Miscible Fluids Research Articles

Influence of miscible viscous fingering of finite slices on an adsorbed solute dynamics

Viscous fingering (VF) between miscible fluids of different viscosities can affect the dispersion of finite width samples in porous media. We investigate here the influence of such VF due to a difference between the viscosity of the displacing fluid and that of the sample solvent on the spatiotemporal dynamics of the concentration of a passive solute initially dissolved in the injected sample and undergoing adsorption on the porous matrix. Such a three component system is modeled using Darcy’s law for the fluid velocity coupled to mass-balance equations for the sample solvent and solute concentrations. Depending on the conditions of adsorption, the spatial distribution of the solute concentration can either be deformed by VF of the sample solvent concentration profiles or disentangle from the fingering zone. In the case of deformation by fingering, a parametric study is performed to analyze the influence of parameters such as the log-mobility ratio, the ratio of dispersion coefficients, the sample length, and the adsorption retention parameter k′ on the widening of the solute concentration peak. The results highlight experimental evidences obtained recently in reversed-phase liquid chromatography.

Turbulence-induced secondary motion in a buoyancy-driven flow in a circular pipe

We analyze the results of a direct numerical simulation of the turbulent buoyancy-driven flow that sets in after two miscible fluids of slightly different densities have been initially superimposed in an unstable configuration in an inclined circular pipe closed at both ends. In the central region located midway between the end walls, where the flow is fully developed, the resulting mean flow is found to exhibit nonzero secondary velocity components in the tube cross section. We present a detailed analysis of the generation mechanism of this secondary flow which turns out to be due to the combined effect of the lateral wall and the shear-induced anisotropy between the transverse components of the turbulent velocity fluctuations.

An investigation of the processes of heat and mass transfer in a multilayer medium under conditions of injection of a miscible agent with simultaneous electromagnetic stimulation

A numerical investigation is performed of the impact of high-frequency (HF) electromagnetic (EM) field on the process of filtering of miscible fluids and propagation of heat in a uniform stratum. The cross effects of heat and mass transfer, which arise under conditions of nonisothermal motion of a multicomponent medium in porous medium, are taken into account during simulation.

Spatial and temporal features of density-dependent contaminant transport: Experimental investigation and numerical modeling

We investigate the spatial and temporal features of variable-density contaminant plumes migration in porous materials. Our analysis is supported by novel experimental results concerning concentration profiles inside a vertical column setup that has been conceived at CEA to this aim. The experimental method relies on X-ray spectrometry, which allows determining solute profiles as a function of time at several positions along the column. The salient outcomes of the measurements are elucidated, with focus on miscible fluids in homogeneous saturated media. The role of the injected solution molarity is evidenced. As molarity increases, the solutes plume transport progressively deviates from the usual Fickian behavior, and pollutants distribution becomes skewed in the direction dictated by gravity. By resorting to a finite elements approach, we numerically solve the nonlinear equations that rule the pollutants migration: a good agreement is found between the simulated profiles and the experimental data. At high molarity, a strong dependence on initial conditions is found. Finally, we qualitatively explore the (unstable) interfacial dynamics between the dense contaminant plume and the lighter resident fluid that saturates the column, and detail its evolution for finite-duration contaminant injections.

Miscible ferrofluid patterns in a radial magnetic field

Pattern formation in a miscible ferrofluid system is experimentally investigated. The experiment is performed by immersing a thin ferrofluid droplet in a cylindrical container, overfilling it with a nonmagnetic miscible fluid, and applying an in-plane radial magnetic field. Visually striking patterns are obtained whose morphologies change from circular at zero field to complex starburst-like structures at finite field. The evolution of miscible ferrofluid droplets of various initial diameters subjected to different magnetic-field strengths is considered. Proper rescaling of the experimental data indicates that the time evolution of the droplets' area increments obeys a universal 4/3 power-law behavior at long times.

