Predicting turbulence modulations at different Reynolds numbers in dilute-phase turbulent liquid–particle flow simulations

The present work examines the predictive capability of two-fluid CFD model based on the kinetic theory of granular flow in capturing the Reynolds number (Re) dependence of fluid-phase turbulence modulations in dilute-phase turbulent liquid–particle flows. The model predictions are examined using turbulent liquid–particle flow data in a vertical pipe at Re=17,000, 48,000, 65,000, and 76,000 in the particle concentration range of between 0.5% and 4.0% (v/v). The experimental data indicate that the fluid-phase turbulence intensities are enhanced with respect to the single-phase flow at Re≤48,000 but are attenuated at Re≥65,000. The simulation results indicate that the CFD model can successfully predict the turbulence modulations at Re=17,000, 65,000, and 76,000 both qualitatively and quantitatively, but not at the intermediate Re of 48,000. In this regard, (1) different drag correlations to describe the fluctuating drag force are needed to accurately predict the trends in the turbulence modulations as a function of Re, and (2) appropriate combinations of the drag correlations and turbulence closure models to describe the long-range fluid–particle interactions must be identified in each phase at different Re in order to accurately predict the turbulence modulation, granular temperature, and particle radial concentration profile.     

Analysis of dilute solid–liquid suspensions in turbulent stirred tanks

In this work, dilute suspensions of solid particles in stirred tanks are investigated by Particle Image Velocimetry measurements, which were specifically designed to determine the effects of the dispersed phase on mean velocity and turbulence levels of the continuous phase and the local solid–liquid slip velocity. In order to determine the effect of particle size and concentration, glass particles of narrow size distribution were selected; the particle content was increased stepwise up the maximum of 0.2 vol.%. Overall, moderate dampening of liquid turbulent fluctuations was found with the smaller particles, while turbulence enhancement was observed with the bigger ones. Continuous phase turbulence was found to affect the local map of the particle settling velocity, which was also discussed on the basis of a force balance analysis. The reduction of particle settling velocity due to free stream turbulence under specific conditions is confirmed.     

Separation of liquid–liquid dispersion in a batch settler: CFD-PBM simulations incorporating interfacial coalescence

Several commercially important chemical processes involve liquid–liquid phase separation. In the present work, we have developed a multi-fluid Eulerian CFD model using OpenFOAM that incorporates binary and interfacial coalescence processes. We simulated separation of kerosene dispersed in water in a batch settler and validated the predictions using the measurements of time-evolution of coalescing and settling interfaces, local dispersed-phase volume fraction (α_O) and drop size distribution (DSD). Simulations are performed to understand the contributions of binary and interfacial coalescence processes to the phase separation process. While the time-evolution of coalescing and settling fronts can be predicted reasonably well using the two-fluid model with empirically-corrected drag models, local α_O and DSD could not be predicted. We have shown that the comprehensive multi-fluid Eulerian model, which incorporates binary and interfacial coalescence, predicts the time-evolution of the coalescing and settling fronts, local α_O and the DSD in an excellent agreement with the measurements.     

Effect of operating factors on liquid–liquid mass transfer and dispersion pattern of sedimentary liquid in a mechanically stirred vessel

Liquid–liquid dispersion and mass transfer were investigated in mechanically stirred vessels without baffles by changing operation factors such as an impeller rotation speed, off-bottom clearance, volumetric liquid ratio, etc. The dispersion regime was categorized into five groups: the sedimentary liquid was kept at the vessel bottom (I), partially elevated without any collision (II), partially dispersed by colliding with the impeller bottom (III), both liquids were partially dispersed by collisions with impeller blades (III’), and the sedimentary liquid was completely dispersed (IV). The dispersion switched to I → II → III → IV with the increasing rotation speed and decreasing off-bottom clearance. The liquid–liquid mass transfer rate was significantly enhanced with the collision of the sedimentary liquid with the impeller bottom, and subsequently increased with the increasing rotation speed, volumetric liquid ratio, and vessel diameter and with the decreasing off-bottom clearance. A multiple regression analysis method was applied to determine the mass transfer rates of III and III’.     

Study of the rate of liquid–solid mass transfer controlled processes in helical tubes under turbulent flow conditions

The liquid–solid mass transfer behaviour of helical tubes was studied by the diffusion controlled dissolution of copper tubes in acidified dichromate. Variables studied were solution velocity, tube diameter, coil diameter and physical properties of the solution. The effect of drag reducing polymers on the rate of mass transfer in the helical tubes was also studied. The blank solution mass transfer data were correlated for the conditions 850 < Sc < 1322; 6000 < Re < 23,400 and 5 < d_c/d < 25 by the equation.

