Miscible Fluids Research Articles

Investigation of longitudinal and transverse dispersion in stable displacements with a high viscosity and density contrast between the fluids

Transverse and longitudinal dispersion in gravity stable, favourable viscosity ratio flows are investigated and compared with earlier data obtained for miscible fluids and for tracer flow. Data from laboratory measurements of longitudinal dispersion in low viscosity ratio (8.63 × 10 − 4) and high density contrast (471 kg m − 3) displacements are compared with literature data for more modest viscosity ratios and density differences and with earlier theoretical analysis. The longitudinal dispersivity was reduced by a factor of 2 for flows influenced by gravity. This reduction was relatively insensitive to the magnitude of the density contrast and the flow rate, for Peclet numbers less than 100 and found to be consistent with earlier theoretical predictions. Additional transverse dispersion data was obtained for fluids with a density contrast of 225 kg m − 3 and a matched viscosity ratio over a range of Peclet numbers (1 < Pe < 1000). A similar reduction in transverse dispersivity in gravity stable flow, independent of Peclet number, was observed and found to be consistent with observations in the literature for more modest density contrasts.

A Hybrid Approach to Multiple Fluid Simulation using Volume Fractions

AbstractThis paper presents a hybrid approach to multiple fluid simulation that can handle miscible and immiscible fluids, simultaneously. We combine distance functions and volume fractions to capture not only the discontinuous interface between immiscible fluids but also the smooth transition between miscible fluids. Our approach consists of four steps: velocity field computation, volume fraction advection, miscible fluid diffusion, and visualization. By providing a combining scheme between volume fractions and level set functions, we are able to take advantages of both representation schemes of fluids. From the system point of view, our work is the first approach to Eulerian grid‐based multiple fluid simulation including both miscible and immiscible fluids. From the technical point of view, our approach addresses the issues arising from variable density and viscosity together with material diffusion. We show that the effectiveness of our approach to handle multiple miscible and immiscible fluids through experiments.

Volume fraction based miscible and immiscible fluid animation

AbstractWe propose a volume fraction based approach to effectively simulate the miscible and immiscible flows simultaneously. In this method, a volume fraction is introduced for each fluid component and the mutual interactions between different fluids are simulated by tracking the evolution of the volume fractions. Different techniques are employed to handle the miscible and immiscible interactions and special treatments are introduced to handle flows involving multiple fluids and different kinds of interactions at the same time. With this method, second‐order accuracy is preserved in both space and time. The experiment results show that the proposed method can well handle both immiscible and miscible interactions between fluids and much richer mixing detail can be generated. Also, the method shows good controllability. Different mixing effects can be obtained by adjusting the dynamic viscosities and diffusion coefficients. Copyright © 2010 John Wiley &amp; Sons, Ltd.

Asymptotics for the Muskat problem

The Muskat problem is a simple model for the displacement of one fluid by another in a porous medium or Hele-Shaw cell. Solutions of the problem are unstable to small-wavelength disturbances, and there is evidence that the problem is ill-posed. A well-posed problem may be developed by including additional regularising physical effects, primarily surface tension. In practical situations involving oil recovery, one can engineer for there to be a gradual change in the viscosity of the fluids, either by the gradual introduction of a polymer capable of altering the viscosity of water, or by gradual diffusion between two miscible fluids. The regularising effect of smoothing the initial data is investigated. Thus rather than a sharp interface between the two fluids, and therefore a sharp jump in viscosity, there is a smooth transition from one viscosity to another. It is shown how the standard Muskat problem may be recovered as an asymptotic limit and the effective free-surface model that may be recovered is discussed. The stability of solutions to the smoothed Muskat problem is investigated, and the important effect of smoothing for disturbances with a large wavenumber is demonstrated.

