Showing papers on "Viscous fingering published in 2007"

Experimental study on miscible viscous fingering involving viscosity changes induced by variations in chemical species concentrations due to chemical reactions

Abstract: When a reactive and miscible less-viscous liquid displaces a more-viscous liquid in a Hele-Shaw cell, reactive miscible viscous fingering takes place. We succeed in showing experimentally how a reactive miscible viscous fingering pattern in a radial Hele-Shaw cell changes when the viscosity of the more-viscous liquid is varied owing to variation in chemical species concentration induced by an instantaneous chemical reaction. This is done by making use of a polymer solution's dependence of viscosity on pH. When the viscosity is increased by the chemical reaction, the shielding effect is suppressed and the fingers are widened. As a result, the ratio of the area occupied by the fingering pattern in a circle whose radius is the length of the longest finger is larger in the reactive case than in the non-reactive case. When the viscosity is decreased by the chemical reaction, in contrast, the shielding effect is enhanced and the fingers are narrowed. These lead to the area ratio being smaller in the reactive case than in the non-reactive case. A physical model to explain this change in the fingering pattern caused by the chemical reaction is proposed.

Viscous fingering during replenishment of felsic magma chambers by continuous inputs of mafic magmas: field evidence and fluid-mechanics experiments

Abstract: Vegetation Island outcrops (Terra Nova Intrusive Complex, Antarctica) offer a unique example of the replenishment of a felsic magma chamber fossilized at the initial stages of intrusion of a mafic magma. The morphology of interfaces between the mafic and the felsic magma ranges from rounded to finger-like, and their quantification by means of fractal dimension indicates a wide variability of morphological complexity. Fluid-mechanics experiments of viscous fingering have been performed by injecting water + glycerin solutions with different viscosity ratios into pure glycerin using the Hele-Shaw cell. The fact that interface morphologies between the injected and the host fluid are identical to those observed on outcrops indicates that the latter shows the development of viscous fingering processes during the initial stages of intrusion of the mafic magma into the felsic magma chamber. The fractal dimension of the simulated structures was measured, and a very good exponential empirical relationship between the logarithm of viscosity ratio and fractal dimension has been derived. The empirical relationship is used to estimate viscosity ratios of natural structures by using measured values of fractal dimension. Results indicate that in the same magmatic system, a wide range of viscosity ratio existed between the two magmas. These results are used to reconstruct the mechanism of replenishment of the felsic magma chamber as characterized by continuous heating of the resident felsic magma by continuous inputs of the mafic magma.

Convection Patterns in Liquid Oxide Films on ZrB2–SiC Composites Oxidized at a High Temperature

Abstract: During the high-temperature oxidation of ZrB2–SiC composites, liquid boron oxide (B2O3) is formed at the zirconium diboride–zirconium oxide interface and transported through the overlying layer of silica liquid by convection, forming distinct convection cells arranged like the petals of a flower. The convection cells are localized by a viscous fingering phenomenon, as the fluid B2O3 rich liquid solution rises through the viscous silica layer. The upwelling B2O3 rich liquid contains dissolved zirconium dioxide, which deposits in the center of the flower-like structure as the B2O3 evaporates. The driving force for the B2O3 liquid flow is the volume increase upon oxidation of ZrB2. Convective transport of B2O3 liquids suggests a novel mechanism for the high-temperature oxidation of these materials.

Viscous and gravitational contributions to mixing during vertical brine transport in water-saturated porous media

Abstract: The transport of fluids miscible with water arises in groundwater contamination and during remediation of the subsurface environment. For concentrated salt solutions, i.e., brines, the increased density and viscosity determine mixing processes between these fluids and ambient groundwater. Under downward flow conditions, gravitational and viscous forces work against each other to determine the interfacial mixing processes. Historically, mixing has been modeled as a dispersive process, as viscous fingering, and as a combination of both using approaches that were both analytical and numerical. A compilation of previously reported experimental data on vertical miscible displacements by fluids with significant density and viscosity contrasts reveals some agreement with a stability analysis presented by Hill (1952). Additional experimental data on one-dimensional dispersion during downward displacement of concentrated salt solutions by freshwater and freshwater displacement by brines support the stability analysis and provides an empirical representation for dispersion coefficients as functions of a gravity number and a mobility ratio.