Sh=0.107Sc0.33Re0.68$Sh=0.107S{c}^{0.33}R{e}^{0.68}$

The effect of scale and interfacial tension on liquid–liquid dispersion in in-line Silverson rotor–stator mixers

The effect of scale, processing conditions, interfacial tension and viscosity of the dispersed phase on power draw and drop size distributions in three in-line Silverson rotor–stator mixers was investigated with the aim to determine the most appropriate scaling up parameter. The largest mixer was a factory scale device, whilst the smallest was a laboratory scale mixer. All the mixers were geometrically similar and were fitted with double rotors and standard double emulsor stators. 1 wt.% silicone oils with viscosities of 9.4 mPa s and 339 mPa s in aqueous solutions of surfactant or ethanol were emulsified in single and multiple pass modes. The effect of rotor speed, flow rate, dispersed phase viscosity, interfacial tension and scale on drop size distributions was investigated.     

Experimental investigation and CFD simulation of liquid–solid–solid dispersion in a stirred reactor

For understanding the monosodium aluminate hydrate crystallization from the supersaturated aluminate solution containing red mud as the leaching liquor of bauxite, the liquid–solid–solid dispersion of a simulant system, i.e. glycerite, red mud and sand, in a stirred reactor has been experimentally investigated as well as simulated using computational fluid dynamics model (CFD) for the first time. The computational model is based on the Eulerian multi-fluid model along with RNG k–ε turbulence model, where Syamlal–obrien-symmetric drag force model (Syamlal, 1987) of the inter-phase momentum transfer between two dispersed solid phases is taken into account. A good agreement is obtained between the experimental data of solid distributions and the simulation results in the flow fields of liquid–solid–solid as well as liquid–solid systems. The solid suspension qualities of both liquid–solid and liquid–solid–solid systems in the stirred reactors with and without draft tube were also studied in detail based on mixing time, the standard deviation of solid concentration proposed by Bohnet and Niesmak (1980), the flow pattern and power number. The influence of the interaction between two dispersed solid phases on the suspension of red mud is found significantly greater than that of sand. The holdup of sand below the impeller is considerably larger than that above the impeller and the red mud dispersion approaches homogeneous in the reactor. The mixing time of liquid–solid–solid suspension is longer than that of liquid–solid suspension under the same conditions, and the mixing times of both systems in the stirred reactor with draft tube are longer than that in the reactor without draft tube. Furthermore, the distributions of sand and red mud in the reactor with draft tube were found less homogeneous than those without draft tube in most cases.     

Micro-computed tomography for the investigation of stationary liquid–liquid and liquid–gas interfaces in capillaries

For better understanding and optimization of multiphase flow in miniaturized devices, micro-computed tomography (μCT) is a promising visualization tool, as it is nondestructive, three-dimensional, and offers a high spatial resolution. Today, computed tomography (CT) is a standard imaging technique. However, using CT in microfluidics is still challenging, since X-ray related artifacts, low phase contrast, and limited spatial resolution complicate the exact localization of interfaces. We apply μCT for the characterization of stationary interfaces in thin capillaries. The entire workflow for imaging stationary interfaces in capillaries, from image acquisition to the analysis of interfaces, is presented. Special emphasis is given to an in-house developed segmentation routine. For demonstration purposes, contact angles of water, liquid polydimethylsiloxane, and air in FEP, glass, and PMMA are determined and the influence of gravity on interface formation is discussed. This work comprises the first steps for a systematic 3D investigation of multiphase flows in capillaries using μCT.     

Classification and identification of gas–liquid dispersion states in a jet bubbling reactor

Three gas–liquid dispersion states including flooding, loading, and complete dispersion are observed sequentially in a jet bubbling reactor with an increase of the liquid jet velocity at the nozzle outlet (u_j). The gas–liquid dispersion states are identified through the slope (k) of the curve of fluctuation distribution index (FI) versus u_j as follows: (a) under the flooding, k = 0; (b) under the loading, k > 0; (c) under the complete dispersion, k < 0. In particular, the u_j at the transition points from flooding to loading and from loading to complete dispersion are referred to flooding jet velocity (u_jf, the transition point between k = 0 and k > 0) and complete dispersion jet velocity (u_jcd, the transition point from k > 0 to k < 0), respectively. The average relative deviations of the u_j at the transition points obtained through the acoustic emission measurement and visual observation are less than 5%.     