Uncertainty quantification in modeling flow and transport in porous media

This special issue of Stochastic Environmental Research and Risk Assessment in honor of Shlomo P. Neuman presents recent developments in uncertainty quantification in predictions of flow and transport in heterogeneous porous media. It covers subjects as diverse as stochastic hydrogeology, aquifer characterization, effective (average) descriptions of subsurface processes, inverse modeling, and scaling theory, all of which benefited from the insightful contributions of Shlomo P. Neuman. We hope that this volume will become a reference point for students learning these subject, scientists pursuing innovative research, and professionals and water resources planners looking to quantify predicting uncertainty arising from the intrinsic complexity of the subsurface environment. S. P. Neuman is one of the pioneers in the use of stochastic modeling as a means of dealing with uncertainty in hydraulic and transport parameters of heterogeneous subsurface environments. This special issue contains a number of contributions in this field. Riva et al. introduce a stochastic approach to interpret field-scale tracer tests conducted in heterogeneous aquifers. By using Monte Carlo simulations, the authors demonstrate that directly linking porosity and permeability distribution to the spatial variability of soil particle sizes renders the best prediction of the observed heavy tailing of measured breakthrough curves. Zhang et al. compare the performance of Monte Carlo and stochastic collocation methods to evaluate the probability of the concentration of a conservative solute attaining a given threshold. Their analysis shows that Latin Hypercube sampling and Quasi Monte Carlo outperform standard Monte Carlo simulations, and that a sparse-grid collocation and a probabilistic collocation method provide an accurate and efficient alternative to Monte Carlo simulations. Broyda et al. develop partial differential equations satisfied by the probability density function (PDF) of the concentration of solutes undergoing heterogeneous reactions in porous media with uncertain chemical properties. The authors obtain a semi-analytical solution for the concentration PDF and demonstrate that its shape and evolution are significantly affected by both spatial variability of advective velocity and the Damkohler number. Tartakovsky presents a novel Lagrangian particle model based on smoothed particle hydrodynamics (SPH). His analysis reveals the advantages of Lagrangian methods for the stochastic analysis of miscible density-driven fluid flows in the presence of RayleighTaylor instability. When used in the context of Monte Carlo simulations, the method can provide reliable estimated of the probability of occurrence of rare events. Two papers are concerned with the estimation of hydrogeological parameters governing groundwater flow. Liu et al. present an approach to efficient and accurate parameter estimation for nonlinear flow and transport problems in porous media. They discuss the relative merits and weaknesses of different schemes, including Maximum a posteriori (MAP) and Monte Carlo based methods, used to parameterize a DNAPL dissolution/transport model. Methods to diagnose Markov Chain Monte Carlo (MCMC) samples are introduced, compared and discussed in the context of computationally demanding parameter estimation A. Guadagnini (&) Dipartimento di Ingeneria Idraulca, Ambientale, Infrastrutture Viarie e Rilevamento, Politecnico di Milano, Piazza L. Da Vinci, 32, 20133 Milan, Italy e-mail: alberto.guadagnini@polimi.it

Bistability in a simple fluid network due to viscosity contrast

We study the existence of multiple equilibrium states in a simple fluid network using Newtonian fluids and laminar flow. We demonstrate theoretically the presence of hysteresis and bistability, and we confirm these predictions in an experiment using two miscible fluids of different viscosity-sucrose solution and water. Possible applications include blood flow, microfluidics, and other network flows governed by similar principles.

A two-dimensional unstructured cell-centered multi-material ALE scheme using VOF interface reconstruction

We present a new cell-centered multi-material arbitrary Lagrangian–Eulerian (ALE) scheme to solve the compressible gas dynamics equations on two-dimensional unstructured grid. Our ALE method is of the explicit time-marching Lagrange plus remap type. Namely, it involves the following three phases: a Lagrangian phase wherein the flow is advanced using a cell-centered scheme; a rezone phase in which the nodes of the computational grid are moved to more optimal positions; a cell-centered remap phase which consists of interpolating conservatively the Lagrangian solution onto the rezoned grid. The multi-material modeling utilizes either concentration equations for miscible fluids or the Volume Of Fluid (VOF) capability with interface reconstruction for immiscible fluids. The main original feature of this ALE scheme lies in the introduction of a new mesh relaxation procedure which keeps the rezoned grid as close as possible to the Lagrangian one. In this formalism, the rezoned grid is defined as a convex combination between the Lagrangian grid and the grid resulting from condition number smoothing. This convex combination is constructed through the use of a scalar parameter which is a scalar function of the invariants of the Cauchy–Green tensor over the Lagrangian phase. Regarding the cell-centered remap phase, we employ two classical methods based on a partition of the rezoned cell in terms of its overlap with the Lagrangian cells. The first one is a simplified swept face-based method whereas the second one is a cell-intersection-based method. Our multi-material ALE methodology is assessed through several demanding two-dimensional tests. The corresponding numerical results provide a clear evidence of the robustness and the accuracy of this new scheme.

