Pressure drop and holdup predictions in horizontal oil-water flows for curved and wavy interfaces

In this work a modified two-fluid model was developed based on experimental observations of the interface configuration in stratified liquid-liquid flows. The experimental data were obtained in a horizontal 14. mmID acrylic pipe, for test oil and water superficial velocities ranging from 0.02. m/s to 0.51. m/s and from 0.05. m/s to 0.62. m/s, respectively. Using conductance probes, average interface heights were obtained at the pipe centre and close to the pipe wall, which revealed a concave interface shape in all cases studied. A correlation between the two heights was developed that was used in the two-fluid model. In addition, from the time series of the probe signal at the pipe centre, the average wave amplitude was calculated to be 0.0005. m and was used as an equivalent roughness in the interfacial shear stress model. Both the interface shape and roughness were considered in the two-fluid model together with literature interfacial shear stress correlations. Results showed that the inclusion of both the interface curvature and the equivalent roughness in the two-fluid model improved its predictions of pressure drop and interface height over the range of studied superficial oil and water velocities. Compared to the two-fluid model with other interfacial shear stress correlations, the modified model performed better particularly for predicting pressure drop

Spectral density analysis of the interface in stratified oil-water flows

In this work the wavy interface of stratified oil-water flows was investigated using wire conductance probes. The experiments were carried out in a 38mm ID acrylic pipe using water and oil (Exxsol D140 oil: ρ=830kgm, μ=0.0055kgms) as test fluids. High-speed imaging revealed that almost two-dimensional interfacial waves develop at the inlet junction for input oil-to-water flow rate ratios different from one. Downstream the inlet section, however, the interface has a complex three dimensional structure with very small amplitude contributions. The structure of such interfaces can be properly investigated from the power spectrum of the conductance probe signal. A rigorous and detailed methodology is presented for estimating the power spectrum of the interface signal that is based on the Wiener-Khinchine theorem and makes extensive use of a Fast Fourier Transform (FFT) algorithm. Interface spectra were studied at two locations, close to the inlet of the test section and at 7m downstream. The results showed that the waves at the inlet have a unique peak frequency of about 19Hz and that, at the downstream location, this frequency is still present but has a smaller significance compared to that caused by the mechanical vibrations of the set up. This frequency was independent of the flow rates and could be a characteristic of the pair of the test fluids used rather than of the flow. © 2014 The Authors

Liquid-liquid dispersions in intensified impinging-jets cells

The formation of dispersions of two immiscible liquids in a confined impinging-jets cell was studied experimentally. The jets of the liquids formed at two opposing channels and collided in a main channel, which was perpendicular to the previous two. Jet channels with diameters either 0.25 or 0.5 mm and main channels with diameters either 2 or 3 mm were used. The jet velocities varied from 0.17 to 6.2 m/s and the dispersed to continuous phase ratios varied from 0.05 to 0.28. Deionised water and kerosene (Exxsol D80: ρ = 795 kg/m3 and μ = 1.73 mPa s) were used as test fluids. Drop sizes were measured with high-speed imaging. It was found that the total velocity of the two jets was the main parameter that affected both the average drop size and the interfacial area, whilst the dispersed to continuous phase flow rate ratio was less significant. Both phases could become continuous depending on the phase flowrate ratio; drops were, however, larger in the organic continuous dispersions. The interfacial area produced with the impinging-jets cell was almost 3 times larger than in capillary contactors at similar conditions (umix = 0.024–0.19 m/s). The size of the main channel affected the drop size and smaller drops formed in the large channel compared to the small one. With increasing energy dissipation rate, ε, in the impingement zone, the Sauter mean diameter decreased following a relation of the form ∼ε−b. Apart from the lower velocities, the drop sizes did not change significantly at distances equal to 15 channel diameters downstream the impingement area

Intensified Eu(III) extraction using ionic liquids in small channels

The extraction of Eu(III) from nitric acid solutions was studied in intensified small scale separation units using an ionic liquid solution (0.2 M n-octyl(phenyl)-N,N-diisobutylcarbamoylmethyphosphine oxide (CMPO)-1.2 M Tributylphosphate) (TBP)/1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]amide; ([C4min][NTf2])as the extraction phase. The investigations were carried out in channels with 0.2 mm and 0.5 mm diameter for phase flowrates that result in plug flow with the aqueous solution as the dispersed phase. The interfacial area in plug flow and the velocity profiles within the plugs were studied with high speed imaging and bright field micro Particle Image Velocimetry. Distribution and mass transfer coefficients were found to have maximum values at nitric acid concentration of 1M. Mass transfer coefficients were higher in the small channel, where recirculation within the plugs and interfacial area are large, compared to the large channel for the same mixture velocities and phase flow rate ratio. Within the same channel, mass transfer coefficients decreased with increasing residence time indicating that significant mass transfer takes place at the channel inlet where the two phases come into contact. The experimental results were compared with previous correlations on mass transfer coefficients in plug flows

Experimental and numerical hydrodynamic studies of ionic liquid-aqueous plug flow in small channels

