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1
Ait Abderrahmane, Hamid, Shahid Rabbani, and Mohamed Sassi. "Inertia Effects in the Dynamics of Viscous Fingering of Miscible Fluids in Porous Media: Circular Hele-Shaw Cell Configuration." Energies 14, no. 19 (October 8, 2021): 6432. http://dx.doi.org/10.3390/en14196432.
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We present a numerical study of viscous fingering occurring during the displacement of a high viscosity fluid by low viscosity fluid in a circular Hele-Shaw cell. This study assumes that the fluids are miscible and considers the effects of inertial forces on fingering morphology, mixing, and displacement efficiency. This study shows that inertia has stabilizing effects on the fingering instability and improves the displacement efficiency at a high log-mobility-viscosity ratio between displacing and displaced fluids. Under certain conditions, inertia slightly reduces the finger-split phenomenon and the mixing between the two fluids.
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Holloway, Kristi E., and John R. de Bruyn. "Viscous fingering with a single fluid." Canadian Journal of Physics 83, no. 5 (May 1, 2005): 551–64. http://dx.doi.org/10.1139/p05-024.
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We study fingering that occurs when hot glycerine displaces cooler, more viscous glycerine in a radial Hele-Shaw cell. We find that fingering occurs for a sufficiently large initial viscosity contrast and for sufficiently high flow rates of the displacing fluid. The wavelength of the fingering instability is proportional to the cell width for thin cells, but the ratio of wavelength to cell width decreases for our thickest cell. Similar fingering is seen in numerical simulations of this system.PACS Nos.: 47.54.+r, 68.15.+e, 47.20.k
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Shiri, Yousef, and Alireza Shiri. "NUMERICAL INVESTIGATION OF FLUID FLOW INSTABILITIES IN PORE-SCALE WITH HETEROGENEITIES IN PERMEABILITY AND WETTABILITY." Rudarsko-geološko-naftni zbornik 36, no. 3 (2021): 143–56. http://dx.doi.org/10.17794/rgn.2021.3.10.
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Quadrant geometry with permeability and wettability contrast occurs in different events, such as faults, wellbore damage, and perforation zones. In these events, understanding the dynamics of immiscible fluid displacement is vital for enhanced oil recovery. Fluid flow studies showed that viscous fingering occurs due to viscous instabilities that depend on the mobility of fluids and capillary forces. Besides, the porous domain heterogeneity is also effective on the formation of fingering. So, the purpose of the current research is to numerically investigate the effect of heterogeneity in wettability and permeability, and flow properties in Saffmann-Taylor instabilities. Numerical simulations with different flow rates in the permeability contrast model illustrated the nodal crossflow, growth of viscous fingering in the nodal part, and bypass flow in the second zone. In the wettability contrast model, a capillary fingering pattern is observed and fluid patches are isolated because of capillary force and the end effects are trapped within the quadrant. Moreover, the consequences of wettability on apparent wettability that alters the fluid-front pattern and displacement efficiency are shown.
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Li, Peisheng, Chengyu Peng, Peng Du, Ying Zhang, Boheng Dong, and Ming Ma. "The investigation of the viscous fingering phenomenon of immiscible fluids displacement by the Lattice Boltzmann method." Canadian Journal of Physics 98, no. 7 (July 2020): 650–59. http://dx.doi.org/10.1139/cjp-2019-0120.
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In this paper, the viscous fingering phenomena of two immiscible fluids with a large viscosity ratio was simulated by the Lattice Boltzmann method. The Rothman–Keller Lattice Boltzmann model was applied to study the viscous fingering phenomena in a microchannel where the high viscosity fluids were displaced by low viscosity fluids. We have investigated the influences of parameters such as viscosity ratio (M), surface wettability, capillary number (Ca), and Reynolds number (Re) on finger structures, breakthrough time (Ts), and areal sweep efficiency (Se). In particular, the effects of surface tension and large viscosity ratio on the phenomenon of fluid accumulation were intensively studied. The simulation results showed that the fluid accumulation became more obvious gradually with the increase of M, which led to more serious displacement effects. Moreover, Se increased as the contact angle increased. Besides, as the viscous fingering phenomenon weakened, the phenomenon of fluid accumulation became more evident. Furthermore, the finger pattern had a tendency to increase as the value of Ca and Re increased, and the phenomenon of fluid accumulation decreased with the decrease of Ts and Se.
