3 , where ε is the average energy dissipation rate, and using dimensional analysis, Kolmogorov and Hinze first derived an estimate for the maximum droplet size for which surface tension is able to resist the pressure fluctuations [7,18,19]: ...
The dynamics of droplet fragmentation in turbulence is described in the Kolmogorov-Hinze framework. Yet, a quantitative theory is lacking at higher concentrations when strong interactions between the phases and coalescence become relevant, which is common in most flows. Here, we address this issue through a fully-coupled numerical study of the droplet dynamics in a turbulent flow at high Reynolds number. By means of time-space spectral statistics, not currently accessible to experiments, we demonstrate that the characteristic scale of the process, the Hinze scale, can be precisely identified as the scale at which the net energy exchange due to capillarity is zero. Droplets larger than this scale preferentially break up absorbing energy from the flow; smaller droplets, instead, undergo rapid oscillations and tend to coalesce releasing energy to the flow. Further, we link the droplet-size-distribution with the probability distribution of the turbulent dissipation. This shows that key in the fragmentation process is the local flux of energy which dominates the process at large scales, vindicating its locality.
... Drops dispersed in a continuous phase under turbulent flow conditions can break upon the action of viscous or inertial stress acting on their surface. The dominant stress depends on the ratio of the drop size to the size of the smallest turbulent vortices in the flow (Kolmogorov, 1949). This size depends on the viscosity and density of the continuous phase, as well as on the rate of energy dissipation per unit mass of the fluid, which characterizes the hydrodynamic conditions during emulsification. ...
... This size depends on the viscosity and density of the continuous phase, as well as on the rate of energy dissipation per unit mass of the fluid, which characterizes the hydrodynamic conditions during emulsification. The seminal studies of the emulsification process in turbulent flow by Kolmogorov (1949) and Hinze (1955) revealed two regimes of emulsification referred to as "turbulent inertial" and "turbulent viscous" regimes. In the turbulent inertial regime, the drops are bigger than the smallest turbulent vortices in the continuous phase, whereas in the turbulent viscous regime the drops are smaller than the size of the smallest vortices. ...
Propolis has many benefits for human health. To facilitate its oral consumption, we designed propolis-in-water dispersions to be used as nutraceuticals. Propolis was first dissolved either in ethanol or in a hydroalcoholic solution. Water being a non-solvent for propolis, its addition produced propolis precipitation. We explored the ternary phase diagram of water, propolis and ethanol to identify the line separating the one phase region where propolis is fully dissolved, and the two-phase region where a concentrated propolis solution coexists with a dilute one. Droplets rich in propolis were produced during the phase separation process under mechanical stirring induced by a rotor-stator device or a microfluidizer, and they were stabilized using gum Arabic as an emulsifier. Ethanol was finally removed by distillation under reduced pressure. Propolis dispersions in the micron and submicron size range could be obtained. They contained between 1.75 and 10.5 wt% polyphenols relative to the total mass.
... However, the presence of walls significantly impacts the behaviour of emulsion droplets, leading to the formation of clusters and complex structures (Scarbolo, Bianco & Soldati 2015). The classical Kolmogorov-Hinze theory (Kolmogorov 1949;Hinze 1955) explains fluid breakup based on the balance between surface tension and inertial forces. However, in turbulent RB convection flows, buoyancy becomes a significant factor that can impact the breakup criteria (Liu et al. 2021), altering the heat transfer mechanism. ...
This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, , and ratios of dynamic viscosity, , and thermal diffusivity, , within the range [0.1\unicode{x2013}10] . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at , 4 , 6000 and 1 , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at and . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.
... However, the presence of walls significantly impacts the behavior of emulsion droplets, leading to the formation of clusters and complex structures (Scarbolo et al. 2015). The classical Kolmogorov-Hinze theory (Kolmogorov 1949;Hinze 1955) explains fluid breakup based on the balance between surface tension and inertial forces. However, in turbulent RB convection flows, buoyancy becomes a significant factor that can impact the breakup criteria (Liu et al. 2021), altering the heat transfer mechanism. ...
This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh-B\'enard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, 0.0 \leq \Upphi \leq 0.5, and ratios of dynamic viscosity, , and thermal diffusivity, , within the range . The Rayleigh, Prandtl, Weber, and Froude numbers are held constant at , 4, 6000, and 1, respectively. Initially, when both fluids share the same properties, a 10\% Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25\% at \Upphi=0.2 and . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50\% reduction in the Nusselt number compared to the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.
... For example, Wang Tiefeng [13] developed a model for bubble rupture frequency and subbubble size distribution, which can predict the size distribution of bubbles in known turbulent environments. Kolmogorov [14] and Hinze [15] proposed theories on bubble rupture in turbulent fields, suggesting that bubble rupture is caused by the interaction of turbulence and eddies. Based on these theoretical models, it has been concluded that four main mechanisms lead to bubble fragmentation in turbulent fields [16][17][18]: (1) collision of turbulent pulsations and vortices; (2) viscous shear; (3) fluid erosion; (4) instability of large bubble interfaces. ...
