Liquids Of Different Densities Research Articles

Determination of the Liquid Hold-up Volume and the Interface Radius of an Annular Centrifugal Contactor using the Liquid-Fast-Separation Method

Annular centrifugal contactors (ACCs), which use centrifugal force to separate the dispersion of two immiscible liquids of different densities, have been utilized in many industrial fields, such as the petroleum, hydrometallurgy, wastewater treatment, pharmaceutical processing, protein extraction, enantioselective chemical separation, biodiesel synthesis, and nuclear industries. Detailed hydrodynamic information, such as the liquid hold-up volume and the interface radius, is very important for successful design and operation of ACCs. A new method, namely, the liquid-fast-separation method, was developed to (1) obtain the parameters of the liquid hold-up volume, the actual phase ratio (aqueous phase/organic phase, a/o) of two phases in the mixing zone, and the interface radius, and (2) investigate the effects of the rotor speed, the total flow rate, the flow ratio (a/o), and the diameter of the heavy phase weir on these parameters. The experimental results indicated that the parameters of the liquid hold-up volume, the actual phase ratio (a/o) of two phases in the mixing zone, and the interface radius could be obtained using the liquid-fast-separation method. Moreover, the effects of the rotor speed, the total flow rate, the flow ratio (a/o), and the diameter of the heavy phase weir on these parameters could also be obtained. These results provide a more complete understanding of the fluid flow in ACCs to enable further advancements in their design and operation.

Impact of liquids with different densities

AbstractThe collision of liquids of different densities is studied theoretically for the case of liquids having wedge-shaped configuration before the impact. Both liquids are assumed to be ideal and incompressible, and the velocity potential theory is used for the flow of each liquid. Surface tension and gravity effects are neglected. The problem is decomposed into two self-similar problems, one for each liquid. Across the interface between the liquids, continuity of the pressure and the normal component of the velocity is enforced through iteration. This determines the shape of the interface and other flow parameters. The integral hodograph method is employed to derive the solution consisting of analytical expressions for the complex-velocity potential, the complex-conjugate velocity, and the mapping function. They are all defined in the first quadrant of a parameter plane, in which the original boundary-value problem is reduced to a system of integro-differential equations in terms of the velocity magnitude and the velocity angle relative to the flow boundary. They are solved numerically using the method of successive approximations. The results are presented through streamlines, interface and free-surface shapes, the pressure and velocity distributions. Special attention is given to the structure of the splash jet rising as a result of the impact.

On vortex flows of a two-phase fluid in porous media

The results of numerical modeling of the two-phase isothermal motion of immiscible incompressible liquids in porous media taking into account capillary and gravitational forces are presented. The problem is solved by the control volume method in the variables “velocity-saturation”. To solve the equation of hyperbolic type, the scheme WENO of the third order of accuracy in a combination with the Runge-Kutta method is used. It is shown that in the presence of capillary and gravitational forces vortex flows may occur in every phase under certain conditions. In particular, vortex flows arise after infiltration of a heavy liquid into the porous body saturated with easy liquid, and at segregation of liquids in a reservoir if there are inclusions of different permeability in it. It has been found that vortex flows change the configuration of the displacement front. In previous works, the occurrence of vortex flows in porous media has been studied by introducing in the consideration a new desired variable - function of vorticity. In such a statement of the problem, the occurrence of vortex flows in porous media has been studied at the interface of two liquids of different density, on the boundaries of a jump wise change of permeability and in some other cases. In the present work, it is shown that the existence of vorticity in a two-phase flow in porous media can be revealed by performing direct calculations of the velocity field in each phase.

A Lattice Boltzmann Simulation of Three-Dimensional Displacement Flow of Two Immiscible Liquids in a Square Duct

A three-dimensional (3D), multiphase lattice Boltzmann approach is used to study a pressure-driven displacement flow of two immiscible liquids of different densities and viscosities in a square duct. A three-dimensional, 15-velocity (D3Q15) lattice model is used. The effects of channel inclination, viscosity, and density contrasts are investigated. The contours of the density and the average viscosity profiles in different planes are plotted and compared with those obtained in a two-dimensional (2D) channel. We demonstrate that the flow dynamics in a 3D channel is quite different as compared to that of a 2D channel. We found that the flow is relatively more coherent in a 3D channel than that in a 2D channel. A new screw-type instability is seen in the 3D channel that cannot be observed in the 2D channel.