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Gao, Wanxiang, Sheng Zhang, Nanxi Zhang, Xiaowu Xiong, Zhaojun Shi, and Ka Sun. "Generating Fingerings for Piano Music with Model-Based Reinforcement Learning." Applied Sciences 13, no. 20 (October 15, 2023): 11321. http://dx.doi.org/10.3390/app132011321.
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The piano fingering annotation task refers to assigning finger labels to notes in piano sheet music. Good fingering helps improve the smoothness and musicality of piano performance. In this paper, we propose a method for automatically generating piano fingering using a model-based reinforcement learning algorithm. We treat fingering annotation as a partial constraint combinatorial optimization problem and establish an environment model for the piano performance process based on prior knowledge. We design a reward function based on the principle of minimal motion and use reinforcement learning algorithms to decide the optimal fingering combinations. Our innovation lies in establishing a more realistic environment model and adopting a model-based reinforcement learning approach, compared to model-free methods, to enhance the utilization of samples. We also propose a music score segmentation method to parallelize the fingering annotation task. The experimental section shows that our method achieves good results in eliminating physically impossible fingerings and reducing the amount of finger motion required in piano performance.
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Ērglis, K., A. Tatulcenkov, G. Kitenbergs, O. Petrichenko, F. G. Ergin, B. B. Watz, and A. Cēbers. "Magnetic field driven micro-convection in the Hele-Shaw cell." Journal of Fluid Mechanics 714 (January 2, 2013): 612–33. http://dx.doi.org/10.1017/jfm.2012.512.
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AbstractMicro-convection caused by ponderomotive forces of the self-magnetic field of a magnetic fluid in the Hele-Shaw cell under the action of a vertical homogeneous magnetic field is studied both experimentally and numerically. It is shown that a non-potential magnetic force at magnetic Rayleigh numbers greater than the critical value causes fingering at the interface between the miscible magnetic and non-magnetic fluids. The threshold value of the magnetic Rayleigh number depends on the smearing of the interface between fluids. Fingering with its subsequent decay due to diffusion of particles significantly increases the mixing at the interface. Velocity and vorticity fields at fingering are determined by particle image velocimetry measurements and qualitatively correspond well to the results of numerical simulations of the micro-convection in the Hele-Shaw cell carried out in the Darcy approximation, which account for ponderomotive forces of the self-magnetic field of the magnetic fluid. Gravity plays an important role at the initial stage of the fingering observed in the experiments.
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Suekane, Tetsuya, Tomotaka Koe, and Pablo Marin Barbancho. "Three-Dimensional Interaction of Viscous Fingering and Gravitational Segregation in Porous Media." Fluids 4, no. 3 (July 12, 2019): 130. http://dx.doi.org/10.3390/fluids4030130.
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Viscous fingering is fluid dynamics instability induced on the displacement front when a less viscous fluid (LVF) displaces a more viscous fluid (MVF), thereby reducing the displacement efficiency. The displacement of a denser fluid by a less dense fluid produces a gravitational tongue. This gravitational segregation also reduces the displacement efficiency. In this study, the three-dimensional structure of the fingering pattern at the viscous fingering to gravitational segregation boundary was examined using X-ray microtomography on a packed bed of particles. At low gravity numbers, viscous fingering resembled that without gravity characterized by nonlinear interaction including tip-splitting, shielding, and coalescence. At intermediate gravity numbers, viscous fingering is associated with the gravitational tongue due to segregation. At high gravity numbers, a clear gravitational tongue penetrates from the inlet to the outlet. Consequently, the concentration near the injection point decreases and exhibits a flat profile in the flow direction. The displacement efficiency decreases with increasing gravity number, with the highest value achieved without gravity but depends on many factors, including the viscosity ratio and Péclet number.
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Mafi, MD, Zhen Qin, Yuting Wu, Sung-Ki Lyu, and Chicheng Ma. "Research on the Interfacial Instability of Non-Newtonian Fluid Displacement Using Flow Geometry." Coatings 13, no. 11 (October 27, 2023): 1848. http://dx.doi.org/10.3390/coatings13111848.
