Fingering Instability Research Articles

Stability analysis of miscible displacement by non-Newtonian nanofluid with different diffusion coefficients

This paper investigates the effect of nanoparticles on the thermo-viscous fingering instability of non-Newtonian fluids during miscible displacements in homogeneous porous media. Nanoparticles are added to the fluid with variable and constant diffusion coefficients, and both the displacing fluid and the displaced fluid are considered as non-Newtonian fluids. The results indicate that the nanoparticles demonstrate efficacy in mitigating the thermo-viscous fingering instability when variable diffusion coefficients are employed, in contrast to scenarios where constant diffusion coefficients are utilized. In contrast to the situation with a constant diffusion coefficient, the shear thinning characteristics and the yield stress properties of the displaced fluid contribute to an increase in instability. Furthermore, the thermal parameters positively influence the rate of Brownian motion exhibited by the nanoparticles.

Dewetting Fingering Instability in Capillary Suspensions: Role of Particles and Liquid Bridges.

This study investigates the fingering instability that forms during the stretching of capillary suspensions with and without added nanoparticles. The dewetting process is observed using a transparent lifted Hele-Shaw cell. The liquid bridge is stretched under constant acceleration, and the resulting instability patterns are recorded using two high-speed cameras. Finger-like structures, characteristic of the Saffman-Taylor instability, are observed. The total length of the dendrites and the intersecting number of branches are quantified. We reveal the roles of microparticles, nanoparticles, and the secondary liquid during the fingering instability. The addition of microparticles to pure liquid enhanced finger length due to increased particle interactions and nucleation sites for bubbles. The addition of secondary fluid reduces fingering length by forming a strong interparticle network. Incorporation of nanoparticles induces an early onset of cavitation and enhances fingering instability. However, nanoparticles make the capillary suspensions' overall microstructure more homogeneous, reduce the sample variation in fingering patterns, and promote the even distribution of gel on both slides during splitting. These findings highlight the complex interactions governing dewetting in capillary (nano)suspensions. This knowledge has potential applications in microfluidics, 3D printing, and thin-film coatings, where controlling dewetting is crucial.

Flow-driven pattern formation during coacervation of xanthan gum with a cationic surfactant.

We experimentally demonstrate that the coacervation of a biopolymer can trigger a hydrodynamic instability when a coacervate is formed upon injection of a xanthan gum dispersion into a cationic surfactant (C14TAB) solution. The local increase of the viscosity due to the coacervate formation induces a viscous fingering instability. Three characteristic displacement regimes were observed: a viscous fingering dominated regime, a buoyancy-controlled "volcano" regime and a "fan"-like regime determined by the coacervate membrane dynamics. The dependence of the spatial properties of the viscous fingering pattern on the Péclet and Rayleigh numbers is investigated.

Experimental study of fluid displacement and viscous fingering in fractured porous media: effect of viscosity ratio

Viscous fingering instability has been analyzed through empirical studies using miscible flow displacement in fractured porous media. While significant research has been conducted on viscous fingering, limited information is available regarding its behavior in fractured porous structures. The experiments were conducted in rectangular porous models with fractures oriented at 0∘, 45∘, and 90∘, to investigate how fracture orientation influences fluid displacement, where both channeling and fingering mechanisms play significant roles. This paper, which is the second part of a previous study, places particular emphasis on the impact of the viscosity ratio, a crucial parameter in determining the complexity of the fingering patterns. Quantitative parameters such as sweep efficiency, tip location, and breakthrough time were evaluated and analyzed using image processing techniques. The results indicate that increasing the viscosity ratio leads to more complex finger formations. Additionally, as the injection rate increases, the size of the finger patterns slightly increases, while the channeling effect becomes less pronounced. Notably, fractures aligned at 0∘ had the most significant impact on the rate of sweep efficiency and tip location, increasing the tip velocity of the fingers by up to 90%.