Experimental characterization of liquid film behavior during droplets–polyethylene particle collision

Nowadays, the droplet–particle collision characteristics in the gas-phase ethylene polymerization process are still unclear. The high-speed photography and a quasi-circle imaging approach are employed to study the collision interaction characteristics between liquid droplets and polyethylene particles. The liquid film evolution is studied through variations of the film thickness on the particle north pole, the dynamic contact angle, center angle and film thickness at the maximum extension. Results have found that for n-hexane the threshold temperature of the recoil happening increases with increasing initial Weber number, but for 1-hexene it is stable. Over 70°C evaporation and splash occurs immediately. Under low Weber numbers, the water droplet stays for damping oscillations, the reference stable height of which is linearly related to temperatures. Moreover, three regimes of film thickness variation with time are identified and mathematically described, while Regime 3 characteristics are found strongly dependent on the liquid species, Weber number, and particle temperature.     

Modeling the disintegration of cavitating turbulent liquid jets using a novel VOF–CIMD approach

In this article, a novel modeling approach capable of simultaneously tracking the events of cavitation, occurring within an injector nozzle, and the liquid jet breakup process, inclusive of spray formation, in the nozzle exterior is presented. A single fluid model, embedded with a Volume-of-Fluid (VOF)-based interface capturing methodology for monitoring the liquid–gas interface dynamics, is supplemented with a vapor transport model for predicting cavitation events triggered within the liquid. While the surface forces due to liquid–gas interfacial instabilities are modeled using a Continuum Surface Force model, a Cavitation-Induced-Momentum-Defect (CIMD) correction approach is employed to account for the effects of cavitation dynamics within the liquid flow. Liquid turbulence is modeled using the well-known RNG k–ε model inclusive of new source terms due to cavitation-induced turbulent kinetic energy production and dissipation. The combined VOF–CIMD methodology is validated by examining the effects of cavitation on the disintegration of turbulent planar liquid jets exiting a two-dimensional nozzle. Different flow Reynolds and Cavitation number configurations are tested. The results predicted by the model including those of the transport vapor dynamics and the liquid jet disintegration processes match, both qualitatively and quantitatively, very well with the available experimental data. In comparison with experimental observation, our model predicts different regimes of liquid jet behavior such as wavy jet, spray formation simultaneously with events of developing or super-cavitation. The numerical approach elaborated in this article can be extensively applied in the design and development of efficient spray applicators and other industrial fluidic devices.     

Equilibrium morphology of gas–liquid Janus droplets: A numerical analysis of buoyancy effect

In this article, a theoretical model for predicting the equilibrium morphology of gas–liquid Janus droplets was built. Based on this model, the effects of bubble radius and volume ratio on morphology change was systematically studied. The increase of bubble radius causes the two parts (bubble and oil drop) in Janus droplets tend to merge while the impact of volume ratio is complicated. When volume ratio increases, these two parts firstly tend to merge, then gradually separate. The accuracy of this model was verified by experimental results.     

Analysis of the flow pattern and periodicity of gas–liquid–liquid three-phase flow in a countercurrent mixer-settler

In contrast to the concurrent mixer-settler, the interaction between the mixing and settling chambers have to be taken into account in the simulation of the countercurrent mixer-settler, and no work has been reported for this equipment. In this work, a three-phase flow model based on the Eulerian multiphase model, coupled with a sliding mesh model is proposed for a countercurrent mixer-settler. Based on this, the dispersed phase distribution, flow pattern, and pressure distribution are investigated, which can help to fill the gap in the operation mechanism. In addition, the velocity vector distribution at the phase port shows an intriguing phenomenon that two types of vectors with opposite directions are distributed on the left and right sides of the same plane, which indicates that the material exchange in the mixing and settling chambers is simultaneous. Analysis of this variation at this location by a fast Fourier transform (FFT) method reveals that it is mainly influenced by the mixing chamber and is consistent with the main period of the outlet flow fluctuations. Therefore, by monitoring the fluctuation of the outlet flow and then analyzing it by the FFT method, the state of the whole tank can be determined, which makes it promising for the design of control systems for countercurrent mixer-settlers.     

Copolymerization in dispersion of divinyl benzene–maleic anhydride in the presence of silylated montmorillonite clays

Sodium montmorillonite (NaMMT clay) derivatives were encapsulated in polymer particles obtained through dispersion copolymerization of divinyl benzene (DVB) with maleic anhydride (MA). To evidence the effect of alkyl monoalkoxysilanes upon MMT reaction, a variety of MMT clay functional derivatives were investigated. Particles with an increased size of modified MMT clay dispersed in dichloromethane were obtained using alkyl monoalkoxysilanes with a longer hydrocarbon chain. Relatively long hydrocarbon chains can exhibit a low substitution degree of MMT clay with alkyl monoalkoxysilanes. MMT class with a low substitution degree leads in the presence of alkoxysilanes to particles with average size between 700 and 1200 nm, and when DVB–MA copolymer is added the particles size decreases (~480 nm). The influence of layered silicates on the thermal stability of DVB–MA copolymer as a function of the used vinyl siloxanes derivatives for functionalization of MMT, on one hand, and the nonlinear variation of refractive index of used silanes on the other hand, pointing out the autoassociation during initial reaction of substitution.     