To enhance the performance of tubular microbubble generators, the Volume of Fluid (VOF) multiphase flow model in COMSOL Multiphysics was used to simulate the bubble fragmentation characteristics within a throttling hole microbubble generator. The effects of the inlet speed of the throttling hole pipe, the diameter of the throttling hole, and the length of the expansion section on bubble fragmentation performance were analyzed. The results indicated that an increase in the inlet speed of the throttling hole pipe gradually improved the bubble fragmentation performance. However, an increase in the throttling hole diameter significantly reduced the bubble fragmentation performance. Changes in the length of the expansion section had a minor impact on the bubble fragmentation performance. Experimental methods were used to verify the characteristics of bubble fragmentation, and it was found that the simulation and experimental results were consistent. This provides a theoretical basis and practical guidance for the design optimization of tubular microbubble generators.
... Several authors have devoted their attention to the development of models for the unresolved scales to be used in direct numerical simulations and large eddy simulations. In their original works Kolmogorov (1949) and Hinze (1955) identified the maximum size of a non-breaking droplet in turbulence. Experimental measurements (Garrett, Li & Farmer 2000;Deane & Stokes 2002) later showed the existence of two different regimes in the droplet size distribution, separated by the Kolmogorov-Hinze scale. ...
We perform direct numerical simulations of surfactant-laden droplets in homogeneous isotropic turbulence with Taylor Reynolds number . The droplets are modelled using the volume-of-fluid method, and the soluble surfactant is transported using an advection–diffusion equation. Effects of surfactant on the droplet and local flow statistics are well approximated using a lower, averaged value of surface tension, thus allowing us to extend the framework developed by Hinze ( AIChE J. , vol. 1, no. 3, 1955, pp. 289–295) and Kolmogorov ( Dokl. Akad. Navk. SSSR , vol. 66, 1949, pp. 825–828) for surfactant-free bubbles to surfactant-laden droplets. We find that surfactant-induced tangential stresses play a minor role in this set-up, thus allowing us to extend the Kolmogorov–Hinze framework to surfactant-laden droplets. The Kolmogorov–Hinze scale is indeed found to be a pivotal length scale in the droplets’ dynamics, separating the coalescence-dominated (droplets smaller than ) and the breakage-dominated (droplets larger than ) regimes in the droplet size distribution. We find that droplets smaller than have a rather compact, regular, spheroid-like shape, whereas droplets larger than have long, convoluted, filamentous shapes with a diameter equal to . This results in very different scaling laws for the interfacial area of the droplet. The normalized area, , of droplets smaller than is proportional to , while the area of droplets larger than is proportional to , where d is the droplet characteristic size. We further characterize the large filamentous droplets by computing the number of handles (loops of the dispersed phase extending into the carrier phase) and voids (regions of the carrier fluid completely enclosed by the dispersed phase) for each droplet. The number of handles per unit length of filament scales inversely with surface tension. The number of voids is proportional to the droplet size and independent of surface tension. Handles are indeed an unstable feature of the interface and are destroyed by the restoring effect of surface tension, whereas voids can move freely in the interior of the droplets, unaffected by surface tension.
... The seminar works by Kolmogorov [20] and Hinze [18], i.e. Kolmogorov-Hinze (KH) theory, assumed that the bubble/droplet in homogeneous isotropic turbulence could only be broken by eddies with similar sizes. ...
The dispersed phase in liquid-liquid emulsions and air-liquid mixtures can often be fragmented into smaller sizes by the surrounding turbulent carrier phase. The critical parameter that controls this process is the breakup frequency, which is defined from the breakup kernel in the population balance equation. The breakup frequency controls how long it takes for the dispersed phase reaches the terminal size distribution for given turbulence. In this article, we try to summarize the key experimental results and compile the existing datasets under a consistent framework to find out what is the characteristic timescale of the problem and how to account for the inner density and viscosity of the dispersed phase. Furthermore, by pointing out the inconsistency of existing experimental data, the key important unsolved questions and related problems on the breakup frequency of bubbles and droplets are discussed.
... There have been studies on bubble break up and deformation in turbulent flow. Kolmogorov [11] and Hinze [12] showed that bubbles/droplets will break when the ratio of dynamic force to surface tension force will exceed a critical value. Bazán et. ...
Turbulent dispersed multiphase flow can be seen in various environmental and engineering applications where particles/droplets/bubbles are dispersed in a fluid medium. Studying and understanding these kinds of problems are complicated due to the interactions of multiple turbulent eddies with the multiple bubbles/particles in these flows. In the present work, we study an idealization of this problem, by studying the interaction of a single vortex ring (vortex structure) with a single bubble. In such kind of studies, both the vorticity dynamics and bubble dynamics are important aspects. In particular, the focus of the work is on the effect of the relative size of the bubble to the vortex ring size, which is characterized by a volume ratio defined as the ratio of the bubble volume to vortex ring core volume. We perform high speed imaging and PIV measurements to understand the two way coupled interaction of the vortex ring and the bubble. We observe significant changes in the vorticity and bubble breakup dynamics as the volume ratio is varied.