Miscible viscous fingering with linear adsorption on the porous matrix

Abstract: Viscous fingering between miscible fluids of different viscosities can affect the dispersion of finite samples in porous media. In some applications, as typically in chromatographic separations or pollutant dispersion in underground aquifers, adsorption onto the porous matrix of solutes (the concentration of which rules the viscosity of the solution) can affect the fingering dynamics. Here, we investigate theoretically the influence of such an adsorption on the stability and nonlinear properties of viscous samples displaced in a two-dimensional system by a less viscous and miscible carrying fluid. The model is based on Darcy’s law for the evolution of the fluid velocity coupled to a diffusion-convection equation for the concentration of a solute in the mobile phase inside the porous medium. The adsorption-desorption dynamics of the solute onto the stationary phase is assumed to be at equilibrium, to follow a linear isotherm and is characterized by a retention parameter κ′ equal to the adsorption-desorptio...

Viscous fingering in a horizontal flow through a porous medium induced by chemical reactions under isothermal and adiabatic conditions.

Abstract: In this work we analyze the viscous fingering instability induced by an autocatalytic chemical reaction in a liquid flowing horizontally through a porous medium. We have analyzed the behavior of the system for isothermal as well as adiabatic conditions. The kinetics of the reaction is chosen so that the rate depends on the concentration of only a single species. Since the reaction is autocatalytic the system admits a traveling wave solution. For endothermic reactions the concentration wave and temperature wave are mirror images, whereas for an exothermic reaction they are similar or parallel. The viscosity of the fluid is assumed to depend strongly on the concentration of the product and temperature of the medium. The dependence of viscosity on concentration (decrease with concentration) can destabilize the traveling wave resulting in the formation of viscous fingers. We have performed a linear stability analysis to determine the stability of the base traveling wave solution. The stability predictions have been confirmed by nonlinear simulations of the governing equations based on a finite difference scheme. We observe that including the temperature dependency of viscosity stabilizes the flow for an endothermic reaction, i.e., regions which exhibited viscous fingering now demonstrate stable displacement. For exothermic systems, however, the system exhibits less stable behavior under adiabatic conditions, i.e., it is destabilized by both concentration and temperature dependencies of viscosity.

Miscible displacements in Hele-Shaw cells: Nonmonotonic viscosity profiles

Abstract: The influence of nonmonotonic viscosity–concentration relationships on viscous fingering of neutrally buoyant, miscible fluids in a Hele–Shaw cell has been investigated. In a first step, quasisteady base states are obtained by means of nonlinear Stokes simulations. The properties of these base states are analyzed as a function of the Peclet number, the viscosity ratio, and the profile parameters. Subsequently, the stability of these base states is investigated by means of a linear stability analysis. Overall, the nonmonotonicity of the viscosity–concentration relationship is seen to have a much smaller influence on Hele–Shaw displacements than on corresponding Darcy flows. The reason for this difference lies in the nature of the respective base states. For Darcy flows, the base state is characterized by constant velocity and a diffusively decaying concentration (and hence viscosity) profile. This base viscosity profile is strongly affected by the nonmonotonicity. On the other hand, for Hele–Shaw displacements the quasisteady base states are convectively dominated and characterized by sharp fronts, so that their shape depends only weakly on the details of the viscosity–concentration relationship. Hence, for Hele–Shaw displacements both the eigenfunctions and the associated growth rates are quite similar for monotonic and nonmonotonic profiles, in contrast to the findings by [O. Manickam, G.M. Homsy, Stability of miscible displacements in porous media with nonmonotonic viscosity profiles, Phys. Fluids A 5 (1993) 1356–1367] for Darcy flows.