Nanowire-in-Microtube Structured Core/Shell Fibers via Multifluidic Coaxial Electrospinning

A multifluidic coaxial electrospinning approach is reported here to fabricate core/shell ultrathin fibers with a novel nanowire-in-microtube structure from more optional fluid pairs than routine coaxial electrospinning. The advantage of this approach lies in the fact that it introduces an extra middle fluid between the core and shell fluids of traditional coaxial electrospinning, which can work as an effective spacer to decrease the interaction of the other two fluids. Under the protection of a proper middle fluid, more fluid pairs, even mutually miscible fluids, can be operated to generate "sandwich"-structured ultrathin fibers with a sharp boundary between the core and shell materials. It thereby largely extends the scope of optional materials. Selectively removing the middle layer of the as-prepared fibers results in an interesting nanowire-in-microtube structure. Either homogeneous or heterogeneous fibers with well-tailored sandwich structures have been successfully fabricated. This method is an important extension of traditional co-electrospinning that affords a more universal avenue to preparing core/shell fibers; moreover, the special hollow cavity structure may introduce some extra properties into the conventional core/shell structure, which may find potential applications such as optical applications, microelectronics, and others.

Evaluation of viscous fingers width in Hele-Shaw flows

Abstract High viscosity fluid displacement from a Hele-Shaw cell by less viscous one is considered. The cell is a pair of parallel plates separated by a small gap. While viscous fluid is displaced from a cell, the displacement front is unstable (Saffman and Taylor, 1958). The less viscous fluid penetrates through the higher viscous one forming channels called viscous fingers. It is known that the surface tension determines the finger width for the condition of immiscible fluid displacement and diffusion controls the process in the case of miscible fluids. The modified capillary number and fluid viscosity ratio are the criteria of the flows self-similarity in the first case and the Peclet number and the viscosity ratio serve as the criteria for the later one. It is shown in the paper that there is one more factor influencing the finger width. The viscous forces, acting in the flow plane, control the width of the viscous fingers if there is no surface tension at the phase interface and the fluid diffusion has no time for manifestation. It occurs under a rapid displacement of miscible fluids when Pe→∞. The criterion of self-similarity for the flows of such a kind is suggested in the paper.

Influence of an imposed flow on the stability of a gravity current in a near horizontal duct

We study experimentally the effect of a mean flow imposed on a buoyant exchange flow of two miscible fluids of equal viscosity in a long tube oriented close to horizontal. We measure the evolution of the front velocity Vf as a function of the imposed velocity V0. At low V0, an exchange-flow dominated regime is found, as expected, and is characterized here by Kelvin–Helmholtz-like instabilities. With increasing V0 we observed that the flow becomes stable. Here also Vf increases linearly with V0 with slope of &amp;gt;1. At large V0 we find Vf∼V0.

Controlled Self-Assembly of Monodisperse Niosomes by Microfluidic Hydrodynamic Focusing

Niosomes are synthetic membrane vesicles formed by self-assembly of nonionic surfactant, often in a mixture with cholesterol and dicetyl phosphate. Because of their inner aqueous core and bilayer membrane shell, niosomes are commonly used as carriers of treatment agents for pharmaceutical and cosmetic applications or contrast agents for clinical imaging applications. In those applications, niosomes are considered as a more economical and stable alternative to their biological counterpart (i.e., liposomes). However, conventional bulk method of niosome preparation requires bulk mixing of two liquid phases, which is time-consuming and not well-controlled. Such mixing conditions often lead to large niosomes with high polydispersity in size and thus affect the consistency of niosome dosage or imaging quality. In this study, we present a new method of niosome self-assembly by microfluidic hydrodynamic focusing to improve on the size and size distributions of niosomes. By taking advantage of the rapid and controlled mixing of two miscible fluids (i.e., alcohol and water) in microchannels, we were able to obtain in seconds nanoscaled niosomes with approximately 40% narrower size distributions compared to the bulk method. We further investigated different parameters that might affect on-chip assembly of niosomes, such as (1) conditions for the microfluidic mixing, (2) chemical structures of the surfactant used (i.e., sorbitan esters Span 20, Span 60, and Span 80), and (3) device materials for the microchannel fabrication. This work suggests that microfluidics may facilitate the development and optimization of biomimetic colloidal systems for nanomedicine applications.