... There have been studies on bubble break up and deformation in turbulent flow. Kolmogorov [13] and Hinze [14] showed that bubbles/droplets will break when the ratio of dynamic force to surface tension force will exceed some critical value. Bazán et. ...
... It has been well established that the local flow pattern can determine the deformation and breakup of the bubbles, depending mainly on the Weber number, W e = ρ 2/3 R 5/3 b /σ, representing the ratio between the turbulent stresses acting on the surface of the bubble and the confining stresses due to surface tension, where is the turbulent dissipation rate, R b is the bubble radius and σ is the surface tension (Martínez-Bazán 2015). The early works of Kolmogorov (1949) and Hinze (1955) have proposed two mechanisms for bubble breakup, as reviewed by Martínez-Bazán (2015). The inertial mechanism leads to bubble breakup as the Weber number is high, when the pressure fluctuations acting on the bubble surface are sufficiently large to overcome the confining surface tension forces (Martinez-Bazan et al. 1999a,b). ...
The interactions between a vortex ring and a gas bubble released at the axis are studied numerically, which shed light on understanding more complicated bubble–turbulence coupling. We fix the Reynolds number at and consider various Weber numbers in the range of We=130\unicode{x2013}870 . We find that the translating speed of the vortex ring is substantially lower than the case of the vortex ring without a bubble. It is explained with two different mechanisms, depending on the Weber number. In the low- We range, the reduction of translating speed of the ring is due to the capture of bubbles into the ring core, leading to significant changes in the vorticity distribution within the core. In the high- We range, the repeatedly generated secondary vortex rings perturb the primary one, which bring about an earlier flow transition, thereby reducing the translating speed of the vortex ring. On the other hand, the evolution of a gas bubble is also affected by the presence of the vortex ring. In the low- We range, we observe binary breakup of the bubble after it is captured by the primary vortex ring. In contrast, in the high- We range, it is interesting to find that the bubble experiences sequentially stretching, spreading and breakup stages. In the high- We range, the numbers of smaller bubbles predicted by the classical Rayleigh–Plateau instability of a stretched cylindrical bubble agree well with our numerical simulations. Consistent with the previous experiments, this number keeps unchanged at 16 as We further increases. An additional comparison is made between two higher Reynolds numbers, indicating that the finer eddies in a vortical field with a higher Reynolds number tend to tear the bubble into more fragments.
... The critical wavelength, λ cr , marks the threshold between longer waves that can grow in amplitude due to the strong inertial forces, and shorter waves that do not grow because of the overwhelming effect of the restoring surface tension forces and of the increasing role of dissipation at large wavenumbers (Deike, Berhanu & Falcon 2012;Deike et al. 2014;Issenmann et al. 2016;Falcon & Mordant 2022). This consideration is similar to that postulated by Kolmogorov (1949) and recalled by Hinze (1955) to estimate the maximum size of a drop/bubble that will not break in a given turbulent flow, i.e. D cr = 0.725(ρ/σ ) −3/5 | c | −2/5 , with c the turbulent kinetic energy dissipation. ...
We study the dynamics of capillary waves at the interface of a two-layer stratified turbulent channel flow. We use a combined pseudo-spectral/phase field method to solve for the turbulent flow in the two liquid layers and to track the dynamics of the liquid–liquid interface. The two liquid layers have same thickness and same density, but different viscosity. We vary the viscosity of the upper layer (two different values) to mimic a stratified oil–water flow. This allows us to study the interplay between inertial, viscous and surface tension forces in the absence of gravity. In the present set-up, waves are naturally forced by turbulence over a broad range of scales, from the larger scales, whose size is of order of the system scale, down to the smaller dissipative scales. After an initial transient, we observe the emergence of a stationary capillary wave regime, which we study by means of temporal and spatial spectra. The computed frequency and wavenumber power spectra of wave elevation are in line with previous experimental findings and can be explained in the frame of the weak wave turbulence theory. Finally, we show that the dispersion relation, which gives the frequency ( ) as a function of the wavenumber ( k ), is in good agreement with the well-established theoretical prediction, .
... In turbulent flows, the deformation is induced by δu 2 (d) which is the mean square velocity difference over a distance equal to d. Kolmogorov [36] postulated that the criteria becomes independent of viscosity if the Reynold number is high enough. Assuming isotropic turbulence, δu 2 (d) can be replaced by the dominant hitting eddy influence in Equation (10). ...