The hydrodynamic characteristics of liquid-liquid plug flow were studied in microchannels with 0.2 and 0.5 mm ID both experimentally and numerically. For the experiments high speed imaging and bright field micro-Particle Image Velocimetry were used, while the numerical simulations were based on the volume-of-fluid (VOF) method. The two immiscible liquids were a 1 M HNO3 aqueous solution which formed the dispersed plugs and a mixture of 0.2 M n-octyl(phenyl)-N,N-diisobutylcarbamoylmethyphosphine oxide (CMPO) and 1.2 M Tributylphosphate (TBP) in the ionic liquid 1-butyl-3-methylimidazolium bis[(trifluoromethyl)sulfonyl]amide ([C4min][NTf2]). The thickness of the film surrounding the plugs, and the plug velocity and length were measured and compared against literature correlations. For the cases studied (0.0224 < Ca < 0.299) it was observed that the liquid film was largely affected by the changes in the shape of the front cap of the plug. The plug length was affected by both the Capillary number and the ratio of the aqueous to ionic liquid phase flow rates while the plug volume depended on the channel diameter and the mixture velocity. The numerical simulations showed that, in agreement with the measurements, a parabolic velocity profile develops in the middle of the plugs while the circulation patterns in the plug are affected by the channel size. The pressure profile along the channel with a series of plugs and slugs was predicted numerically while the pressure drop agreed well with a correlation which included the dimensionless slug length and the ratio Ca/Re

Intensified Nd extraction in small channels for NdFeB magnet recycling

Neodymium (Nd) was continuously extracted from aqueous solutions by trioctylphosphine oxide (TOPO) dissolved in the ionic liquid 1-Butyl-3-methylimidazolium Bis (trifluoromethanesulfonyl)imide ([C4mim][Tf2N]) in small channel contactors. Kinetic studies confirmed a 1:6 Nd:TOPO extraction mechanism at high initial Nd concentrations of 0.005 and 0.01 M in a 0.001 M nitric acid aqueous phase. The continuous flow extractions were carried out in channels with 0.5 and 1 mm diameter and the effects of mixture velocity and residence time on the extraction efficiency and the mass transfer coefficient were investigated. At equal phase mixture velocities, the flow pattern studies highlighted a plug flow regime at mixture velocities of 0.01 to 0.05 m/s for both channels, resulting in interfacial areas of up to 4900 m2/m3 in the 0.5 mm channel and 2500 m2/m3 in the 1 mm channel. After 37.5 s residence time, extraction efficiencies of 80 % were found in the 0.5 mm channel at a KLα of 0.09 s−1 and 70 % at 0.04 s−1 in the 1 mm channel. The same extraction efficiencies were achieved in 1–2 h in the batch systems

Perturbation theory and singular perturbations for input-to-state multistable systems on manifolds

We consider the notion of Input-to-State Multistability, which generalizes ISS to nonlinear systems evolving on Riemannian manifolds and possessing a finite number of compact, globally attractive, invariant sets, which in addition satisfy a specific condition of acyclicity. We prove that a parameterized family of dynamical systems whose solutions converge to those of a limiting system inherits such Input-to-State Multistability property from the limiting system in a semi-global practical fashion. A similar result is also established for singular perturbation models whose boundary-layer subsystem is uniformly asymptotically stable and whose reduced subsystem is Input-to-State Multistable. Known results in the theory of perturbations, singular perturbations, averaging, and highly oscillatory control systems, are here generalized to the multistable setting by replacing the classical asymptotic stability requirement of a single invariant set with attractivity and acyclicity of a decomposable invariant one

Input-to-state stability for cascade systems with multiple invariant sets

In a recent paper Angeli and Efimov (2015), the notion of Input-to-State Stability (ISS) has been generalized for systems with decomposable invariant sets and evolving on Riemannian manifolds. In this work, we analyze the cascade interconnection of such ISS systems and we characterize the finest possible decomposition of its invariant set for three different scenarios: 1. the driving system exhibits multistability (convergence to fixed points only); 2. the driving system exhibits multi-almost periodicity (convergence to fixed points as well as periodic and almost-periodic orbits) and the driven system is assumed to be incremental ISS; 3. the driving system exhibits multiperiodicity (convergence to fixed points and periodic orbits) whereas the driven system is ISS in the sense of Angeli and Efimov (2015). Furthermore, we provide marginal results on the backward/forward asymptotic behavior of incremental ISS systems and on the response of a contractive system under asymptotically almost-periodic forcing. Three examples illustrate the potentiality of the proposed framework

Nuclear Transparency in Heavy Ion Collisions at 14.6 GeV/nucleon

The probability of a projectile nucleon to traverse a target nucleus without interaction is calculated for central Si-Pb collisions and compared to the data of E814. The calculations are performed in two independent ways, via Glauber theory and using the transport code UrQMD. For central collisions Glauber predictions are about 30 to 50% higher than experiment, while the output of UrQMD does not show the experimental peak of beam rapidity particles.Comment: 9 pages, 4 figures. submitted to Nucl. Phys.