Non-modal linear stability analysis of reactive front A+B→C for infinitely fast chemical reactions

A theoretical analysis of viscous fingering instability for a reactive system A + B → C with an infinitely fast reaction in a porous medium for a rectilinear flow is presented. By contrast to the traditional quasi-steady-state analysis (QSSA), a non-modal analysis (NMA) based on the fundamental matrix formulation is employed to study the reactive displacement, considering reactants and products with mismatched viscosities. This study investigates the transient growth of perturbations by analysing the singular values and singular vectors to address the optimal energy amplification. We illustrate that an increase in the viscosity contrast, | R b − R c | , resulting from a chemical reaction for a given endpoint viscosity contrast R b , leads to a more unstable system. However, there exist some reactions when R c > R b , the onset delays than the equivalent non-reactive case, R c = R b . It suggests that the stability of the flow is primarily influenced when instability develops downstream within the flow. Furthermore, R b is found to significantly affect the spatio-temporal evolution of perturbations and the underlying physical mechanism. It is demonstrated that the QSSA is inadequate to address the transient growth, and NMA is the most suitable approach to studying the underlying physical mechanism of instability. Furthermore, NMA results align more consistently with non-linear simulations compared with QSSA.

Opposite effects of a reaction-driven viscosity decrease on miscible viscous fingering depending on the injection flow rate

When a less-viscous solution of a reactant $A$ displaces a more-viscous solution of another reactant $B$ , a fast bimolecular $A + B \rightarrow C$ reaction decreasing locally the viscosity can influence the viscous fingering (VF) instability taking place between the two miscible solutions. We show both experimentally and numerically that, for monotonic viscosity profiles, this decrease in viscosity has opposite effects on the fingering pattern depending on the injection flow rate. For high flow rates, the reaction enhances the shielding effect, creating VF patterns with a lower surface density, i.e. thinner fingers covering a smaller area. In contrast, for lower flow rates, the reaction stabilises the VF dynamics, i.e. delays the instability and gives a less-deformed displacement, reaching in some cases an almost-stable displacement. Nonlinear simulations of reactive VF show that these opposite effects at low or high flow rates can only be reproduced if the diffusivity of $A$ is larger than that of $B$ , which favours a larger production of the product $C$ and, hence, a larger viscosity decrease. The analysis of one-dimensional viscosity profiles reconstructed on the basis of a one-dimensional reaction–diffusion–advection model confirms that the VF stabilisation at low Péclet number and in the presence of differential diffusion of reactants originates from an optimum reaction-driven decrease in the gradient of the monotonic viscosity profile.

Modelling and semi-analytical solutions for fingering instability during zero-dimensional nano floodings

Fingering instability, a pivotal phenomenon in multiphase flow within porous media, is thoroughly examined. It stems from the interplay of capillary and viscous forces, yielding distinctive finger-like patterns, and holds critical implications for oil recovery and environmental remediation. A comprehensive mathematical model, fortified by the Method of Directly Defining the inverse Mapping, is established. This study scrutinizes the efficacy of zero-dimensional nanoparticles: aluminium oxide, magnesium oxide, and silicon dioxide. Nano-powders were infused at 0.4% concentration in a brine solution, a pioneering approach to enhanced oil recovery. The model was established to identify the saturation of injected fluid where a layer of crude oil is positioned at an angle relative to the horizontal plane. This means that instead of being perfectly flat, the layer tilts or slopes in a particular direction. Such inclined formations are common in natural reservoirs, and understanding their geometry and properties is crucial for effective oil extraction and recovery processes. Gravity now plays a more pronounced role in determining the direction of oil movement. Analysis of the resulting graph, generated through Maple 16, indicates that the injection of aluminium oxide leads to the highest saturation levels in comparison to the other fluids. Conversely, the use of magnesium oxide results in the lowest saturation. This finding underscores the potential significance of aluminium oxide in optimizing oil extraction techniques and contributes valuable insights into optimizing oil recovery processes and managing subsurface fluid dynamics, fostering advancements in enhanced oil recovery methodologies.