Most bubble breakage models have been developed for multiphase simulations using Euler-Euler (EE) approaches. Commonly, they are linked with population balance models (PBM) and are validated by making use of Reynolds-averaged Navier-Stokes (RANS) turbulence models. The latter, however, may be replaced by alternate approaches such as Large Eddy simulations (LES) that play a pivotal role in current developments based on lattice Boltzmann (LBM) technologies. Consequently, this study investigates the possibility of transferring promising bubble breakage models from the EE framework into Euler-Lagrange (EL) settings aiming to perform LES. Using our own model, it was possible to reproduce similar bubble size distributions (BSDs) for EL and EE simulations. Therefore, the critical Weber (Wecrit) number served as a threshold value for the occurrence of bubble breakage events. Wecrit depended on the bubble daughter size distribution (DSD) and a set minimum time between two consecutive bubble breakage events. The commercial frameworks Ansys Fluent and M-Star were applied for EE and EL simulations, respectively. The latter enabled the implementation of LES, i.e., the use of a turbulence model with non-time averaged entities. By properly choosing Wecrit, it was possible to successfully transfer two commonly applied bubble breakage models from EE to EL. Based on the mechanism of bubble breakage, Wecrit values of 7 and 11 were determined, respectively. Optimum Wecrit were identified as fitting the shape of DSDs, as this turned out to be a key criterion for reaching optimum prediction quality. Optimum Wecrit values hold true for commonly applied operational conditions in aerated bioreactors, considering water as the matrix.
... An oil droplet can breakup into smaller droplets (emulsion formation) depending on the balance between the external forces caused by the motion of the surrounding fluid, which act on the oil-water interface and induce deformation and breakup, and the capillary forces, which oppose deformation. The breakup of oil droplets in well-defined flow fields has been explored theoretically and experimentally in the engineering literature (Taylor, 1932(Taylor, , 1934Kolmogorov, 1949;Hinze, 1955;Walstra, 1993;Grace, 1982;Stone et al., 1986;Stone and Leal, 1990;Bentley and Leal, 1986a,b;Zhao, 2007;Milliken et al., 1993;Eggers and Villermaux, 2008), and the points that are relevant to filter feeding are briefly summarized here. Where µ w and ρ w are the viscosity and density of the surrounding fluid (water), respectively, R o is the radius of the oil droplet, and U w is the free stream velocity. ...
Filter feeding is ubiquitous in aquatic invertebrate clades. Species feeding this way are found in almost every animal phyla. Filter feeders capture food particles from the water column using ramified appendages. These particles can then be manipulated, tasted and potentially ingested. Captured particles generally include unicellular algae, various debris and protists. However, these filter feeders can also filter, capture and consume lipid particles. These lipid particles can come from decaying organisms or from the release of hydrocarbons during an oil spill. The main goal of this thesis was to identify the main capturing mechanisms of oil droplets and to describe the parameters controlling the capture and detachment from a filtering appendage. At first, the general principles of fluid mechanics required to describe the capture of solid particles and the flow around a cylindrical fiber were adapted to liquid particles. An exhaustive review of the literature was published as a review paper. A study of the critical volume needed for vertical detachment in function of the interfacial tension was presented. Also, the feeding mechanisms of daphnids and barnacles were described. Then, we used high speed videography to observe the detachment process of oil droplets from fibers. We described the key factors responsible for detachment and established a curve to predict whether a captured droplet will remain on the fiber or detach and re-enter the water column. Indeed, for a droplet to detach from a fiber, the ratio of inertial to capillary forces must reach a critical value. The smaller the droplet to fiber size ratio, the higher this critical value will be. This predictive tool was then validated using the size of droplets captured by three marine copepods. This result allows us to predict the size distribution of droplets that will remain captured by filtering appendages, following a quick survey of the filter feeding species in the vicinity of the spill. Afterward, I studied the capture mechanisms of oil droplets. To do so, the feeding behavior of Daphnia magna,Balanus crenatus and Balanus glandula was observed under the microscope and in a flume using high speed videography to precisely describe capture events. Daphnia magna captures droplets using the thick boundary layers around the third and fourth pair of thoracic legs. Thus, the oil droplets are captured without direct contact with the fibers. At low Reynolds number, barnacles capture droplets using a similar process. However, at high Reynolds number, droplets are mainly captured via direct interception. Using scanning electron microscopy and fluorescence microscopy, we observed that the filtering surfaces of the organisms are smooth and extremely lipophobic. Indeed, the contact angles of captured droplets were well above 90 degrees. Finally, because chemical dispersion is one of the main clean-up methods used after an oil spill, the effect it can have on capture and detachment of droplets needed further research. I studied the impact of a chemical surfactant on the size distribution of oil droplets in the water column and in the gut of Daphnia magna. I also compared the detachment conditions of droplets with and without a surfactant present during the mixing of the emulsion. Adding a surfactant significantly reduces and narrows the size distribution of droplets in the water column. With or without a surfactant, the size of ingested droplets remains the same. The presence of a surfactant facilitates droplet detachment from a fiber by lowering the interfacial tension. For similar droplet to fiber size ratios, a chemically dispersed droplet will detach at a lower velocity than a mechanically dispersed droplet. This research brings a better understanding on how oil droplets are handled by the zooplankton. These results are significant considering that most spilled crude oil enters the marine food webs via this group of organisms. This thesis describes the main mechanisms of capture, detachment and the impact of a surfactant on the latter.
