Dynamical deformation of a flat liquid–liquid interface

The passage of solid spheres through a liquid–liquid interface was experimentally investigated using a high-speed video and PIV (particle image velocimetry) system. Experiments were conducted in a square Plexiglas column of 0.1 m. The Newtonian Emkarox (HV45 50 and 65% wt) aqueous solutions were employed for the dense phase, while different silicone oils of different viscosity ranging from 10 to 100 mPa s were used as light phase. Experimental results quantitatively reveal the effect of the sphere’s size, interfacial tension and viscosity of both phases on the retaining time and the height of the liquid entrained behind the sphere. These data were combined with our previous results concerning the passage of a rising bubble through a liquid–liquid interface in order to propose a general relationship for the interface breakthrough for the wide range of Mo ₁/Mo ₂ ∈ [2 × 10⁻⁵–5 × 10⁴] and Re ₁/Re ₂ ∈ [2 × 10⁻³–5 × 10²].     

The hydrodynamics of liquid–liquid upflow through a venturimeter

The present work reports the influence of a venturimeter on liquid–liquid phase distribution during upflow through a vertical pipe. The optical probe technique has been adopted for the characterization of flow. The probability density function and the wavelet multi-resolution analysis of the random probe signals have provided an insight into the details of the flow patterns and the intrinsic differences at the upstream, throat and the downstream sections. The experiments have indicated the flow pattern transitions to occur at lower velocities at the downstream region of the venturi. The pressure drop readings across the venturi have been used to estimate the mass flow rate of the mixture by using suitable models for the different patterns.     

Investigation of liquid–liquid drop coalescence using tomographic PIV

High-speed tomographic PIV was used to investigate the coalescence of drops placed on a liquid/liquid interface; the coalescence of a single drop and of a drop in the presence of an adjacent drop (side-by-side drops) was investigated. The viscosity ratio between the drop and surrounding fluids was 0.14, the Ohnesorge number (Oh = μ_d/(ρ_dσD)^1/2) was 0.011, and Bond numbers (Bo = (ρ _d  − ρ _s )gD ²/σ) were 3.1–7.5. Evolving volumetric velocity fields of the full coalescence process allowed for quantification of the velocity scales occurring over different time scales. For both single and side-by-side drops, the coalescence initiates with an off-axis film rupture and film retraction speeds an order of magnitude larger than the collapse speed of the drop fluid. This is followed by the formation and propagation of an outward surface wave along the coalescing interface with wavelength of approximately 2D. For side-by-side drops, the collapse of the first drop is asymmetric due to the presence of the second drop and associated interface deformation. Overall, tomographic PIV provides insight into the flow physics and inherent three-dimensionalities in the coalescence process that would not be achievable with flow visualization or planar PIV only.     

Friction factor correlations for gas–liquid/liquid–liquid flows with drag-reducing polymers in horizontal pipes

In the present paper, two correlations have been developed to predict the effect of DRP on friction factor of two-phase flow for any pipe diameter. The correlations have been verified using published experimental results of DRP added to air–liquid annular flow and for oil–water flows with any flow pattern at the asymptotic state (maximum drag reduction). Such correlations are not available in literature and considered to be very useful in predicting the drag reduction using DRP and in understanding the most significant parameters that affecting the mechanism of drag reduction by polymers in multiphase flow.     

Jet pinch-off and drop formation in immiscible liquid–liquid systems

The behavior of glycerin–water jets flowing into immiscible ambients of Dow Corning 200 fluid was investigated using laser induced fluorescence (LIF). Undistorted images were obtained by matching the index of refraction of the fluids. A sinusoidal perturbation was superposed on the flow to phase lock the drop formation. The forcing frequency dramatically affected the size, spacing, and number of drops that formed within a forcing cycle and the angle between drops and the jet interface just before pinch-off. Two fluid combinations were studied with similar density ratios, but viscosity ratios differing by a factor of 20. The viscosity ratio affected the jet stability as well as pinch-off angles and drop size. Received: 28 January 1999/Accepted: 20 January 2000     