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The variation of the classical viscous fingering instability is studied numerically in this work. An investigation of the viscous fingering phenomenon of immiscible displacement in the Hele–Shaw cell (HSC), where the displaced fluid is a shear-thinning fluid, was carried out numerically using the volume of fluid (VOF) method by adding a minor depth gradient or altering the geometry of the top plate in the HSC. The findings demonstrate how the presence of depth gradients can change the stability of the interface and offer a chance to regulate and adapt the fingering instability in response to the viscous fingering properties of air driving non-Newtonian fluids under various depth gradients. The relative breadth will shrink under the influence of the depth gradient, and the negative consequences of the gradient will be increasingly noticeable. Specifically, under different power-law indices, we found that with the enhancement of shear-thinning characteristics (lower power-law exponent n) in both positive and negative depth gradients, the fingers that protrude from the viscous fingers become shorter and thicker, resulting in higher displacement efficiency. Additionally, several modifications were performed to the upper plate’s design, and the findings revealed that the shape had no effect on the viscous fingering and only had an impact on the longitudinal amplitude. Based on the aforementioned traits, we may alter the HSC’s form or depth gradient to provide high-quality and effective work.
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Kessler, David A., and Herbert Levine. "Microscopic Selection of Fluid Fingering Patterns." Physical Review Letters 86, no. 20 (May 14, 2001): 4532–35. http://dx.doi.org/10.1103/physrevlett.86.4532.
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Alsac, E., C. Laroche, E. Lemaire, and H. Van Damme. "Viscochemical fingering in a colloidal fluid." Chemical Physics Letters 165, no. 4 (January 1990): 277–82. http://dx.doi.org/10.1016/0009-2614(90)87188-w.
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GRILLET, ANNE M., ALEX G. LEE, and ERIC S. G. SHAQFEH. "Observations of ribbing instabilities in elastic fluid flows with gravity stabilization." Journal of Fluid Mechanics 399 (November 25, 1999): 49–83. http://dx.doi.org/10.1017/s002211209900628x.
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We have investigated the role of elasticity in the stability of air–fluid interfaces during fluid displacement flows. Our investigations of the stability of coating flows with an eccentric cylinder geometry for both a viscous Newtonian fluid and ideal elastic Boger fluids are discussed in terms of three classes of phenomena. To begin, we have documented several new features in traditional fingering instabilities in elastic displacement flows. These include a very strong elastic destabilization of forward roll coating: a destabilization which can be correlated directly with the elasticity of the coating fluid and which appears to be present even in the absence of diverging channel walls. Moreover, elastic effects are shown to create a novel saw-toothed cusped pattern in the eccentric cylinder roll-and-plate geometry. Secondly, we have found that purely elastic bulk flow instabilities in the neighbourhood of air–fluid interfaces can cause surface deformations if the secondary flow is of sufficient strength. Finally, flows created by the displacement of less viscous air by a more viscous elastic fluid are found to display a new class of purely elastic instabilities which appear to be independent of traditional viscous fingering instabilities and elastic bulk flow instabilities. Thus interfaces which are stable for Newtonian fluids are unstable via purely elastic mechanisms. We have found that indeed elasticity has a dramatic effect on the stability of interfaces, not only changing the critical conditions, but also changing the manifestation of traditional fingering instabilities, and causing new purely elastic interfacial instabilities.
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McCue, Scott W. "Short, flat-tipped, viscous fingers: novel interfacial patterns in a Hele-Shaw channel with an elastic boundary." Journal of Fluid Mechanics 834 (November 17, 2017): 1–4. http://dx.doi.org/10.1017/jfm.2017.692.
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Injecting a less viscous fluid into a more viscous fluid in a Hele-Shaw cell triggers two-dimensional viscous fingering patterns which are characterised by increasingly long fingers undergoing tip splitting and branching events. These complex structures are considered to be a paradigm for interfacial pattern formation in porous media flow and other related phenomena. Over the past five years, there has been a flurry of interest in manipulating these interfacial fingering patterns by altering the physical components of the Hele-Shaw apparatus. In this Focus on Fluids article, we summarise some of this work, concentrating on a very recent study in which the alterations include replacing one of the two bounding plates with an elastic membrane (Ducloué et al., J. Fluid Mech., vol. 826, 2017, R2). The resulting experimental set-up gives rise to a wide variety of novel interfacial patterns including periodic sideways fingers, dendritic-like patterns and short, flat-tipped viscous fingers that appear to resemble molar teeth. These latter fingers are similar to those observed in the printer’s instability and when peeling off a layer of adhesive tape. This delightful work brings together a number of well-studied themes in interfacial fluid mechanics, including how viscous and surface tension forces compete to drive fingering patterns, how interfaces are affected by fluid–solid interactions and, finally, how novel strategies can be implemented to control interfacial instabilities.