... In at a much lower rate via the drainage of oil through the interstitial films and channels that separate water droplets so that H S decreases much more slowly over time than initially, as revealed by Fig. 2.7b). During the early stages of the first settling regime, since water-oil interfaces are still unsaturated with surfactant molecules, water droplets may easily merge because of coalescence [36]. The larger and heavier drops that form upon the fusion of two droplets, settle faster to the bottom of the tank than the smaller initial droplets. ...
For the oil industries, the development of enhanced oil recovery techniques represents a major challenge since these techniques increase oil yields on the company's fields. Hydrocarbons are produced in the form of emulsions which must be destabilized as quickly as possible. This process of separating the crude from the water is essential to control the costs of operations, linked to transport and refining. To speed up this separation step, chemical additives are used. The choices of the concentrations and types of additives used are mostly made empirically. Indeed, a thorough understanding, making it possible to select and predict the performance of such additives, has not yet been acquired.The aim of this thesis is therefore to take a first step in this direction. We therefore propose to study, using model systems, the destabilization of these in-situ emulsions as a function of various physicochemical parameters representative of the situations encountered in the operations in practice. This study aims to better understand the various physical phenomena involved in order to include the appropriate physics in the simulation tools allowing in the laboratory a better screening of chemical additives and their formulations in terms of performance of the selected product and the time required. to its selection.------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
... It is usually admitted that Kolmogorov's turbulent scaling suits at determining the size of the largest stable bubble in a turbulent liquid, for which the inertial stress ρ1u( ) 2 equilibrates capillary confinement σ/ , with u( ) ∼ ( ) 1/3 . The typical turbulence dissipation rate immediately after the breaking wave event is ≈ 0.1 − 1 m 2 s −3 , while the typical turbulence dissipation rate under a breaking wave field is rather ≈ 0.001 − 0.01 m 2 s −3 (the broad interval is due to the transient character of the breaking event, as well as to the large variations in breaking strength in the field (55)) and we have (56) ∼ σ ρ1 ...
Ocean spray aerosol formed by bubble bursting are at the core of a broad range of atmospheric processes: They are efficient cloud condensation nuclei, and carry a variety of chemical, biological and biomass material from the surface of the ocean to the atmosphere. The origin and composition of these aerosols is sensibly controlled by the detailed fluid mechanics of bubble bursting. This perspective summarizes our present-day knowledge on how bursting bubbles at the surface of a liquid pool contribute to its fragmentation, namely to the formation of droplets stripped from the pool, and associated mechanisms. In particular, we describe bounds and yields for each distinct mechanism, and the way they are sensitive to the bubble production and environmental conditions. We also underline the consequences of each mechanism on some of the many air-sea interactions phenomena identified to date. Attention is specifically payed at delimiting the known from the unknown, and the certitudes from the speculations.
... The counterparts of turbulent emulsion rheology from the point of microscopic view are the mean droplet size, the droplet size distributions (DSDs), and the interactions between droplets, which highly depend on the flow configuration and the droplet property. One of the simplest cases is first addressed by Kolmogorov (1949) and Hinze (1955) characterizing droplets of low volume fraction dispersed in homogeneous and isotropic turbulence (HIT). By balancing the surface tension force and turbulent energy fluctuation, Hinze (1955) proposes a critical Weber number W e c ∼ O(1) beyond which the droplet breakup happens, and further, the maximum droplet diameter that can stably exist (i.e., Hinze scale) is derived as ...
The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, , ranging from 0.53 to 8.02. The droplet volume fraction, , is varied from 0\% to 10\% with a spacing of 2\%. The global transport quantity, quantified by the normalized friction coefficient , shows a weak dependence on the turbulent intensity due to the vanishing finite-size effect of the droplets. The interesting fact is that, with increasing , the first increases and then saturates to a plateau value which is similar to that of the rigid particle suspension. By performing image analysis, this drag modification is interpreted from the aspect of droplet deformability, which is responsible for the breakup and coalescence effect of the droplets. The statistics of the droplet size distribution show that, with increasing , the stabilizing effect induced by interfacial tension comes to be substantial and the pure inertial breakup process becomes dominant. The measurement of the droplet distribution along the radial direction of the system shows a bulk-clustering effect, which can be attributed to the non-negligible coalescence effect of the droplet. It is found that the droplet coalescence effect could be suppressed as the increases, thereby affecting the contribution of interfacial tension to the total stress, and accounting for the observed emulsion rheology.