Direct numerical simulation of droplet impact onto dry stationary and moving walls at low to high Weber numbers

Direct numerical simulation of droplet impact onto dry stationary and moving walls at low to high Weber numbers

Supramolecular Assemblies in Active Motor-Filament Systems: Micelles, Bilayers, and Foams

Active matter systems evade the constraints of thermal equilibrium, leading to the emergence of intriguing collective behavior. A paradigmatic example is given by motor-filament mixtures, where the motion of motor proteins drives alignment and sliding interactions between filaments and their self-organization into macroscopic structures. After defining a microscopic model for these systems, we derive continuum equations, exhibiting the formation of active supramolecular assemblies such as micelles, bilayers, and foams. The transition between these structures is driven by a branching instability, which destabilizes the orientational order within the micelles, leading to the growth of bilayers at high microtubule densities. Additionally, we identify a fingering instability, modulating the shape of the micelle interface at high motor densities. We study the role of various mechanisms in these two instabilities, such as contractility, active splay, and anchoring, allowing for generalization beyond the system considered here. Published by the American Physical Society 2024

Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface

Nonlinear flow phenomenon of a power-law non-Newtonian fluid falling down a cylinder surface

Emergence of lobed wakes during the sedimentation of spheres in viscoelastic fluids

The motion of rigid particles in complex fluids is ubiquitous in natural and industrial processes. The most popular toy model for understanding the physics of such systems is the settling of a solid sphere in a viscoelastic fluid. There is general agreement that an elastic wake develops downstream of the sphere, causing the breakage of fore-and-aft symmetry, while the flow remains axisymmetric, independent of fluid viscoelasticity and flow conditions. Using a continuum mechanics model, we reveal that axisymmetry holds only for weak viscoelastic flows. Beyond a critical value of the settling velocity, steady, non-axisymmetric disturbances develop peripherally of the rear pole of the sphere, giving rise to a four-lobed fingering instability. The transition from axisymmetric to non-axisymmetric flow fields is characterized by a regular bifurcation and depends solely on the interplay between shear and extensional properties of the viscoelastic fluid under different flow regimes. At higher settling velocities, each lobe tip is split into two new lobes, resembling fractal fingering in interfacial flows. For the first time, we capture an elastic fingering instability under steady-state conditions, and provide the missing information for understanding and predicting such instabilities in the response of viscoelastic fluids and soft media.

Synergies of storing hydrogen at the crest of CO2${\rm CO}_{2}$ or other gas storage

AbstractThere are mutual benefits in storing in sedimentary reservoirs jointly with another gas serving as a cushion gas, such as the of a carbon capture and storage (CCS) operation or the natural gas of seasonal storage or left in a depleted hydrocarbon reservoir. When occupies the crest of the reservoir, the presence of either gas is beneficial to the other. reinforces the sealing efficiency of the caprock due to its very favorable interfacial properties with respect to brine and rock‐forming minerals. storage safety and capacity are also increased with cushion gases such as , which alleviate the buoyancy pressure at the top of the gas column. The potential drawback of this storage scheme is gas/gas mixing, which can, however, be strongly reduced if, by an appropriate choice of well completion and placement, is positioned in the upper zones of the reservoir, and its injection rate is kept below a critical value corresponding to the incipient fingering instability of the gas mixing zone. This value, which depends on reservoir permeability, the dip angle of the mixing front, and how density varies with viscosity in the mixing front, turns out to be well above practical injection rates. Therefore, dispersive mixing is the only cause of front spreading, which is acceptable for not‐too‐heterogeneous reservoirs. The mutual benefits identified in this study are the strongest when the cushion is made up of dense , which suggests that the crest of offshore storage reservoirs is a good candidate for storage. © 2024 The Authors. Greenhouse Gases: Science and Technology published by Society of Chemical Industry and John Wiley & Sons Ltd.