Simulation of an optically induced asymmetric deformation of a liquid–liquid interface

Deformations of liquid interfaces by the optical radiation pressure of a focused laser wave were generally expected to display similar behavior, whatever the direction of propagation of the incident beam. Recent experiments showed that the invariance of interface deformations with respect to the direction of propagation of the incident wave is broken at high laser intensities. In the case of a beam propagating from the liquid of smaller refractive index to that of larger one, the interface remains stable, forming a nipple-like shape, while for the opposite direction of propagation, an instability occurs, leading to a long needle-like deformation emitting micro-droplets. While an analytical model successfully predicts the equilibrium shape of weakly deformed interface, very few work has been accomplished in the regime of large interface deformations. In this work, we use the Boundary Integral Element Method (BIEM) to compute the evolution of the shape of a fluid–fluid interface under the effect of a continuous laser wave, and we compare our numerical simulations to experimental data in the regime of large deformations for both upward and downward beam propagation. We confirm the invariance breakdown observed experimentally and find good agreement between predicted and experimental interface hump heights below the instability threshold.     

Prediction of the entrained liquid fraction in vertical annular gas–liquid two-phase flow

The study considers the prediction of the entrained liquid fraction in adiabatic gas–liquid annular two-phase flow in vertical pipes. Nine empirical correlations have been tested against an experimental data bank drawn together in this study containing 1504 points for 8 different gas–liquid combinations and 19 different tube diameters from 5.00 mm to 57.1 mm. The correlation of Sawant, Ishii and Mishima and the one of Oliemans, Pots and Trompé were found to best reproduce the available data. A new correlating approach, derived from both physical intuition and dimensional analysis and capable of providing further physical insight into the liquid film atomization process, was proposed and worked better than any of the existing methods. This new correlation is based on the core flow Weber number that is also a controlling dimensionless group in determining the wall shear stress and associated frictional pressure gradient of annular flows.     

Separation efficiency of liquid–solid undergoing vibration based on breakage of liquid bridge

Vibrating separation is a significant method for liquid–solid separation. A typical example is the vibrating screen to dewater wet granular matter. The properties of granular matter and the vibrating parameters significantly affect the separation efficiency. This study investigates the effect of vibration parameters in separation based on the breakage of large-scale liquid bridge numerically by using a calibrated simulation model. Through analysing the simulation results, the liquid bridge shape and the volume between two sphere particles for various particle sizes and particle distances were studied in the static condition under the effect of gravity. The results show a general reducing trend of liquid bridge volume when the radius ratio of two particles increases, particularly when the ratio increases to 5. Additionally, a set of vibrating motion was applied to the liquid bridge in the simulation model. A group of experiments were also performed to validate the simulation model with vibration. Then, the effect of vibrating peak acceleration, distance between spheres and radius on the separation efficiency which was reflected by the residual water were investigated. It is found that separation efficiency increased obviously with the peak acceleration and the increase slowed down after the peak acceleration over 1 m/s².     

Gas–liquid mass transfer in the gas–liquid–solid mini fluidized beds

The gas–liquid–solid mini fluidized bed (GLSMFB) combines the advantages of fluidized bed and micro-reactor, and meets the requirements for safety and efficiency of green development of process industry. However, there are few studies on its flow performance and no studies on its mass and heat transfer performance. In this paper, the characteristics of gas–liquid mass transfer in a GLSMFB were studied in order to provide basic guidance for the study of GLSMFB reaction performance and application. Using CO₂ absorption by NaOH as the model process, the gas–liquid mass transfer performance of GLSMFB was investigated. The results show that the liquid volumetric mass transfer coefficient and the gas–liquid interfacial area both increase with the increase of the superficial gas velocity within the experimental parameter range under the same given superficial liquid velocity. At the same ratio of superficial gas to liquid velocity, the liquid volumetric mass transfer coefficient increases with the increase of the superficial liquid velocity. Fluidized solid particles strengthen the liquid mass transfer process, and the liquid volumetric mass transfer coefficient is about 13% higher than that of gas–liquid mini bubble column.     