... The next question we focus on is what sets the droplet size in the current system. Droplet breakup in a turbulent flow is widely investigated using the Kolmogorov-Hinze (KH) theory, in which the droplet breakup is governed by the competition between the resisting interfacial tension and the deforming external dynamic pressure force (turbulent fluctuations) over the droplet size [41,42]. The ratio of these two forces is usually indicated by the droplet Weber number We = ρδu 2 D/γ , where ρ is the density of the continuous phase, δu 2 the meansquare velocity difference over the distance of one droplet diameter D and γ the interfacial tension between the two liquids. ...
Emulsions are common in many natural and industrial settings. Recently, much attention has been paid to understanding the dynamics of turbulent emulsions. This paper reviews some recent studies of emulsions in turbulent Taylor–Couette flow, mainly focusing on the statistics of the dispersed phase and the global momentum transport of the system. We first study the size distribution and the breakup mechanism of the dispersed droplets for turbulent emulsions with a low volume-fraction (dilute) of the dispersed phase. For systems with a high volume-fraction (dense) of the dispersed phase, we address the detailed response of the global transport (effective viscosity) of the turbulent emulsion and its connection to the droplet statistics. Finally, we will discuss catastrophic phase inversions, which can happen when the volume-fraction of the dispersed phase exceeds a critical value during dynamic emulsification. We end the manuscript with a summary and an outlook including some open questions for future research.
This article is part of the theme issue ‘Taylor–Couette and related flows on the centennial of Taylor’s seminal Philosophical Transactions paper (part 1)’.
... The droplet size distribution (DSD) is a key aspect of emulsions, as its prediction becomes fundamental in most applications. In his early seminal work, Kolmogorov (1949) discussed the criteria under which a droplet undergoes breakup when subject to surrounding turbulence. Kolmogorov first proposed a dimensional argument according to which surface tension forces need to be balanced locally by turbulent energy fluctuations. ...
We present a numerical study of emulsions in homogeneous and isotropic turbulence (HIT) at . The problem is addressed via direct numerical simulations, where the volume of fluid is used to represent the complex features of the liquid–liquid interface. We consider a mixture of two iso-density fluids, where fluid properties are varied with the goal of understanding their role in turbulence modulation, in particular the volume fraction ( 0.01 ) and large-scale Weber number ( -10/3 and -3/2$ scaling on droplet size distributions, suggesting that the dimensional arguments that led to their derivation are verified in HIT conditions.
... The dispersed liquid-liquid systems are usually characterized by Sauter mean diameter and drop size distribution. Based on Hinze -Kolmogorov theory (Kolmogorov, 1949;Hinze, 1955), the relation between equilibrium Sauter mean diameter, 32 , and impeller Weber number can be correlated with the exponent of -0.6. Unlike this, Rodgers and Cooke (2012) proposed the shear tip speed as a correlating parameter for 32 diameter dependence on mixing intensity. ...
The homogeneity of an immiscible liquid-liquid system was investigated in a baffled vessel agitated by a Rushton turbine. The dispersion homogeneity was analyzed by comparing Sauter mean diameters and drop size distribution (DSD) determined in different measured regions for various impeller speeds. The sizes of droplets were obtained by the in-situ measurement technique and by the Image Analysis (IA) method. Dispersion kinetics was successfully fitted with Hong and Lee (1983) model. The effect of intermittency turbulence on drop size reported by Bałdyga and Podgórska (1998) was analyzed and the multifractal exponent was evaluated.
... P erhaps no other area of fluid dynamics has borne a twin problem more than bubble breakup 1 and turbulence cascade 2 both by Andrey N. Kolmogorov, based on a key idea of elementary entities, i.e., bubbles and eddies, being fragmented into smaller and smaller sizes, following a universal mechanism. In 1955, Hinze 3 extended Kolmogorov's original idea 1 , and this Kolmogorov-Hinze (KH) framework has since posed deep and lasting impacts on modeling turbulent bubble/ drop fragmentation in various flow configurations 4-6 and applications, including emulsion 7 , spray formation 8 , and raindrop dynamics 9 . ...
From air-sea gas exchange, oil pollution, to bioreactors, the ubiquitous fragmentation of bubbles/drops in turbulence has been modeled by relying on the classical Kolmogorov-Hinze paradigm since the 1950s. This framework hypothesizes that bubbles/drops are broken solely by eddies of the same size, even though turbulence is well known for its wide spectrum of scales. Here, by designing an experiment that can physically and cleanly disentangle eddies of various sizes, we report the experimental evidence to challenge this hypothesis and show that bubbles are preferentially broken by the sub-bubble-scale eddies. Our work also highlights that fragmentation cannot be quantified solely by the stress criterion or the Weber number; The competition between different time scales is equally important. Instead of being elongated slowly and persistently by flows at their own scales, bubbles are fragmented in turbulence by small eddies via a burst of intense local deformation within a short time.