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Li, J. S., Q. Li, W. H. Cai, F. C. Li, and C. Y. Chen. "Mixing Efficiency via Alternating Injection in a Heterogeneous Porous Medium." Journal of Mechanics 34, no. 2 (May 15, 2017): 167–76. http://dx.doi.org/10.1017/jmech.2017.32.
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AbstractWe numerically verify better fluid mixing efficiency can be achieved by alternating injection scheme in a heterogeneous porous medium, whose permeability heterogeneity is characterized by two statistical parameters, i.e., the variance s and the correlation length l. Nevertheless, the fingering pattern is strongly affected by permeability distribution to result in similar fingering interface on each of injected layer of less viscous fluids. Instead of randomly chaotic fingering interaction in a homogeneous condition, more orderly channeling interaction occurs in a heterogeneous medium. As a result, higher Peclet number Pe (relative measure of advection and diffusion effects) generally leads to worse mixing efficiency in a heterogeneous medium, which might contradict the result found in a homogeneous case. By the same token, in the cases which strong chaotic fingering interaction already exists in homogeneous conditions, e.g., sufficiently short alternating injection interval Δt, large viscosity contrast A and high Pe, the presence of permeability heterogeneity would constrain the randomly chaotic fingering interaction and favors the more orderly channeling interaction, so that mixing efficiency is deteriorated compared with the corresponding homogeneous case.
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Rabbani, Harris Sajjad, Dani Or, Ying Liu, Ching-Yao Lai, Nancy B. Lu, Sujit S. Datta, Howard A. Stone, and Nima Shokri. "Suppressing viscous fingering in structured porous media." Proceedings of the National Academy of Sciences 115, no. 19 (April 23, 2018): 4833–38. http://dx.doi.org/10.1073/pnas.1800729115.
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Finger-like protrusions that form along fluid−fluid displacement fronts in porous media are often excited by hydrodynamic instability when low-viscosity fluids displace high-viscosity resident fluids. Such interfacial instabilities are undesirable in many natural and engineered displacement processes. We report a phenomenon whereby gradual and monotonic variation of pore sizes along the front path suppresses viscous fingering during immiscible displacement, that seemingly contradicts conventional expectation of enhanced instability with pore size variability. Experiments and pore-scale numerical simulations were combined with an analytical model for the characteristics of displacement front morphology as a function of the pore size gradient. Our results suggest that the gradual reduction of pore sizes act to restrain viscous fingering for a predictable range of flow conditions (as anticipated by gradient percolation theory). The study provides insights into ways for suppressing unwanted interfacial instabilities in porous media, and provides design principles for new engineered porous media such as exchange columns, fabric, paper, and membranes with respect to their desired immiscible displacement behavior.
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Mahabadi, Nariman, Leon van Paassen, Ilenia Battiato, Tae Sup Yun, Hyunwook Choo, and Jaewon Jang. "Impact of Pore-Scale Characteristics on Immiscible Fluid Displacement." Geofluids 2020 (May 15, 2020): 1–10. http://dx.doi.org/10.1155/2020/5759023.
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Immiscible fluid flows (drainage displacement) where nonwetting fluid invades porous media filled with wetting fluid are frequently observed. Numerous studies have confirmed the existence of three different displacement patterns which depend on the viscosity ratio and capillary number: stable displacement, viscous fingering, and capillary fingering. However, the phase boundary and displacement efficiency of each displacement pattern can vary significantly depending on the characteristics of the experimental and numerical tools employed. In this study, a three-dimensional (3D) tube network model was extracted from 3D X-ray computed tomography images of natural sand. The extracted network model was used to quantitatively outline the phase boundary of the displacement pattern and to examine the displacement efficiency for wide ranges of viscosity ratios and capillary numbers. Moreover, the effects of the tube size distribution and tube connectivity on the displacement characteristics were investigated. A transition regime between the viscous fingering and capillary fingering zones with regard to the displacement efficiency was observed for the first time. As the tube size distribution became uniform, the viscosity effect increased. As the tube connectivity decreased to ~4.6, the phase boundary became similar to that of a two-dimensional network. The characteristic changes of the phase boundary and displacement efficiency were highlighted through local gradient diagrams.