Granular fingers on jammed systems: new fluidlike patterns arising in grain-grain invasion experiments.

Abstract: In this Letter we report spontaneous pattern formation in dense granular assemblies confined to a Hele-Shaw cell and quasistatic regime. Varied unexpected patterns, ranging from rounded to fingered, are observed due to the displacement of one granular material by another. Computer simulations reproduce the major features observed in these experiments. Two mechanisms are responsible for the pattern formation: crystallization of the injected grains and plastic deformation of the displaced grains. The experiment suggests analogies with viscous fingering and jamming transition experiments.

Stokes instability in inhomogeneous membranes: application to lipoprotein suction of cholesterol-enriched domains.

Abstract: We examine the time-dependent distortion of a nearly circular viscous domain in an infinite viscous sheet when suction occurs. Suction, the driving force of the instability, can occur everywhere in the two phases separated by an interface. The model assumes a two-dimensional Stokes flow; the selection of the wavelength at short times is determined by a variational procedure. Contrary to the viscous fingering instability, undulations of the boundary may be observed for enough pumping, whatever the sign of the viscosity contrast between the two fluids involved. We apply our model to the suction by lipoproteins of cholesterol-enriched domains in giant unilamellar vesicles. Comparison of the number of undulations given by the model and by the experiments gives reasonable values of physical quantities such as the viscosities of the domains.

Experimental studies of labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell

Abstract: The first systematic experimental studies on the labyrinthine instabilities of miscible ferrofluids in a Hele-Shaw cell are presented. Two distinct features of instabilities are observed: (i) the miscible labyrinthine fingers caused by the magnetic dipolar forces; (ii) the secondary waves dominated by the third-dimensional effects. Prominence of the labyrinthine fingers is confirmed to be affected significantly by both the magnetic field strength and the cell gap width. On the other hand, wave selection of the secondary wave numbers is mainly dominated by the gap width. The characteristic wavelength λ of the secondary waves follows a nearly linear correlation with the gap width h, which is consistent with earlier findings on the viscous fingering instability. The wavelength can be approximated as λ≈(7±1)h.

Dynamics of viscous fingers in rotating Hele-Shaw cells with Coriolis effects.

Abstract: A growing number of experimental and theoretical works have been addressing various aspects of the viscous fingering formation in rotating Hele-Shaw cells. However, only a few of them consider the influence of Coriolis forces. The studies including Coriolis effects are mostly restricted to the high-viscosity-contrast limit and rely on either purely linear stability analyses or intensive numerical simulations. We approach the problem analytically and use a modified Darcy's law including the exact form of the Coriolis effects to execute a mode-coupling analysis of the system. By imposing no restrictions on the viscosity contrast $A$ (dimensionless viscosity difference) we go beyond linear stages and examine the onset of nonlinearities. Our results indicate that when Coriolis effects are taken into account, an interesting interplay between the Reynolds number Re and $A$ arises. This leads to important changes in the stability and morphological features of the emerging interfacial patterns. We contrast our mode-coupling approach with previous theoretical models proposed in the literature.

2D Parametric Study of Viscous Fingering

Abstract: When a low viscosity fluid is forced to displace another immiscible fluid with a higher viscosity inside of a porous media a particular flow structure called viscous fingering is generated. The study of that particular flow structure has special relevance in understanding the diffusion process and the transport characteristics of a fluid inside of a porous media. This work examined the effect of two fundamental parameters like the injected volumetric flow rate and the domain aspect ratio over the viscous fingering pattern. In order to perform that parametric study, a set of numerical simulations using the 2D network simulator model are used. A large viscosity ratio between the injected and displaced fluid is used to focus the work only on the unstable behavior state.Copyright © 2007 by ASME