Effect of aspect ratio on transverse diffusive broadening: A lattice Boltzmann study

We study scaling laws characterizing the interdiffusive zone between two miscible fluids flowing side by side in a Y-shape laminar micromixer using the lattice Boltzmann method. The lattice Boltzmann method solves the coupled three-dimensional (3D) hydrodynamics and mass transfer equations and incorporates intrinsic features of 3D flows related to this problem. We observe the different power-law regimes occurring at the center of the channel and close to the top/bottom wall. The extent of the interdiffusive zone scales as the square root of the axial distance at the center of the channel. At the top/bottom wall, we find an exponent 1/3 at early stages of mixing as observed in the experiments of Ismagilov [Appl. Phys. Lett. 76, 2376 (2000)]. At a larger distance from the entrance, the scaling exponent close to the walls changes to 1/2 [J.-B. Salmon and A. Adjari, J. Appl. Phys. 101, 074902 (2007)]. Here, we focus on the effect of the finite aspect ratio on diffusive broadening. Interestingly, we find the same scaling laws regardless of the channel's aspect ratio. However, the point at which the exponent 1/3 characterizing the broadening at the top/bottom wall reverts to the normal diffusive behavior downstream strongly depends on the aspect ratio. We propose an interpretation of this observation in terms of the shear rate at the side walls. A criterion for the range of aspect ratios with non-negligible effect on diffusive broadening is also provided.

Effects of vibrations on dynamics of miscible liquids

We report on a numerical study of the mixing of two miscible fluids in gravitationally stable configuration. In the absence of external forces the diffusion process leads to the mixing of species. The aim of this study is to analyze the physical mechanism by which vibrations affect the mixing characteristic of two stratified miscible fluids. The translational periodic vibrations of a rigid cell filled with different mixtures of water–isopropanol are imposed. The vibrations with a constant frequency and amplitude are directed along the interface. In absence of gravity vibration-induced mass transport is incomparably faster than in diffusion regime. Our results highlight the strong interplay between gravity and vibrational impact, the relative weight of each effect is determined by ratio vibrational and classical Rayleigh numbers.

The influence of surface tension gradients on drop coalescence

We present the results of a combined experimental and numerical investigation of the coalescence of a drop with a liquid reservoir of a miscible but distinct fluid. Particular attention is given to elucidating the influence on the coalescence process of a surface tension difference between drop and reservoir. Drops are gently deposited on the surface of the reservoir, and so coalesce with negligible initial vertical velocity. Depending on the drop size and reservoir composition, partial or total coalescence may occur. Three distinct regimes, depending on the reservoir to drop surface tension ratio, Rσ, are identified and delineated through both experiments and numerics. If Rσ<0.42, droplets are ejected from the top of the drop, while satellite droplets are left in its wake. For 0.42≤Rσ<0.93, only total coalescence is observed. When Rσ≥0.93, partial coalescence is increasingly favored as the reservoir’s surface tension increases.

Numerical study of unstable reaction-diffusion fronts in porous media

Numerical simulations using a lattice-gas method (FHP-III) were performed. The method was modified for simulating two miscible fluids into a rectangular cell with obstacles (porous medium) and without obstacles (Hele-Shaw cell). An external force can be applied to each fluid. A suitable combination of this force and initial conditions can develop an unstable interface front (Rayleigh-Taylor instability). A chemical reaction between the fluids was also introduced, with a parameter that controls the reaction rate. The influence of the parameters that control the force and the chemical reaction on the development of the instability was studied.

Miscible viscous fingering in microgravity

To address the issue of miscible viscous fingering instability in buoyancy free conditions, experiments have been performed under microgravity conditions in parabolic flights. A Hele-Shaw cell, two parallel plates separated by a small gap, has been used with two miscible fluids of viscosity ratio 100 (the injected fluid is the less viscous). The influence of the initial thickness of the pseudointerface between the two fluids has been studied, using flow rates large enough to prevent further mixing during displacement. The selected wavelength, measured on the observed fingering pattern, does not depend on the initial front thickness: It is around three times the gap of the cell, i.e., significantly lower than the value of five, observed on earth. However, the initial thickness does control the displacement length required for the instability to occur. Our results are in reasonable agreement with existing and new numerical simulations.