On the Streamwise Development of Density Jumps

The analysis of density jumps in two-layer channel flows of miscible fluids controlled by a downstream obstruction, in which one of the layers is infinitely deep and at rest, is extended to consider the dependence of its features on its streamwise dimension. The momentum conservation equation in the entrainment and roller regions, and the energy conservation equation after the jump are corrected to account for friction. The streamwise coordinate is related to the increase in the density layer height through a linear expression derived from CFD calculations. Three regimes are distinguished: (1) for short distances from the origin to the obstruction, only an entrainment region exists; (2) for medium distances, two regions can be distinguished, i.e., the entrainment region, and the roller region, in which no entrainment is assumed; and (3) for long distances, three regions can be distinguished—the entrainment, the roller, and the postjump regions, characterized by approximate energy conservation. It is shown that initially the dimensionless total entrainment ratio increases as the distance to the obstruction increases, until a roller region appears. A further increase in distance to the obstruction does not have a significant effect on the total entrainment, until the appearance of a postjump region, resulting in a gradual decrease in the total entrainment. These results are supported by numerical calculations using the FLUENT CFD software package, which are in good agreement with experimental results.

On the critical non-additivity driving segregation of asymmetric binary hard sphere fluids

A previously proposed version of thermodynamic perturbation theory, appropriate for singular pair interactions between particles, is applied to binary mixtures of hard spheres with non-additive diameters. The critical non-additivity ΔC required to drive fluid–fluid phase separation is determined as a function of the ratio ξ ≤ 1 of the diameters of the two species. ΔC(ξ) is found to decrease with ξ and to go through a minimum for ξ ≃ 0.015 before increasing sharply as ξ → 0, irrespective of the total packing-fraction η of the mixture. These results are the basis of an estimate of the range of size ratios for which a binary mixture of additive hard spheres exhibit a fluid–fluid miscibility gap. This range is conjectured to be 0.01 ≲ ξ ≲ 0.1.

Numerical study of Rayleigh-Taylor instability between miscible fluids with spectral element method

Rayleigh-Taylor instabilities between miscible fluids are studied with a specially-developed unsteady three-dimensional high order spectral element method code. The numerical model used in this code consists of Navier-Stokes equations and a transport-diffusive equation, and the code is validated with results of linear stability perturbation theory. Several characteristics of the Rayleigh-Taylor instabilities are studied including: instantaneous turbulent structures, and statistical turbulent mixing heights under different initial wave numbers. These results indicate that turbulent structures of Rayleigh-Taylor instabilities are strongly dependent on the initial conditions. The results also suggest that the spectral element method should provide the capability of simulating small scale fluctuations in Rayleigh-Taylor instabilities turbulent flows.

Effects of Subphase on Collapse Behavior of Lung Surfactant

The phase behavior of binary fluids next to interfaces can be complex. If one fluid has a more favored interaction with the interface the fluids can phase separate in some interfacial region extending into the bulk. Using neutron and x-ray reflectivity, we show phase separation of water/glycerol mixtures next to lipid monolayer interfaces. The glycerol forms a thin layer ten angstroms deep underneath the monolayer. This non-equillibrium interfacial phase separation greatly impacts the mechanical properties of the lipid monolayer. Moreover, the thermodynamic driving force for this de-mixing is complex. Usually such de-mixing is observed when two miscible fluids have significantly different surface tensions at a given interface. However glycerol and water are miscible and have nearly identical surface tensions at the air/water interface. Our work probes what surface tension and interfacial free energy mean in the setting of more complex interfaces. The preference partitioning of glycerol to the interface affects the collapse behavior of the lipid film and has implications on the collapse mechanism of lung surfactant which sits atop an alveolar lining fluid enriched in sugar biopolymers.

Transverse diffusive mixing of solutes in pressure driven microchannels: a Lattice Boltzmann study of the scaling laws

We study scaling laws characterizing the inter-diffusive zone of two miscible fluids flowing side by side in a Y-shape laminar micromixer using the lattice Boltzmann method. The lattice Boltzmann m...