In the under-resolved simulation of the high-speed liquid injection into stagnant air, the attention in subgrid-scale models is focused on events of intense gradients of the velocity in turbulent flow, i.e., on effects of intermittency. Three typical flows are considered—the in-nozzle flow, primary atomization zone, and secondary atomization of spray droplets. In the simulation of the first two flows, the filtered Navier–Stokes equations are forced by stochastic processes with properties which incorporate the statistical physics of fluid acceleration at the high Reynolds number—in this way we update the under-resolved acceleration. In the case of in-nozzle flow, the proposed stochastic subgrid acceleration model is combined with wall-damping function, and the ability in prediction of the velocity statistics is demonstrated. In the simulation of primary atomization, the approach with stochastic subgrid acceleration is combined with the volume of fluid method. This leads to intensification of the interface dynamics, resulting in additional corrugation, with more intense shearing and stretching of liquid structures are observed. Thereby, the experimental profiles of the time-averaged liquid volume fraction distribution for four different axial locations are rather well predicted. The secondary atomization of droplets is simulated by a new stochastic model for the breakup rate along the droplet path. To this end, the breakup rate is expressed as a function of turbulent viscous dissipation which evolves along the droplet path according to the proposed stochastic process. Preliminary assessment performed against the recent experiments shows the correct predictability of this model and its low sensibility to the grid density.
Numerical modeling of self-aerated flows is essential for understanding water systems and designing hydraulic structures. This work discusses and extends a theoretical/numerical model to represent air entrainment in self-aerated flows, which includes a criterion to define the occurrence of air entrainment, based on a balance between disturbing and stabilizing energies. The impact of the turbulence closure on the modeling of the onset of air entrainment and the distribution of bubble concentration is studied with particular emphasis. This work shows that uniform-density formulations of Reynolds-averaged Navier–Stokes closures lead to severe overprediction of air entrainment due to unphysical transport of turbulent kinetic energy generated in the air phase to the water phase. In contrast, combining variable-density turbulence closures with the energy balance criterion enables accurate prediction of the regions where air is entrained for stepped spillways and plunging jets. The choice of turbulence closure significantly influences the proposed criterion, emphasizing the importance of selecting an appropriate closure for an accurate description of the air entrainment process. Based on the conducted tests, the standard k−ε and buoyancy modified k−ε models better predict the onset of air entrainment and bubble distribution in stepped spillways, while the k−ω SST model proves to be more effective in capturing air entrainment at the impingement point in plunging jets. This study expands the capabilities of numerical models in predicting air entrainment and provides valuable insights into the effects and interrelations of the turbulence modeling, the air entrainment occurrence criteria, and the bubble transport equations.
The hydrodynamics and mass transfer in the Taylor-Couette mixing field are important activities for concurrent process intensification work for miniaturization of the chemical reactor volume and enhancing the energy input per unit volume. In the literature, many studies have been reported for mixing of conventional two-phase systems of industrial interest. However reported studies on mixing of PUREX aqueous organic pair in Taylor-Couette field are rare and few. Utilizing an indigenously developed Taylor-Couette column, hydrodynamic and mass transfer studies with PUREX aqueous-organic pair are reported in this study. Mass transfer and hydrodynamics runs were conducted with PUREX aqueous-organic pair. Aqueous dispersed conditions were employed for d→c mass transfer. Mass transfer performance was highly dependent on rotor speed till a critical value. Macro, meso and micromixing time values were evaluated for Taylor-Couette mixing. Prototyping of the system was completed with a special run with 0.1 M TODGA/n-dodecane nitric acid pair for mutual separation of Cs(I) and Sr(II).
Turbulent drop breakup is of large importance for applications such as food and pharmaceutical processing, as well as of substantial fundamental scientific interest. Emulsification typically takes place in the presence of surface-active emulsifiers (natural occurring and/or added). Under equilibrium conditions, these lower the interfacial tension, enabling deformation and breakup. However, turbulent deformation is fast in relation to emulsifier kinetics. Little is known about the details of how the emulsifier influences drop deformation under turbulent conditions. During the last years, significant insight in the mechanism of turbulent drop breakup has been reached using numerical experiments. However, these studies typically use a highly simplistic description of how the interface responds to turbulent stress. This study investigates how the limited exchange rate of emulsifier between the bulk and the interface influences the deformation process in turbulent drop breakup for application-relevant emulsifiers and concentrations, in the context of state-of-the-art single drop breakup simulations. In conclusion, if the Weber number is high or the emulsifier is supplied at a concentration giving an adsorption time less than 1/10th of the drop breakup time, deformation proceeds as if the emulsifier adsorbed infinitely fast. Otherwise, the limited emulsifier kinetics delays breakup and can alter the breakup mechanism.