Gaseous bubble dynamics in a pulsational viscous flow

The paper is devoted to the investigation of gaseous bubble dynamics in a pulsational viscous flow. Behaviour of the bubble suspended in a viscous liquid of different density and located near the rigid wall of oscillating container is studied. The effect of the bubble and host liquid characteristics and vibration parameters on the interaction force is examined.

CFD Simulations of the Air/Water Two-phase Flow in an Annular Centrifugal Contactor

Annular centrifugal contactors (ACCs) use centrifugal force to mix and separate two immiscible liquids of different densities. The compact size, small liquid hold-up volume, short liquid residence time and high efficiency of ACCs have made them be favored for nuclear processes and destined to play a more important role for future advanced nuclear processing schemes. Computational fluid dynamics (CFD) simulations can provide a more complete understanding of the flow within the ACC for further advancements in design and operation of future ACCs. In this paper, CFD simulations of the air/water two-phase flow in the mixing zone of the ACC were carried out. The flow patterns and velocity profiles of the steady-state simulations for three different rotor speeds in the annular region and under the rotor are presented.

Dynamics of the interface between immiscible liquids of different densities with low Froude number

Consideration is given to slow interfacial dynamics in a two-layer system of viscous fluids of comparable density. The fluid flow is governed by the two-dimensional Navier–Stokes equations where it is assumed that the inertial terms can be disregarded. A numerical methodology is presented which allows the study of the dynamics in the nonlinear regime. The numerical method is based on rewriting the interface conditions in terms of appropriate Green’s functions which are independent on the governing equations.

Viscous Fingering and Gravity Segregation through Porous Media: Experimental Findings

Abstract During downward vertical flow of a viscous solution, the viscous fingering (VF) phenomenon affects miscible displacement of solutes through a soil profile. On the other hand, during horizontal flow, when the liquid residing in a horizontal bed of porous materials is displaced by another liquid of different density, the resulting hydrodynamic dispersion is modified by the formation of a tongue of denser liquid undershooting the less dense liquid, a phenomenon known as gravity segregation (GS). To explore VF and GS phenomena, the authors present laboratory experimental results on the vertical and horizontal transport of bulk solution and ions of different concentrations and/or densities through inert and reactive porous media. The study showed that, with miscible liquids, breakthrough starts later and ends earlier. The authors predicted the behavior of immiscible liquids by the nondimensional gravity segregation number β: that is, with increase in β, the segregation becomes extreme. The curve fitting technique CXTFIT 2.0 fitted the experimental breakthrough curves well, showing that the apparent coefficients of hydrodynamic dispersion vary much less with pore-water velocity in horizontal than in vertical flow, but retardation factors are not influenced by the orientation of flow. This work is relevant to the preferential flow of viscous liquids such as liquid fertilizers in agricultural fields, oil recovery processes, and the intrusion of saline water into the freshwater of coastal aquifers.

Experimental and numerical study of miscible Faraday instability

A study of the Faraday instability of diffuse interfaces between pairs of miscible liquids of different densities, by means of experiments and by a nonlinear numerical model, is presented. The experimental set-up consisted of a rectangular cell in which the lighter liquid was placed above the denser one. The cell in this initially stable configuration was then subjected to vertical vibrations. The subsequent behaviour of the ‘interface’ between the two liquids was observed with a high-speed camera. This study shows that above a certain acceleration threshold an instability developed at the interface. The amplitude of the instability grew during the experiments which then led to the mixing of the liquids. The instability finally disappeared once the two liquids were fully mixed over a volume, considerably larger than the initial diffuse region. The results of a companion two-dimensional nonlinear numerical model that employs a finite volume method show very good agreement with the experiments. A physical explanation of the instability and the observations are advanced.