Investigation of Potential Distribution and the Influence of Ion Complexation on Diffusion Potentials at Aqueous−Aqueous Boundaries within a Dual-Stream Microfluidic Structure

The occurrence of reactions at boundaries between adjacent miscible but unmixed aqueous streams coflowing in a microfluidic channel structure has been studied by simulation of the diffusion potentials that develop between the two coflowing aqueous electrolyte streams and by measurement of the effects of aqueous ion complexation on diffusion potentials. The microfluidic structure consisted of a Y-shaped microchannel with off-chip electrodes immersed in electrolyte reservoirs connected by capillaries to the Y-microchannel. The time-dependent, one-dimensional Nernst-Planck equation employing the electroneutrality condition was solved numerically to calculate the diffusion potentials established at the boundary between the two coflowing aqueous streams. Under the experimental conditions (channel length and width, flow rate) employed, it was shown that the use of the Henderson equation was appropriate. It was also shown that the cross-channel diffusion potential remained constant from the entrance of the channel to the exit. The influence of cation complexation by a neutral ionophore was investigated by experimentally measured diffusion potentials. It was found that potassium complexation by the cyclic polyether 18-crown-6 altered the experimental diffusion potential, whereas the interaction of sodium or lithium cations with the ionophore did not perturb the diffusion potential. The results are consistent with the literature data for aqueous-phase complexation of these cations by this ionophore. The results of these investigations demonstrate that relatively simple diffusion potential measurements between coflowing streams in microchannels may be used as a basis for study of ion complexation reactions occurring at boundaries between miscible fluids.

Flow boiling of binary solution in horizontal tube

Abstract An experimental study of flow boiling of binary organic solution was conducted in a horizontal tube. An organic mixture of miscible fluids, chlorodifluoromethane (R22)–dimethylacetamide (DMAC) was circulated through the experimental system. The influence of the heat source, flow rate, solution concentration and operating pressure on the flow characteristics and the heat transfer coefficient was examined experimentally. Based on the experimental observation an appropriate flow pattern map was constructed. The experimental values of the heat transfer coefficient (HTC) were compared with predicted HTC obtained by several known correlations. Based on these comparisons the well know Dittus & Boelter correlation deviated up to 30%. A better agreement (up to 15%) was obtained by modified the Kattan et al. [10] , [11] , [12] correlation. The modification includes using the Forster and Zuber correlation [21] for nucleate boiling HTC and multiplying the predicted HTC by a constant of 1.4.

Effect of Korteweg stress on viscous fingering of solute plugs in a porous medium

In this work we first present a unified framework for the analysis of miscible and immiscible viscous fingering. To establish this we introduce the Korteweg stresses for miscible fluids which arise due to concentration gradients and are analogous to surface tension between two immiscible fluids. For the immiscible fingering we use the continuum representation of surface tension which treats surface tension as a body force. This analogy between the two types of fingering helps us obtain a better insight into the role of Korteweg stresses in miscible fluids and enables in resolving ambiguities in the role of these stresses in a dynamic system. Finally we examine the effect of Korteweg stresses to see how they can be a stabilizing influence for miscible viscous fingering of finite slices in a chromatography column and discuss if this can give an extra control option to improve the performance of the separation.

Influence of miscible viscous fingering with negative log-mobility ratio on spreading of adsorbed analytes

Viscous fingering (VF) between miscible fluids of different viscosities can affect the dispersion of localized samples in porous media. This is the case when a given fluid displaces a finite width sample consisting in a solvent of different viscosity and containing a dissolved analyte undergoing adsorption on the porous matrix. We investigate here numerically the influence of VF between the carrier fluid and the sample solvent on the spreading of a retained analyte concentration peak in a three-component system (displacing fluid, sample solvent, analyte). We compare the cases where the sample solvent is, respectively, more or less viscous than the displacing fluid or eluent by varying the log-mobility ratio R = ln ( μ 2 / μ 1 ) where μ 1 and μ 2 are the viscosities of the eluent and sample solvent, respectively. We show that disentanglement of the analyte concentration peak from the fingering zone occurs earlier for less viscous samples, i.e. for R < 0 than for R > 0 . Qualitative agreement with experimental evidences obtained in reversed phase liquid chromatography are shown.