Electrohydrodynamic Deformation of a Miscible Fluid Stream by a Transverse Electric Field

Electrohydrodynamic deformation of a cylindrical fluid stream is analyzed with a quasi-electroneutral model. The stream is miscible with the surrounding liquid, though of different electrical conductivity and permittivity, and is subject to an electric field that acts transverse to the axis of the cylinder. The formulation allows for natural gradients of electrical conductivity and dielectric constant in the transition region between the stream and the surrounding liquid; these property variations are fully coupled to the fluid motion and are assumed to stem from concentration gradients of charge-carrying solutes. Dielectric and Coulombic body forces attendant to the time-dependent, spatial nonuniformities are accounted for. The strength of the electrically driven flows is such that transport of solutes is dominated by advection. As a consequence, the initial conductivity and dielectric constant differences, between the interior of the stream and the surrounding liquid, persist through significant deformation of the stream and characterize the rate at which the stream (continuously) deforms. Calculations for aqueous systems dominated by conductivity effects agree with measurements of stream deformation made by Rhodes et al. [J. Colloid Interface Sci. 1989, 129, 78]. Calculations for systems controlled by dielectric effects show that relative permittivity differences must be at least O(1) if noticeable deformations are to occur in a matter of seconds, which may explain why Trau et al. [Langmuir 1995, 11, 4665] discerned no deformations controlled by dielectric effects in low permittivity, low conductivity systems. An implication of these latter predictions is that experiments to isolate the role of dielectric constant mismatch may not be practicable.

Pressure-driven miscible two-fluid channel flow with density gradients

We study the effect of buoyancy on pressure-driven flow of two miscible fluids in inclined channels via direct numerical simulations. The flow dynamics are governed by the continuity and Navier–Stokes equations, without the Boussinesq approximation, coupled to a convective-diffusion equation for the concentration of the more viscous fluid through a concentration-dependent viscosity and density. The effect of varying the density ratio, Froude number, and channel inclination on the flow dynamics is examined, for moderate Reynolds numbers. We present results showing the spatiotemporal evolution of the flow together with an integral measure of mixing.

Effective Darcy‐scale contact angles in porous media imbibing solutions of various surface tensions

Surface tensions of high‐salinity solutions are significantly different from those of pure water. Our objective was to develop and test a methodology to determine whether these surface tension effects predictably alter imbibition into dry and moist porous media. Static and dynamic experiments were performed using four grades of quartz sand to determine the effects of solution salinity on imbibition. Results were quantified as apparent contact angles between the sand and three solutions (pure water, 5 molal NaNO3, and n‐hexane). Contact angles determined using a static method in initially air dried sand ranged from 23° to 31°, with the same values found for both water and the NaNO3 solution. Effective contact angles determined for the air‐dried sand using a dynamic method based on a modified version of the Green and Ampt model were about twice those found using the static method, averaging 45° and 62° for water and the NaNO3 solution, respectively. In prewetted sands, the dynamic imbibition data yielded apparent contact angles of 2° and 21° for water and the NaNO3 solution, respectively, with the latter value comparing well to a predicted value of 25° for the NaNO3 solution solely on the basis of surface tension contrast. The results of this study indicate that on the Darcy scale, saline solutions appear to follow the relationship of nonzero contact angles with other miscible fluids of different surface tensions used to prewet the sand grains, in agreement with the macroscale infiltration results of Weisbrod et al. (2004).