The Entropy Effects in Binary Mixtures of Polar Mesogenic Solvent/Nonpolar Solute

The paper concerns two aspects of the entropy in mesogenic systems: (i) the entropy jump (Delta S (0) NI) at the phase transition from the isotropic liquid (I) to the nematic liquid crystalline state (N), and (ii) the entropy increment (Delta S) caused by the ordering action of the probing electric field applied to the dipolar system. The system studied are the mixtures of strongly polar mesogenic solvent n-hexylcyanobiphenyl (C 6H 13PhPhCN, 6CB) and the nonpolar nonmesogenic admixture 4-ethylcyclohexyl-4'- n-nonylphenyl (C 2H 5CyHxPhC 9H 19, 2CyPh9). The entropy jump at the I-N phase transition in pure 6CB [Delta S (0) NI= 1.52 J/(mol K)] was evaluated from the analysis of the phase diagram of the mixture 6CB + 2CyPh9 with use of the Landau-Lifshitz theory; the resulting value of the transition enthalpy (Delta H (0) NI = T NIDelta S (0) NI = 0.50 kJ/mol) agrees well to that obtained with the calorimetric methods. The field-induced entropy increment (Delta S) was calculated, at the given temperature, from the static dielectric permittivity derivative value (depsilon s/d T), with use of the Fröhlich theory. The singularities in dependence of the entropy increment on the temperature and on the mixtures composition are discussed in terms of the prenematic molecular self-organization extent in mesogenic liquids of different density of dipoles.

Quantitative comparison of thermal and solutal transport in a T-mixer by FLIM and CFD

The development and adoption of lab-on-a-chip and micro-TAS (total analysis system) techniques requires not only the solving of design and manufacturing issues, but also the introduction of reliable and quantitative methods of analysis. In this work, two complementary tools are applied to the study of thermal and solutal transport in liquids. The experimental determination of the concentration of water in a water–methanol mixture and of the temperature of water in a microfluidic T-mixer are achieved by means of fluorescence lifetime imaging microscopy (FLIM). The results are compared to those of finite volume simulations based on tabulated properties and well-established correlations for the fluid properties. The good correlation between experimental and modelled results demonstrate without ambiguity that (1) the T-mixer is an adiabatic system within the conditions, fluids and flow rates used in this study, (2) buoyancy effects influence the mixing of liquids of different densities at moderate flow rates (Reynolds number Re ≪ 10−2), and (3) the combination of FLIM and computational fluid dynamics has the potential to be used to measure the thermal and solutal diffusion coefficients of fluids for a range of temperatures and concentrations in one single experiment. As such, it represents a first step towards the full-field monitoring of both the extent and the kinetics of a chemical reaction.

Gravity segregation during miscible displacement—re-investigation and re-interpretation

When the liquid residing in a horizontal bed of porous material is displaced by another liquid of different density, the resulting hydrodynamic dispersion is modified by the formation of a tongue of denser liquid undershooting the less dense liquid, a phenomenon known as gravity segregation. An earlier account of gravity segregation contained a substantial error (that of an incorrect frame of reference for flow) and several printing mistakes. In this paper we (i) correct these errors, (ii) extend the analysis to describe the course of breakthrough in beds of rectangular and circular cross-sections, (iii) re-interpret the existing experimental evidence, and (iv) present new experimental results on the vertical and horizontal transport of ionic solutions of different concentrations and densities through inert and reactive porous materials, ballotini, and sepiolite, respectively. The behaviour of immiscible liquids is predicted by the non-dimensional gravity segregation number, β, segregation becoming more extreme as β increases. With miscible liquids, however, breakthrough starts later and ends earlier then predicted for immiscible liquids, mixing by hydrodynamic dispersion moderating the effect of segregation. Breakthrough curves are well fitted by CXTFIT 2.0; apparent coefficients of hydrodynamic dispersion vary much less with pore-water velocity in horizontal than in vertical flow, but retardation factors are not influenced by orientation. Although a formal analysis of the combined effect of gravity segregation and hydrodynamic dispersion was not possible, the statistically significant inverse relation between β and column Peclet number was explained qualitatively. Gravity segregation occurs during the intrusion of saline groundwater into coastal aquifers. The simple theory for immiscible displacement overestimates the actual intrusion that occurs with miscible liquids and so provides an effective safety margin.

Liquid-liquid critical point: an analytical approach

Theoretical simulations and experimental studies have showed that many systems (like liquid metals) can exhibit two phase transitions: gas-liquid and liquid-liquid. Consequently the fluid phase of these systems presents two critical points, namely the usual gas-liquid (G-L) critical point and the liquid-liquid critical point that results from a phase transition between two liquids of different densities: a low density liquid (LDL) and a high density liquid (HDL). The van der Waals theory for simple fluids [Phys. Rev. E 50, 2913 (1994)] is based on taking a system with purely repulsive forces as a reference, is able to describe two stable first-order phase transitions between fluids of different densities. The particles in our system interact via a total pair potential, which splits into a repulsive VR and a density-dependent attractive VA part.