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Lindner, Anke, Daniel Bonn, and Jacques Meunier. "Viscous fingering in a shear-thinning fluid." Physics of Fluids 12, no. 2 (February 2000): 256–61. http://dx.doi.org/10.1063/1.870303.
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SORIMACHI, Kazunori, Tomiichi HASEGAWA, and Takatsune NARUMI. "Bifurcation of Viscous Fingering in Polymer Fluid." Proceedings of the JSME annual meeting 2004.2 (2004): 167–68. http://dx.doi.org/10.1299/jsmemecjo.2004.2.0_167.
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Lindner, Anke, Philippe Coussot, and Daniel Bonn. "Viscous Fingering in a Yield Stress Fluid." Physical Review Letters 85, no. 2 (July 10, 2000): 314–17. http://dx.doi.org/10.1103/physrevlett.85.314.
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COUSSOT, PHILIPPE. "Saffman–Taylor instability in yield-stress fluids." Journal of Fluid Mechanics 380 (February 10, 1999): 363–76. http://dx.doi.org/10.1017/s002211209800370x.
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When a fluid is pushed by a less viscous one the well-known Saffman–Taylor instability phenomenon arises, which takes the form of fingering. Since this phenomenon is important in a wide variety of applications involving strongly non-Newtonian fluids – in other words, fluids that exhibit yield stress – we undertake a full theoretical examination of Saffman–Taylor instability in this type of fluid, in both longitudinal and radial flows in Hele-Shaw cells. In particular, we establish the detailed form of Darcy's law for yield-stress fluids. Basically the dispersion equation for both flows is similar to equations obtained for ordinary viscous fluids but the viscous terms in the dimensionless numbers conditioning the instability contain the yield stress. As a consequence the wavelength of maximum growth can be extremely small even at vanishing velocities. Additionally an approximate analysis shows that the fingers which are left behind at the beginning of destabilization should tend to stop completely. Fingering of yield-stress fluids therefore has some peculiar characteristics which nevertheless are not sufficient to explain the fractal pattern observed with colloidal systems.
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Lyubimova, Tatyana, Andrey Ivantsov, and Dmitry Lyubimov. "Control of fingering instability by vibrations." Mathematical Modelling of Natural Phenomena 16 (2021): 40. http://dx.doi.org/10.1051/mmnp/2021031.
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In applications involving the injection of a fluid in a porous medium to displace another fluid, a main objective is the maximization of the displacement efficiency. Displacement fronts moving in porous media are subjected to hydrodynamic instability when a liquid of low viscosity displaces a high-viscosity liquid and consequently finger-like structure forms along the interface. This finger instability is usually undesirable in technical applications and natural filtration processes. We discuss the external periodic forcing as one of the promising ways to control the instability and perform numerical simulation of an initially spherical drop in a porous media under vertical vibrations. The drop is a favorable object to study since in this case one can observe the effect of vibrations on fluid interface domains inclined by different angles with respect to vibration axis. It is shown that under vibrations small-scale perturbations of interface are suppressed and in the case of vibrations of large enough intensity the drop becomes stable. The stability criterion is derived.
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Mistry, Piyush R., Vikas H. Pradhan, and Khyati R. Desai. "Mathematical Model and Solution for Fingering Phenomenon in Double Phase Flow through Homogeneous Porous Media." Scientific World Journal 2013 (2013): 1–7. http://dx.doi.org/10.1155/2013/470174.
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The present paper analytically discusses the phenomenon of fingering in double phase flow through homogenous porous media by using variational iteration method. Fingering phenomenon is a physical phenomenon which occurs when a fluid contained in a porous medium is displaced by another of lesser viscosity which frequently occurred in problems of petroleum technology. In the current investigation a mathematical model is presented for the fingering phenomenon under certain simplified assumptions. An approximate analytical solution of the governing nonlinear partial differential equation is obtained using variational iteration method with the use of Mathematica software.