Study on two-phase displacement law considering mass transfer and diffusion

The influence of channeling on viscous fingering instability of CO2 miscible displacement is studied in the paper. Due to the viscous fingering not easily observed in porous media, channeling is used to simplify the viscous fingering instability. We adopted nonlinear simulation to investigate the development of viscous fingering instability during the displacement of Newtonian fluids in a channel by miscible fluids, and the influence of different Pe and different viscosity ratio R was studied. Under homogeneous conditions, when R is the same, the larger the Pe is, the more obvious the convection in the process of CO2 displacement is, the earlier the viscous fingering occurs, and the shorter the time for the finger to break through to the right boundary is. When Pe is the same, the larger the R is, the more unstable the contact area of miscible displacement becomes. More finger structures appear, and more complex fingering phenomena occur. The larger the R is, the earlier the fingering phenomenon appears, and the earlier it breaks through to the right boundary. In addition, we studied the change in Relative Mixing Length (RML) during the diffusion process quantitatively. Finally, our investigation delved into the impact of heterogeneity on viscous fingering. We observed that under significant heterogeneity, viscous fingering tends to manifest preferentially in the direction of increasing permeability.

Measurement of pressure gradients near the interface in the viscous fingering instability

The viscous fingering instability, which forms when a less-viscous fluid invades a more-viscous one within a confined geometry, is an iconic system for studying pattern formation. For both miscible and immiscible fluid pairs the growth dynamics change after the initial instability onset and the global structures, typical of late-time growth, are governed by the viscosity ratio. Here we introduce an experimental technique to measure flow throughout the inner and outer fluids. This probes the existence of a new length scale associated with the local pressure gradients around the interface and allows us to compare our results to the predictions of a previously proposed model for late-time finger growth. Published by the American Physical Society 2024

Trade Off between Hydrodynamic and Thermodynamic Forces at the Liquid-Liquid Interface.

Viscous fingering (VF) instability has been investigated in the case of a partially miscible binary system by nonlinear numerical simulations. Partially miscible fluid systems offer the possibility of phase separation coupled with VF instability. The thermodynamics of such systems are governed by the Margules parameter (interaction parameter) as well as the fluid concentrations. Kinetics of the decomposition is also influenced by dynamical parameters such as the viscosity of the fluid, which incidentally also affects the hydrodynamic forces. Here, we explore the effects of concentration and Margules parameter in order to ascertain the trade-offs incurred between hydrodynamic and thermodynamic effects at the interface as well as the thermodynamics of the bulk. Based on the Gibb's free energy versus concentration curve, we select concentrations (i) outside spinodal and binodal regions, (ii) within binodal but outside the spinodal, and (iii) within the spinodal curve. We solve the modified Cahn-Hilliard-Hele-Shaw equation employing the COMSOL Multiphysics software. Applying high-resolution numerical simulations, we show a strong dependence of the thermodynamic forces on the concentration of the mixtures. Rapid phase separation and hence a faster rate of droplet formation have been found when the concentration lies inside the spinodal region. Further, we have investigated the correlation between the fractal dimension and dynamics of the system. The spatiotemporal studies presented in this work clearly illustrate the competition between hydrodynamic and thermodynamic forces and provide insights on the kinetics of decomposition and growth of interfacial instabilities.