How viscous fingering can spoil your separation and you may not even suspect it

Abstract: LEVEL: INTERMEDIATE T echniques of both analytical and preparative liquid chromatography have advanced substantially in recent years. Nowadays, samples are often analyzed or purified in systems that incorporate one or more f low-stream changes from one mobile phase to another. It happens, for example, in column switching, in multidimensional separations, and in simulated moving bed (SMB) chromatography, where a feedstock stream enters continuously into a mobile-phase stream. When f low-stream switching is necessary, care must be paid to the compatibility of the different f low solutions. Obviously, the streams must be miscible, but it is less obvious that their viscosities should be similar. An important consideration is the solvent in which a sample is dissolved before injection. Usually that solvent is the same as the mobile phase, but sometimes a solute must be dissolved in a stronger solvent with a different viscosity. In some instances a mismatch between mobile phase and solute plug, or mobile phases in twodimensional (2D) separations, or feedstock and mobile phase in SMB, leads to viscosity differences large enough to cause a phenomenon known as viscous fingering (1–3). Occurrence of viscous fingering (VF) can have a catastrophic effect on separation performance, leading to separation failure (4). In short, viscous fingering is a f low instability phenomenon that occurs at the interface of two f luids of differing viscosities. When a high-viscosity f luid is displaced by a lower viscosity f luid, their interface is unstable. After a time (depending on the viscosity contrast), the lower viscosity f luid penetrates the other in a pattern resembling a set of fingers. Those “fingers” multiply and develop further into a complex network (1–10). VF can be detrimental to chromatographic separations when a low-viscosity mobile phase fingers into a highviscosity solute plug (2), or conversely, when a low-viscosity sample plug fingers into a higher viscosity mobile phase (1). Similar adverse effects take place when a mobile-phase stream is replaced with one of different viscosity in the complex schemes now developed for 2D chromatography (3). Analysis of polymers and isolation of proteins using size-exclusion chromatography (SEC) present ideal environments for development of VF. Solutions of high molecular weight polymers and proteins are more viscous than their mobile phases and do not dilute appreciably during rapid elution (4). When proteins are isolated at the preparative level, sample solutions have a high viscosity for exactly the same reasons as polymer solutions. In a worst-case scenario, a set of multiple peaks instead of a In an extreme case of VF, the band width expands to the column length

Effect of Medium Dispersivity on the Viscous Fingering Instability in Porous Media

Abstract: Flow processes that involve the displacement of a viscous fluid by a less viscous one often lead to a hydrodynamic instability known as viscous fingering. In this study the viscous fingering instability for anisotropic dispersive flows will be addressed. In order to understand the physics of the flow displacement, the basic equations of conservation of mass and momentum are solved for a two-dimensional porous medium. The linear stability of the flow is analyzed first. The flow is then modeled numerically using a highly accurate spectral method based on the Hartley transformation. The streamfunction and concentration fields are tracked using an iteration process for two dimensional flows in every time-step. In this study, different types of anisotropic dispersions are considered and their effects on finger patterns are examined. We will present physical discussion of how medium dispersivity affects hydrodynamics and could result in interesting instability schemes.

Nonlinear Simulation of Thermo-viscous Fingering in Miscible Displacements in Porous Media

Abstract: The nonlinear simulation of interfacial instabilities in miscible displacements in porous media often requires sophisticated numerical algorithms as well as very fine spatial and temporal resolutions. In this study, Hartley transform based pseudo-spectral method is used to simulate time evolution of thermoviscous fingers in rectilinear geometry. The problem is formulated using continuity equation, Darcy's law, and volume-averaged forms of convection-diffusion equation for mass and energy balance. The numerical code is validated against established results for isothermal displacements. The effects of exponential dependence of viscosity on concentration and temperature, Lewis number, and porosity on the stability of the thermo-viscous flow are examined. It has been generally observed that at practical values of porosity and Lewis number, the thermal front always lags behind the fluid front and the instability is dominated by the viscosity variation due to concentration.