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Saffman, P. G. "Viscous fingering in Hele-Shaw cells." Journal of Fluid Mechanics 173 (December 1986): 73–94. http://dx.doi.org/10.1017/s0022112086001088.
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The phenomenon of interfacial motion between two immiscible viscous fluids in the narrow gap between two parallel plates (Hele-Shaw cell) is considered. This flow is currently of interest because of its relation to pattern selection mechanisms and the formation of fractal, structures in a number of physical applications. Attention is concentrated on the fingers that result from the instability when a less-viscous fluid drives a more-viscous one. The status of the problem is reviewed and progress with the thirty-year-old problem of explaining the shape and stability of the fingers is described. The paradoxes and controversies are both mathematical and physical. Theoretical results on the structure and stability of steady shapes are presented for a particular formulation of the boundary conditions at the interface and compared with the experimental phenomenon. Alternative boundary conditions and future approaches are discussed.
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VERETENNIKOV, IGOR, ALEXANDRA INDEIKINA, and HSUEH-CHIA CHANG. "Front dynamics and fingering of a driven contact line." Journal of Fluid Mechanics 373 (October 25, 1998): 81–110. http://dx.doi.org/10.1017/s0022112098002390.
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Using photographic imaging and dye tracking experiments, we scrutinize the dynamics of a contact line when a finite volume of partially wetting fluid is driven by gravity to spread over a slightly inclined dry plane. Unlike spreading mechanisms driven by molecular forces, gravity-driven spreading over a dry plane is shown to possess a characteristic interfacial ‘nose’ that overhangs the contact line when the film thickness is in excess of the capillary length. A unique recirculating vortex exists within the nose front which spreads at speeds corresponding to capillary numbers in excess of 10−2. Our experiments show that fingering from a gravity-driven straight front occurs when the above nose configuration cannot be sustained across the entire front as the film thins and the apparent contact angle θ reaches π/2. The fingers retain the nose configuration while the remaining segments of the front evolve into a wedge configuration and stop abruptly due to their large resistance to fluid flow. This fingering mechanism is insensitive to fluid wettability, noise or surface heterogeneity. Via matched asymptotics, we obtain accurate estimates of fingering position and speed at θ=π/2 that are in good agreement with measured values. This new mechanism is distinct from other instability and sensitivity fingering mechanisms and can be in play whenever θ of the straight front approaches π/2 from above as the film thins.
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Xu, Feng, and Sungyon Lee. "The enhancement of viscous fingering with bidisperse particle suspension." Journal of Fluid Mechanics 860 (December 7, 2018): 487–509. http://dx.doi.org/10.1017/jfm.2018.846.
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Viscous fingering is observed experimentally when a bidisperse suspension displaces air inside a Hele-Shaw cell, despite the stabilising viscosity ratio between the invading (suspension) and defending (air) phases. Careful experiments are carried out to characterise this instability by either systematically varying the large-particle concentrations $\unicode[STIX]{x1D719}_{l0}$ at constant total concentrations $\unicode[STIX]{x1D719}_{0}$, or changing $\unicode[STIX]{x1D719}_{0}$ with fixed $\unicode[STIX]{x1D719}_{l0}$. Leading to the instability, we observe that larger particles consistently enrich the fluid–fluid interface at a faster rate than small particles. This size-dependent enrichment of the interface leads to an earlier onset of the fingering instability for bidisperse suspensions, compared to their monodisperse counterpart of all small particles. In particular, even the small presence of large particles is shown to effectively lower the total particle concentration needed for fingering, compared to the all-small-particle case. We hypothesise that the key mechanism behind this enhanced viscous fingering is the size-dependent nature of shear-induced migration of particles far upstream from the interface. A reduced equilibrium model is derived based on the modified suspension balance model to verify this hypothesis, in reasonable agreement with experiments.
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Subraveti, Sai Gokul, Petr Nikrityuk, and Arvind Rajendran. "Computational fluid dynamics study of viscous fingering in supercritical fluid chromatography." Journal of Chromatography A 1534 (January 2018): 150–60. http://dx.doi.org/10.1016/j.chroma.2017.12.057.
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TOUVET, T., N. J. BALMFORTH, R. V. CRASTER, and B. R. SUTHERLAND. "Fingering instability in buoyancy-driven fluid-filled cracks." Journal of Fluid Mechanics 672 (February 24, 2011): 60–77. http://dx.doi.org/10.1017/s0022112010005860.