Determination of dynamic contact angles in solid–liquid–liquid systems using the Wilhelmy plate apparatus

The purpose of this work was to carry out a systematic study of the effects of brine composition and rock mineralogy on rock-oil-brine interactions taking place in petroleum reservoirs. These terms are generally lumped into a single term called wettability in petroleum engineering. The extent of wetting of the rock surface by water or oil depends on the dynamic contact angles measured in such a mode as to enable movements of the three-phase contact line. The Wilhelmy plate technique has been used in this study to measure adhesion tension (which is the product of interfacial tension and cosine of the contact angle) at the solid-liquid interface. The water-advancing and water-receding contact angles have been calculated from the adhesion tensions by making independent measurements of the liquid-liquid interfacial tensions using a du Noüy ring tensiometer. The water-advancing and receding angles have been measured in this study for pure hydrocarbons against synthetic brines of different concentrations. Polished surfaces of glass slides and dolomite have been used to simulate the reservoir rock surfaces. A nonionic surfactant (ethoxy alcohol), which is being used in Yates reservoir in West Texas for enhancing oil recovery, was used to quantify its wettability effects. The results of the systematic experimental investigation of the effects of practical variables on wettability are presented. It is found that interactions between surface-active agents at the interface of two liquids have an effect on wettability alteration. The composition and concentrations of different organic and inorganic chemical species have a major effect in making a reservoir oil-wet or water-wet.     

Overcoming the quality–quantity tradeoff in dispersion and printing of carbon nanotubes by a repetitive dispersion–extraction process

Dispersion-printing processes are essential for the fabrication of various devices using carbon nanotubes (CNTs). Insufficient dispersion results in CNT aggregates, while excessive dispersion results in the shortening of individual CNTs. To overcome this tradeoff, we propose here a repetitive dispersion–extraction process for CNTs. Long-duration ultrasonication (for 100 min) produced an aqueous dispersion of CNTs with sodium dodecylbenzene sulfonate with a high yield of 64%, but with short CNT lengths (a few μm), and poor conductivity in the printed films (∼450 S cm⁻¹). Short-duration ultrasonication (for 3 min) yielded a CNT dispersion with a very small yield of 2.4%, but with long CNTs (up to 20–40 μm), and improved conductivity in the printed films (2200 S cm⁻¹). The remaining sediment was used for the next cycle after the addition of the surfactant solution. 90% of the CNT aggregates were converted into conductive CNT films within 13 cycles (i.e., within 39 min), demonstrating the improved conductivity and reduced energy/time requirements for ultrasonication. CNT lines with conductivities of 1400–2300 S cm⁻¹ without doping and sub-100 μm width, and uniform CNT films with 80% optical transmittance and 50 Ω/sq sheet resistance with nitric acid doping were obtained on polyethylene terephthalate films.     

Characteristics of liquid slugs in gas–liquid Taylor flow in microchannels

The hydrodynamics of liquid slugs in gas–liquid Taylor flow in straight and meandering microchannels have been studied using micro Particle Image Velocimetry. The results confirm a recirculation motion in the liquid slug, which is symmetrical about the center line of the channel for the straight geometry and more complex and three-dimensional in the meandering channel. An attempt has also been made to quantify and characterize this recirculation motion in these short liquid slugs (L_s/w<1.5) by evaluating the recirculation rate, velocity and time. The recirculation velocity was found to increase linearly with the two-phase superficial velocity U_TP. The product of the liquid slug residence time and the recirculation rate is independent of U_TP under the studied flow conditions. These results suggest that the amount of heat or mass transferred between a given liquid slug and its surroundings is independent of the total flow rate and determined principally by the characteristics of the liquid slug.     

Analysis of concentration polydispersity in mixed liquid–liquid systems

Inter-phase mass transfer for each chemical component is typically modelled with one material balance for the continuous and one for the dispersed phase. This approach contains inherently an assumption that the phases are well mixed at least locally. For the dispersed phase, this assumption requires that breakage and coalescence are significantly faster compared to the mass transfer, which is not necessarily true. It is important to carry out preliminary assessment whether the dispersed phase segregation is important and should be considered in subsequent modelling efforts, before embarking heavy multidimensional simulations where all possible dispersed phase variations are considered. In this work, relevant time scales are first defined and used for analyzing dispersed phase mixedness in liquid–liquid systems with mass transfer between the phases. Then appropriate dispersed phase modelling tools for the purpose are evaluated. Simple droplet number density based analysis is shown to estimate mixedness reasonably well. Furthermore, the drop number density approach is also shown to predict the average drop sizes with almost comparable accuracy than the full population balances.