Spatiotemporal characterization of interfacial Faraday waves by means of a light absorption technique

We present measurements of the complete spatiotemporal Fourier spectrum of Faraday waves. The Faraday waves are generated at the interface of two immiscible index matched liquids of different density. By use of a light absorption technique we are able to determine the bifurcation scenario from the flat surface to the patterned state for each complex spatial and temporal Fourier component separately. The surface spectra at onset are found to be in good agreement with the predictions from the linear stability analysis. For the nonlinear state our measurements show in a direct manner how energy is transferred from lower to higher harmonics and we quantify the nonlinear coupling coefficients. Furthermore we find that the nonlinear coupling generates static components in the temporal Fourier spectrum leading thus to a contribution of a nonoscillating permanent sinusoidal deformed surface state. A comparison of hexagonal and rectangular patterns reveals that spatial resonance can give rise to a spectrum that violates the temporal resonance conditions given by the weakly nonlinear theory.

Gravity-induced reorientation of the interface between two liquids of different densities flowing laminarly through a microchannel

This paper experimentally quantifies the reorientation of the liquid-liquid interface between fluids of different densities flowing side-by-side in pressure-driven laminar flow in microchannels. A gravity-induced pressure mismatch at the interface will gradually drive the denser fluid to occupy the lower portion of the microchannel. The rate of this process is expected to depend on the interplay of viscous forces--which tend to dominate at the microscale-and inertial and gravitational forces. A correlation that relates the position of such a liquid-liquid interface to physical variables and channel dimensions was derived. The extent of reorientation of the streams was then related to two dimensionless numbers: Fr, the square root of the ratio of inertial to gravitational forces; and Re/Fr2, the ratio of gravitational to viscous forces. Further analysis showed that the reorientation of the streams depends only on the gravitational and viscous forces, but not inertia. The quantitative description of the position of the interface between liquids of different densities described in this paper aids in the rational design of the rapidly growing number of microchemical systems that utilize multistream laminar flow for performing spatially resolved chemistry and biology inside microfluidic channels.

Extensive impact melting on the H-chondrite parent asteroid during the cataclysmic bombardment of the early solar system: Evidence from the achondritic meteorite Dar al Gani 896

DaG 896 is an olivine-rich microporphyritic rock of komatiitic composition. Both the olivine composition (Fa 17.5±2.1, [Mn/Mg] = 0.0061) and the bulk oxygen isotopic composition (δ 17 O = +2.55, δ 18 O = +3.50) indicate that DaG 896 is a sample of the H-chondrite parent body. The bulk chemistry shows an H-chondritic distribution of lithophile elements, whereas chalcophile and siderophile elements are strongly depleted, indicating formation through whole-rock melting (or nearly so) of H-chondrite material, nearly complete loss of the metal plus sulfide component, and crystallization without significant igneous fractionation. Superheated, severely shocked chondritic relics (∼10 vol%), typically in the form of corroded lithic fragments <100 μm in size intimately distributed within the igneous lithology, indicate that melting was triggered by a highly energetic impact, which possibly induced shock pressures of ∼80–100 GPa. The relatively young 3.704 ± 0.035 Ga 40 Ar- 39 Ar crystallization age is consistent with the impact melting origin, as magmatism in the asteroid belt was active only in the first hundred million years of solar system history. Based on textural data and thermodynamic crystallization modelling, we infer that DaG 896 crystallized from a liquidus temperature of ∼1630°C under relatively slow cooling rates (∼10°C h −1) to ∼1300°C, before quenching. The two-stage cooling history indicates that a reasonable formation environment might be a dike intruding cooler basement below a crater floor. Metal-silicate fractionation may have been accomplished, at least at the centimeter-scale of the studied meteorite sample, through differential acceleration of immiscible liquids of different density during the intense flow regimes associated with the excavation and modification stages of the cratering mechanism. Alternatively, DaG 896 may represent a surface sample of a differentiated melt body at the floor of an impact crater, as gravitational settling appears to be an effective process at the surface of a chondritic parent asteroid: for metal particles 1 to 10 mm in size, typically observed in partially differentiated impact melt rocks, Stokes’ Law indicates a settling velocity >1 m h −1 during the first few hours of crystallization on asteroidal bodies of >25 km radius. The ∼3.7 Ga age of DaG 896 nearly overlaps with the slightly older resetting ages of H-chondrites (all impact melts) available from the literature, indicating that the H-chondrite parent asteroid underwent extensive impact melting at the enduring of the cataclysmic bombardment of the early solar system. Such an age overlap may also indicate early disruption of the initial H-chondrite parent asteroid. The close similarity between the bulk composition and degassing age of DaG 896 and silicate inclusions in IIE iron meteorites is further evidence in support of a common origin by impact melting and metal-silicate segregation on the H-chondrite parent asteroid. Our new high-precision oxygen isotopic measurements of H-chondrites (Δ 17 O = 0.77 ± 0.04) should be extended to IIEs to verify this possible petrogenetic link.