We investigate the statistics of turbulence in emulsions of two immiscible fluids of the same density. We compute velocity increments between points conditioned to be located in the same phase or in different phases, and examine their probability density functions (PDFs) and the associated structure functions (SFs). This enables us to demonstrate that the presence of the interface reduces the skewness of the PDF at small scales and therefore the magnitude of the energy flux towards the dissipative scales, which is quantified by the third-order SF. The analysis of the higher-order SFs shows that multiphase turbulence is more intermittent than single-phase turbulence. In particular, the local scaling exponents of the SFs display a saturation below the Kolmogorov–Hinze scale, which indicates the presence of large velocity gradients across the interface. Interestingly, the statistics of the velocity differences in the carrier phase recovers that of single-phase turbulence when the viscosity of the dispersed phase is high.
The dispersed phase in turbulence can vary from almost inviscid fluid to highly viscous fluid. By changing the viscosity of the dispersed droplet phase, we experimentally investigate how the deformability of dispersed droplets affects the global transport quantity of the turbulent emulsion. Different kinds of silicone oil are employed to result in the viscosity ratio, , ranging from 0.53 to 8.02 . The droplet volume fraction, , is varied from 0 % to 10 % with a spacing of 2 %. The global transport quantity, quantified by the normalized friction coefficient , shows a weak dependence on the turbulent intensity due to the vanishing finite-size effect of the droplets. The interesting fact is that, with increasing , first increases and then saturates to a plateau value which is similar to that of the rigid particle suspension. By performing image analysis, this drag modification is interpreted from the point of view of droplet deformability, which is responsible for the breakup and coalescence effect of the droplets. The statistics of the droplet size distribution show that, with increasing , the stabilizing effect induced by interfacial tension becomes substantial and the pure inertial breakup process becomes dominant. The measurement of the droplet distribution along the radial direction of the system shows a bulk-clustering effect, which can be attributed to the non-negligible coalescence effect of the droplet. It is found that the droplet coalescence effect could be suppressed as increases, thereby affecting the contribution of interfacial tension to the total stress, and accounting for the observed emulsion rheology.
A pool scrubber is often used as a wet-type design to mitigate the consequence of a severe nuclear accident. While studies indicated higher decontamination performance of a deeper pool, utilizing a very tall pool can be problematic due to potential structural stability and water backflow issues. This study proposes, as an alternative to a single pool system, a pool scrubber system composed of serially connected multiple pools with lower heights. Since large fraction of aerosol removal takes place in the injection region, serially connected pool scrubber system is expected to enhance the overall decontamination capability of a pool scrubber system. To support the analysis of the proposed system's decontamination capability, a new computer model was developed in the study to describe the bubble size dependent effect on aerosol removal including the effect of pool residence time. The accuracy of the new model was examined against experimental data for its validation. The proposed scrubber system composed of serially connected multiple shorter pools is found to have much improved decontamination performance over the current single pool system design
Turbulent breakup in emulsification devices is a dynamic process. Small viscous drops undergo a sequence of oscillations before entering the monotonic deformation phase leading to breakup. The turbulence-interface interactions prior to reaching critical deformation are therefore essential for understanding and modelling breakup. This contribution uses numerical experiments to characterize the critically deformed state (defined as a state from which breakup will follow deterministically, even if no further external stresses would act on the drop). Critical deformation does not coincide with a threshold maximum surface area, as previously suggested. A drop is critically deformed when a neck has formed locally with a curvature such that the Laplace pressure exceeds that of the smallest of the bulbs connected by the neck. This corresponds to a destabilizing internal flow, further thinning the neck. Assuming that the deformation leads to two spherical bulbs linked by a cylindrical neck, the critical deformation is achieved when the neck diameter becomes smaller than the radius of the smallest bulb. The role of emulsifiers is also discussed.
Gas-liquid mass transfer in non-Newtonian fluids is a crucial aspect of the bioprocess industry. Mass transfer is analyzed using the coefficient kLa, which is limited by the rheology since it exerts a barrier to the fluid deformation, significantly affecting the oxygen diffusivity and the bubble breakup and coalescence. However, the traditional mathematical expressions to model the bubble size distribution from bubble breakup and coalescence in turbulent flows of Newtonian fluids are restricted to the inertial sub-range of turbulence where the kinetic energy is dominated only by the microscales. Application of the Newtonian models to non-Newtonian fluids could result in inaccurate predictions by not considering the continuous phase rheology. The main goal of this research is the numerical determination and experimental comparison of bubble sizes in different axial positions of a bioreactor stirred by a Rushton turbine. Emphasis was placed on the viscosity effects on simulating bubble dispersion in a Newtonian fluid (water) and its comparison with a non-Newtonian fluid (0.4 % CMC). The mathematical framework is constructed by coupling the hydrodynamics (through computational fluid dynamics CFD) and bubble breakup and coalescence from a turbulence perspective using the complete energy spectrum that considers the contributions from the energy containing, inertial, and dissipation sub-ranges. This is achieved by including the second-order structure-function. The results of bubble sizes and kLa were compared with experimental data, and acceptable agreement was achieved. Therefore, it is shown that the viscous effects were captured numerically by the entire energy spectrum and improved the predictions of the kLa and bubble sizes compared to the traditional structure function turbulence models.
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