Residual mass and flow regimes for the immiscible liquid–liquid displacement in a plane channel

The motion of two immiscible liquids in a plane channel is analyzed for the case in which the flow conditions and the interactions between the liquids and the solid surface maintain the displaced fluid attached to the wall. The Galerkin Finite Element Method is used to compute the velocity field and the configuration of the interface between the two fluids. We compare the residual mass fraction left on the wall with its two counterparts in capillary tubes, namely residual mass fraction and dimensionless layer thickness of the displaced fluid. The main result of this comparison was that although there is a qualitative similarity concerning the layer thickness between the two cases, the residual fraction of mass presented an important difference, showing that when the aspect ratio of the capillary passage is large there is an increase in the displacement efficiency. The thickness of the displaced liquid film attached to the channel walls is a function of the capillary number (Ca) and the viscosity ratio (N_μ). A map of streamlines in the Cartesian space (Ca, N_μ) with the different flow regimes of the problem is presented. We also showed that we can adapt the available analytical results obtained for gas-displacement in capillary tubes to the plane channel case, for low values of Ca.     

Analysis of spatial and temporal spectra of liquid film surface in annular gas–liquid flow

Wavy structure of liquid film in annular gas–liquid flow without liquid entrainment consists of fast long-living primary waves and slow short-living secondary waves. In present paper, results of spectral analysis of this wavy structure are presented. Application of high-speed LIF technique allowed us to perform such analysis in both spatial and temporal domains. Power spectra in both domains are characterized by one-humped shape with long exponential tail. Influence of gas velocity, liquid Reynolds number, liquid viscosity and pipe diameter on frequency of the waves is investigated. When gravity effect is much lesser than the shear stress, similarity of power spectra at different gas velocities is observed. Using combination of spectral analysis and identification of characteristic lines of primary waves, frequency of generation of secondary waves by primary waves is measured.     

Characteristics of flow and liquid distribution in a gas–liquid vortex separator with multi spiral arms

Fischer–Tropsch (F–T) synthesis is an important route to achieve the clean fuel production. The performance of gas–liquid separation equipment involving in the progressive condensation and separation of light and heavy hydrocarbons in the oil-gas products has become a bottleneck restricting the smooth operation of the F–T process. In order to remove the bottleneck, a gas–liquid vortex separator with simple structure, low pressure drop and big separation capacity was designed to achieve the efficient separation between gas and droplets for a long period. The RSM (Reynolds Stress Model) and DPM (Discrete Phase Method) are employed to simulate the flow characteristics and liquid distribution in the separator. The results show that the separation efficiency is influenced by the flow field and liquid phase concentration in the annular zone. The transverse vortex at the top of spiral arm entrains the droplets with small diameter into the upper annular zone. The entrained droplets rotate upward at an angle of about 37.4°. The screw pitch between neighbor liquid threads is about 0.3 m. There is a top liquid ring in the top of annular zone, where the higher is the liquid phase concentration, the lower is the separation efficiency. It is found that by changing the operating condition and the annular zone height the vortex can be strengthened but not enlarged by the inlet velocity. The screw pitch is not affected by both inlet velocity and annular zone height. The liquid phase concentration in the top liquid ring decreases with both the increases of inlet velocity and annular zone height. The total pressure drop is almost not affected by the annular zone height but is obviously affected by the inlet velocity. When the height of annular zone is more than 940 mm, the separation efficiency is not changed. Therefore, the annular zone height of 940 mm is thought to be the most economical design.     

Ab initio investigation of a possible liquid–liquid phase transition in MgSiO3 at megabar pressures

We perform density functional molecular dynamics simulations of liquid and solid MgSiO₃ in the pressure range of 120–1600 GPa and for temperatures up to 20,000 K in order to provide new insight into the nature of the liquid–liquid phase transition that was recently predicted on the basis of decaying laser shock wave experiments [Phys. Rev. Lett. 108 (2012) 065701]. However, our simulations did not show any signature of a phase transition in the liquid phase. We derive the equation of state for the liquid and solid phases and compute the shock Hugoniot curves. We discuss different thermodynamic functions and by explore alternative interpretations of the experimental findings.     