Tiling in the geometric model for water

Hydrogen bonded liquids like water present a rich thermodynamic behaviour due to the strength and directionality of the bonds. In a recent paper a geometric model based on Bernal’s model for liquids was proposed to study the effects of the hydrogen bonds on the phase transitions of water, under pressure and temperature variations. Water molecules were assumed to stay at the vertices of coordination r (r = 4; 5; 6) of perfectly tiled polygons, and to have four links which allow up to four hydrogen bonds per particle. Mean field calculations yielded a phase diagram with three phases of different densities and a critical point at the end of the coexistence line between the high and low density phases. The three phases were considered to be liquids of different densities. In the present work we have shown that applying some geometric constraints to particle arrangements (thus correcting the system entropy, which was overestimated in the previous work), and allowing a variable number of links per molecule, leads to substantial alteration of the phase diagram. Three phases of different densities are still present, but no critical point appears. Two of the phases are solid, and one phase is amorphous.

Numerical model to study natural convection in a rectangular enclosure filled with two immiscible fluids

A finite-difference approximation of the Navier–Stokes equations under the Boussinesq-fluid assumption is used to simulate the flow and heat transfer in a two-layer system of an immiscible incompressible fluid. The numerical model is validated with a benchmark solution which is buoyancy-driven flow in a square cavity with differently heated vertical sides. The results of the two-dimensional numerical simulation are compared with the experimental data of the hydrodynamics and heat exchange within a horizontal two-layer medium consisting of two immiscible liquids of different densities and viscosities. Comparisons are made for the profiles of the temperature and for the profiles of the horizontal and vertical components of the velocity vector as well. Qualitative agreement between numerical and experimental results is observed.

2D unsteady motion and deformation of a gaseous bubble in a vibrating liquid at zero gravity

Numerical investigation of a bubble immersed in a liquid of different density in a container subject to translational oscillations in weightlessness conditions shows the following scenario where the bubble, initially located at the container center, starts to move to the container wall due to an attraction mechanism having non-viscous origin. This motion is accompanied by small-amplitude oscillations with the frequency equal to the forcing frequency and by eigen-oscillations with long period excited by the initial acceleration. These eigen-oscillations are gradually damped. Simultaneously, the deformation of the bubble shape averaged over the external forcing period occurs. The bubble is flattened in the direction of vibration axis

Generic mechanism for generating a liquid-liquid phase transition.

Recent experimental results indicate that phosphorus--a single-component system--can have a high-density liquid (HDL) and a low-density liquid (LDL) phase. A first-order transition between two liquids of different densities is consistent with experimental data for a variety of materials, including single-component systems such as water, silica and carbon. Molecular dynamics simulations of very specific models for supercooled water, liquid carbon and supercooled silica predict a LDL-HDL critical point, but a coherent and general interpretation of the LDL-HDL transition is lacking. Here we show that the presence of a LDL and a HDL can be directly related to an interaction potential with an attractive part and two characteristic short-range repulsive distances. This kind of interaction is common to other single-component materials in the liquid state (in particular, liquid metals), and such potentials are often used to describe systems that exhibit a density anomaly. However, our results show that the LDL and HDL phases can occur in systems with no density anomaly. Our results therefore present an experimental challenge to uncover a liquid-liquid transition in systems like liquid metals, regardless of the presence of a density anomaly.