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The stability of buoyancy-driven propagation of a fluid-filled crack through an elastic solid is studied using a combination of theory and experiments. For the theory, the lubrication approximation is introduced for fluid flow, and the surrounding solid is described by linear elasticity. Solutions are then constructed for a planar fluid front driven by either constant flux or constant volume propagating down a pre-cut conduit. As the thickness of the pre-cut conduit approaches zero, it is shown how these fronts converge to zero-toughness fracture solutions with a genuine crack tip. The linear stability of the planar solutions towards transverse, finger-like perturbations is then examined. Instabilities are detected that are analogous to those operating in the surface-tension-driven fingering of advancing fluid contact lines. Experiments are conducted using a block of gelatin for the solid and golden syrup for the fluid. Again, planar cracks initiated by emplacing the syrup above a shallow cut on the surface of the gelatin develop transverse, finger-like structures as they descend. Potential geological applications are discussed.
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NAGATSU, YUICHIRO, YUSUKE KONDO, YOSHIHITO KATO, and YUTAKA TADA. "Effects of moderate Damköhler number on miscible viscous fingering involving viscosity decrease due to a chemical reaction." Journal of Fluid Mechanics 625 (April 14, 2009): 97–124. http://dx.doi.org/10.1017/s0022112008005429.
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We have succeeded in experimentally investigating the effects of a moderate Damköhler number, Da (defined as the ratio between a characteristic time of fluid motion and that of a chemical reaction), for various Péclet numbers, Pe, on miscible viscous fingering involving a decrease in the viscosity of the displaced liquid due to a chemical reaction in Hele-Shaw cells. We achieved this by using a chemical reaction between a polymer solution and metal ions. Main analysis has been done for the radial fingering. In the range of Pe employed here, the fingering patterns without the reaction (Da = 0) were independent of Pe. The fingering patterns with the reaction depended on the single parameter, Da, and the area occupied by the fingering pattern near the injection hole increased with Da in the range of Da employed here. The ratio of the area occupied by the fingering pattern within the circle radius of which is the length of longest finger to the area of the circle increased with Da in the range of Da employed here. This result is opposite to that of Nagatsu et al. (J. Fluid Mech., vol. 571, 2007, p. 475), in which the area was decreased by the reaction decreasing the viscosity involving significantly high Da. Experiments in the linear geometry show that the shape of a single finger also depended on the single parameter, Da, and the finger width increased near the base with Da. This result is also opposite to that in the previous case in which the width of a single finger was considered to be decreased by the reaction. These results, interestingly, show that the effects of the decrease in the displaced liquid's viscosity due to chemical reaction on the fingering pattern for moderate Da are opposite to those for significantly high Da. A mechanism for the opposite effects on the fingering pattern depending on Da is discussed.
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Aoki, Hirotaka, and Tetsuya Suekane. "Fingering of active fluid in Hele-Shaw cells." Proceedings of the Thermal Engineering Conference 2019 (2019): 0012. http://dx.doi.org/10.1299/jsmeted.2019.0012.
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Malhotra, Sahil, and Mukul M. Sharma. "Impact of fluid elasticity on miscible viscous fingering." Chemical Engineering Science 117 (September 2014): 125–35. http://dx.doi.org/10.1016/j.ces.2014.06.023.
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Abdul Afiq Abdul Aziz, Nadiahnor Md Yusop, and Noraishah Othman. "Influence of Injection Rate and Oil Viscosity on Viscous Fingering – Simulation Prediction." CFD Letters 14, no. 6 (June 26, 2022): 24–42. http://dx.doi.org/10.37934/cfdl.14.6.2442.
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Waterflooding is a secondary oil recovery process that commonly utilized. However, there are several factors affecting the efficiency of water-flooding. Current research focused on the effects of injection rate and oil viscosity on the waterflooding efficiency. Fluid Structure Interaction (FSI) is utilized to predict the effect of the injection rate and oil viscosity towards waterflooding. Volume of fluid (VOF) and Realizable k- ɛ models are utilized in this research. Ergun’s equation also utilized in this research for estimation of permeability and inertial loss within the porous medium. The research found viscous fingering occurred when the mobility ratio is more than unity and instability number, Ni > 1000. The phenomenon of viscous fingering is directly affected by injection rate and viscosity ratio. The phenomenon directly affects directly sweep efficiency during waterflooding process thus affecting oil recovery process. The research found as injection rate and viscosity ratio increase; viscous fingering predominantly seen within the porous medium.