Experimental study of Rayleigh–Taylor instability with a complex initial perturbation

Experiments have been performed investigating the Rayleigh–Taylor instability initialized with a complex initial perturbation. The experiments utilize a miscible fluid combination with Atwood number A≈0.2. The initially stably stratified fluids are contained within a Plexiglas tank mounted to a linear rail system. The tank was then oscillated vertically to impose nearly sinusoidal three-dimensional internal waves of varying wavelength and complexity at the fluid interface. After imposing this perturbation, the tank is accelerated down the rails at a rate greater than Earth’s gravity (g0) resulting in a body force of approximately 0.8g0. The flow is visualized with either backlit photography or planar laser induced fluorescence. Image sequences from the experiments show bubble and spike merging, leading to a growth of length scale with time. Averaged vertical concentration distributions show self-similarity after ∼233 ms with a total experiment time of ∼300 ms. In addition, after this time, the square root of the mixing zone width appears to grow linearly with (Ag)1/2t. Values for the self-similar growth parameter, α, obtained by curve fitting to the linear portion of these curves yield values that are lower than those obtained in other experiments but are in good agreement with values found in computational studies initiated with perturbations similar to those used here. The measured α values do not show a dependence on the initial perturbation amplitude. The method for the determination of α using the expression α=ḣ2/4Agh proposed by Cabot and Cook [Nat. Phys. 2, 562 (2006)] yields a value in agreement with that measured by curve fitting the h1/2 versus Agt curves, and which is also in better agreement with computational studies.

Prolonged residence times for particles settling through stratified miscible fluids in the Stokes regime

The behavior of settling particles in stratified fluid is important in a variety of applications, from environmental to medical. We document a phenomenon in which a sphere, when crossing density transitions, slows down substantially in comparison to its settling speed in the bottom denser layer, due to entrainment of buoyant fluid. We present results from an experimental study of the effects of the fluid interface on flight times as well as a theoretical model derived from first principles in the low Reynolds number regimes for stratified miscible fluids. Our work provides a new predictive tool and gives insight into the role of strong stratification in particle settling.

The effect of CO 2 on the speciation of RbBr in solution at temperatures to 579 °C and pressures to 0.26 GPa

Carbon dioxide- and salt-bearing solutions are common in granulite, ore-forming and magmatic environments. The presence of CO 2 affects mineral solubilities, fluid miscibility, and viscosity and wetting properties, and is expected to affect salt speciation. EXAFS measurements of RbBr–H 2O–CO 2 fluids contained in corundum-osed synthetic fluid inclusions (SFLINCs) have been used to investigate the effect of CO 2 on salt speciation at temperatures to 579 °C and pressures to around 0.26 GPa. Forward modelling indicates that solute dehydration is difficult to distinguish from up to around 40% of Rb–Br ion-pairing, so results refer to the total number of nearest neighbours, which are likely to be mostly O present in waters of hydration, but may also include Br, if ion pairing is present. Additionally, results relate to the number of well-ordered neighbours in the first shell, because nearest neighbours with a high degree of disorder may be present but contribute minimally to the EXAFS signal. Analysis of the EXAFS results at the Rb edge for the CO 2-free solution is consistent with previous work and shows that the number of nearest neighbours for Rb in CO 2-free solutions decreases from 6 ± 0.6 to 1.4 ± 0.1 as temperature increases from 20 to 534 °C. The decrease is accompanied by a decrease in Rb- x bondlengths of 0.05 Å, where x is the first shell scatterer. Results for the CO 2-bearing solution are different to those for the CO 2-free solution. The number of nearest neighbours is 16 and 22% less than for the CO 2-bearing solution at 312 and 445 °C respectively. Changes in the numbers of nearest neighbours correlate well with calculated changes in the bulk solution dielectric constant; CO 2-bearing and CO 2-free solutions lie on the same trend, which suggests that it may be possible to calculate the number of nearest neighbours from dielectric constant. Rb- x bondlengths for the CO 2-bearing solution are statistically indistinguishable to those for the CO 2-free inclusions. Results for Br are worse quality than for Rb so EXAFS analysis could not be completed, however XANES spectra for CO 2-free and CO 2-bearing solutions are consistent with solute dehydration similar to that recorded by the Rb spectra. The conclusions of this study provide support for the notion that CO 2 has a fundamental effect on the mechanics of solubility, and that these effects should be incorporated into conceptual and quantitative thermodynamic models.