Air invasion into three-dimensional foam induces viscous fingering instabilities

We conducted an experimental investigation to examine the immiscible radial displacement flows of air invading three-dimensional foam in a Hele-Shaw cell. Our study successfully identified three distinct flow regimes. In the initial regime, characterized by relatively low fingertip velocities, the foam underwent a slow displacement through plug flow. During this process, the three-phase contact lines slipped at the cell walls. Notably, we discovered that the air injection pressure exhibited a proportional relationship with the power of the fingertip velocity. This relationship demonstrated excellent agreement with a power law, where the exponent was determined to be 2/3. Transitioning to the second regime, we observed relatively high velocities, resulting in the displacement of the foam as a plug within single layers of foam bubbles. The movement of these bubbles near the cell walls was notably slower. Similar to the first regime, the behavior in this regime also adhered to a power law. In the third regime, which manifested at higher air injection pressures, the development of air fingers occurred through narrow channels. These channels had the potential to isolate the air fingers as they underwent a process of "healing." Furthermore, our results unveiled a significant finding that the width of the air fingers exhibited a continuous scaling with the air injection pressure, irrespective of the flow regimes being observed.

Interfacial instabilities in confined displacements involving non-Newtonian fluids

The growth of interfacial instabilities during fluid displacements can be driven by gradients in pressure, viscosity and surface tension, and by applying external fields. Since displacements of non-Newtonian fluids such as polymer solutions, colloidal and granular slurries are ubiquitous in natural and industrial processes, understanding the growth mechanisms and fully developed morphologies of interfacial patterns involving non-Newtonian fluids is extremely important. In this perspective, we focus on displacement experiments, wherein competitions between capillary, viscous, elastic and frictional forces drive the onset and growth of primarily viscous fingering instabilities in confined geometries. We conclude by highlighting several exciting open problems in this research area.

Controlling viscous fingering instabilities of complex fluids

Despite their aesthetic elegance, wavy or fingering patterns emerge when a fluid of low viscosity pushes another immiscible fluid of high viscosity in a porous medium, producing an incomplete sweep and hampering several crucial technologies. Some examples include chromatography, printing, coating flows, oil-well cementing, as well as large-scale technologies of groundwater and enhanced oil recovery. Controlling such fingering instabilities is notoriously challenging and unresolved for complex fluids of varying viscosity because the fluids’ mobility contrast is often predetermined and yet the predominant drive in determining a stable, flat or unstable, wavy interface. Here we show, experimentally and theoretically, how to suppress or control the primary viscous fingering patterns of a common type of complex fluids (of shear-thinning with a low yield stress) using a radially tapered cell of linearly varying gap thickness, h(r). Experimentally, we displace a complex viscous (PAA) solution with gas under a constant flow rate (Q), varied between 0.02 and 2 slpm (standard liter per minute), in a radially converging cell with a constant gap-thickness gradient, α=dh/dr<0\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\alpha = dh/dr < 0$$\\end{document}. A stable, uniform interface emerges at low Q and in a steeper cell (i.e., greater |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}) for the complex fluids, whereas unstable fingering pattern at high Q and smaller |α|\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$|\\alpha |$$\\end{document}. Our theoretical predictions with a simplified linear stability analysis show an agreeable stability criterion with experimental data, quantitatively offering strategies to control complex fluid-fluid patterns and displacements in microfluidics and porous media.

Spreading of volatile droplets in a humidity-controlled environment.

When a pure ethanol droplet is deposited on a dry, wettable and conductive substrate, it is expected to spread into a thin, uniform film. Here, we demonstrate that this uniform spreading behaviour can be altered significantly by controlling the ambient relative humidity. We show that higher relative humidity not only promotes faster spreading of the droplet, it also destabilizes the moving contact line, resulting in a fingering instability. We observe that these effects primarily emerge due to the hygroscopic nature of the pure droplet, which eventually leads to solutal-Marangoni effects. Additionally, heat transfer between the evaporating droplet and the underlying substrate also plays a crucial role in the overall dynamics. Thus, the overall spreading of a pure hygroscopic droplet is determined by a delicate interplay between solutal and thermal Marangoni effects.

The subdivision-based IGA-EIEQ numerical scheme for the Cahn–Hilliard–Darcy system of two-phase Hele-Shaw flow on complex curved surfaces

The subdivision-based IGA-EIEQ numerical scheme for the Cahn–Hilliard–Darcy system of two-phase Hele-Shaw flow on complex curved surfaces