Analysis of liquid bridge between spherical particles

A pair of central moving spherical particles connected by a pendular liquid bridge with interstitial Newtonlan fluid is otten encountered in particulate coalescence process. In this paper, by assuming perfect-wet condition, the effects of liquid volume and separation distance on static liquid bridge are analyzed, and the relation between rupture energy and liquid bridge volume is also studied. These points would be of significance in industrial processes related to adhesive particles.     

Application of the PIV technique to measurements around and inside a forming drop in a liquid–liquid system

A particle image velocimetry (PIV) method has been developed to measure the velocity field inside and around a forming drop with a final diameter of 1 mm. The system, including a microscope, was used to image silicon oil drops forming in a continuous phase of water and glycerol. Fluorescent particles with a diameter of 1 μm were used as seeding particles. The oil was forced through a 200 μm diameter glass capillary into a laminar cross-flow in a rectangular channel. The velocity field was computed with a double-frame cross-correlation function down to a spatial resolution of 21 × 21 μm. The method can be used to calculate the shear stress induced at the interface by the cross-flow of the continuous phase and the main forces involved in the drop formation process.     

Roll waves in a gas–liquid medium

The onevelocity motion of a gas–liquid medium with a variable mass fraction of the gas phase, which is equilibrium in terms of phase pressures, is considered. The existence conditions of nonlinear periodic wave packets similar in structure to roll waves in open inclined channels are found. The structure of travelling waves in the medium with continuous addition of energy to the gas phase is studied.     

Experimental study of a liquid jet flowing into another immiscible liquid “a local analysis of the interface”

This paper describes an experimental study of a liquid jet leaving a cylindrical nozzle under gravity. A special optical system was used to study the spatial and temporal interface variations between two liquids. A photoelectric cell was used to measure the light intensity and to obtain the physical parameters of the jet. Spatial analysis revealed a continual contraction of the jet from the nozzle exit to the break-up zone. Fluctuations of the interface over time are characteristic of a random signal with a narrow bandpass. The Fourier transform of the different samples shows a bandpass of finite width centered around a characteristic frequency. The distribution of interface amplitude fluctuations was symmetrical to the average diameter, except in the zone in which the jet breaks up. By systematically tracing the main parameters of the jet diameter, we observed three zones with different jet behavior. The characteristic frequency of interface fluctuations increases as a linear function of the distance from the nozzle. The amplitude of interface fluctuations was an exponential function of the distance at which jet diameter fluctuations were measured.     

Review on vertical gas–liquid slug flow

Vertical slug flow is characterized by the rise of long bullet-shaped gas bubbles with a diameter almost matching that of the tube - Taylor bubbles. Liquid slugs separate consecutive Taylor bubbles, which may interact and coalesce if the distance between them is small. Slug flow has numerous industrial applications, being also observed on physiological and geological systems. In spite of the contribution of the development of non-intrusive experimental techniques to a deeper understanding of slug flow features, the complexity of this flow pattern requires the combined use of numerical approaches to overcome some of the optical problems reported in experimental methods, and other limitations related to the flow aperiodic behavior.The need to systematize the large amount of data published on the subject and to understand the limitations of the techniques employed constitutes the motivation for this review. In the present work, literature on vertical gas–liquid slug flow, with Newtonian fluids, from 1943 to 2015, covering theoretical, experimental and numerical approaches, is reviewed. Focus is given to single and trains of Taylor bubbles rising through stagnant and co-current liquids.It should be emphasized, however, that further research still needs to be conducted in some particular areas, namely the hydrodynamics of the liquid film surrounding the Taylor bubbles, the interaction between consecutive bubbles, and a more detailed approach to the flow of Taylor bubbles through co-current liquids.