Convective/absolute instability in miscible core-annular flow. Part 1: Experiments

We address the issue of the convective or absolute nature of the instability of core-annular pipe flows, in experiments using two miscible fluids of equal density but different viscosities, the core fluid being much less viscous than the wall one. We use a concentric co-current injection of the two fluids. An axisymmetric parallel base state is obtained downstream the injector. The core radiusRIand the Reynolds numberReof the so-obtained base state are varied independently due to the control of the flow rate of each fluid. However, a downstream destabilization of this base state was observed within the explored range of the two control parametersRIandRe. Moreover, the fixed location of this destabilization, observed for some particular parameters, suggests an absolute nature of the instability. We present a tentative delineation of the nature (convective or absolute) of the instability and discuss the accessible measurements to experimentally address this issue.

Surface instability on thin fluid layers of a binary mixture

A long-wave model for thin layers consisting of two miscible fluids is presented. The model is a development of a simplified 2D model variant which considers the temperature and the concentration fields as linear functions on the vertical coordinate and neglect the convective terms from the corresponding equations. Now, the 2D thin film equation is coupled to complete 3D energy and mass conservations equation. We discuss the extended system in the linear approximation and in the initial nonlinear stage.

Simulation of Mass Transfer of Calcium in Concrete by the Lattice Kinetic Scheme for a Binary Miscible Fluid Mixture

The lattice kinetic scheme (LKS) for a binary miscible fluid mixture was applied to the simulation of the mass transfer of calcium in concrete. Cement paste, a major component of concrete, is a porous medium with a complicated three-dimensional geometry. The structure of the model concrete was selected on the basis of experimental data obtained by high-intensity X-ray computed tomography. The LKS, an improved version of the original lattice Boltzmann method, was used to save computational memory and to maintain numerical stability. First, an unsteady convection-diffusion problem was examined, and the accuracy of the method and the error norms with various lattice resolutions were investigated. Next, the problem of the calcium current in concrete was simulated. Pressure drops in the concrete were calculated for various Reynolds numbers, and the results were compared with those of an empirical equation based on experimental data. Also, velocity fields and concentration profiles were obtained at a pore scale for a structure with inhomogeneous mass diffusivities. These simulations showed that the present method might be useful for predicting calcium leaching in concrete from the microscopic point of view.

Differences in miscible viscous fingering of finite width slices with positive or negative log-mobility ratio

When a sample of fluid of finite size is displaced in a porous medium by another miscible fluid, viscous fingering may occur when the two fluids have different viscosities. Depending whether the sample is more or less viscous than the carrier fluid, the log-mobility ratio R [defined as R=ln(mu_{2}mu_{1}) where mu_{2} and mu_{1} are the viscosities of the sample and of the carrier] is respectively positive or negative. In the case of a linear displacement of a finite slice of fluid, R>0 leads to fingering of the rear interface of the sample where the less viscous carrier invades the more viscous sample. If R<0 , it is on the contrary the frontal interface of the sample that develops fingers where the less viscous sample displaces the more viscous bulk solution. We investigate here numerically the differences in fingering dynamics between the positive and negative log-mobility ratio cases leading to the growth of fingers against or along the direction of the flow, respectively. To do so, we integrate Darcy's law coupled to a convection-diffusion equation for the concentration of a solute ruling the viscosity of the finite-size sample. The statistical moments of the solute's concentration distribution are analyzed as a function of dimensionless parameters of the problem such as the length of the slice l , the log-mobility ratio R , and the ratio between transverse and axial dispersion coefficients . We find that, on average, the mixing zones and the width of the sample broadening due to fingering are larger for negative R than for positive R . This is due to the fact that fingers travel quicker in the flow direction than against the flow. Relevance of our results are discussed for interpretation of experimental results obtained in chromatographic separation and for understanding conditions of enhanced spreading of contaminants in aquifers.