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Juanes, Ruben, and Martin Julian Blunt. "Impact of Viscous Fingering on the Prediction of Optimum WAG Ratio." SPE Journal 12, no. 04 (December 1, 2007): 486–95. http://dx.doi.org/10.2118/99721-pa.
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Summary In miscible flooding, injection of solvent is often combined with water to reduce the mobility contrast between injected and displaced fluids and control the degree of fingering. Using traditional fractional-flow theory, Stalkup estimated the optimum water-solvent ratio (or WAG ratio) when viscous fingering effects are ignored, by imposing that the solvent and water fronts travel at the same speed. Here we study how the displacement efficiency and the mobility ratio across the solvent front vary with the WAG ratio when fingering is included in the analysis. We do so by computing analytical solutions to a 1D model of two-phase, three-component, first-contact miscible flow that includes the macroscopic effects of viscous fingering. The macroscopic model, originally proposed by Blunt and Christie (1993, 1994), employs an extension of the Koval fingering model to multiphase flows. The premise is that the only parameter of the model—the effective mobility ratio—must be calibrated dynamically until self-consistency is achieved between the input value and the mobility contrast across the solvent front. This model has been extensively validated by means of high-resolution simulations that capture the details of viscous fingering and carefully-designed laboratory experiments. The results of this paper suggest that, while the prediction of the optimum WAG ratio does not change dramatically by incorporating the effects of viscous fingering, it is beneficial to inject more solvent than estimated by Stalkup's method. We show that, in this case, both the pore volumes injected (PVI) for complete oil recovery and the degree of fingering are minimized. Introduction Solvent flooding is a commonly used technology for enhanced oil recovery in hydrocarbon reservoirs, which aims at developing miscibility, thereby mobilizing the residual oil and enhancing the mobility of the hydrocarbon phase (Stalkup 1983; Lake 1989). Despite its high local displacement efficiency, the overall effectiveness of solvent injection may be compromised by viscous fingering, channeling, and gravity override, all of which contribute negatively to sweep efficiency (Christie and Bond 1987; Christie 1989; Christie et al. 1993; Chang et al. 1994; Tchelepi and Orr 1994). In this paper, we focus on the effect of viscous fingering; that is, the instability that occurs when a low-viscosity fluid (solvent) is injected into a formation filled with more viscous fluids (water and oil). Mobility control of the injected solvent can be achieved by simultaneous coinjection of water—typically in alternating water and solvent slugs (WAG) (Caudle and Dyes 1958). In this way, the mobility contrast between the injected and displaced fluids is reduced, thereby limiting the degree of fingering. There is an optimum ratio of water to solvent that maximizes recovery—in the sense of minimizing the number of pore volumes injected—while providing effective mobility control. For linear floods in homogeneous media, and without consideration of viscous fingering effects, a graphical construction of the optimum WAG ratio was given by Stalkup (1983) for both secondary floods (water/solvent injection into a medium filled with mobile oil and immobile water) and tertiary floods (water-solvent injection into a medium filled with mobile water and immobile oil). The design condition imposed in Stalkup's method is that the velocity of the water and solvent fronts be the same. Walsh and Lake (1989) performed an interesting analysis of the WAG ratio (the ratio of injected water to solvent) on the displacement efficiency for secondary and tertiary floods, using fractional-flow theory. They did not include the effects of viscous fingering, but they estimated the mobility contrast across the solvent front as a measure of the severity of fingering.
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Suzuki, Ryuta X., Risa Takeda, Yuichiro Nagatsu, Manoranjan Mishra, and Takahiko Ban. "Fluid Morphologies Governed by the Competition of Viscous Dissipation and Phase Separation in a Radial Hele-Shaw Flow." Coatings 10, no. 10 (October 6, 2020): 960. http://dx.doi.org/10.3390/coatings10100960.
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The displacement of a less viscous fluid by a more viscous fluid in a radial Hele-Shaw cell makes a circular pattern because the interface is hydrodynamically stable in this condition. Very recently, it has been experimentally reported that the hydrodynamically stable displacement in a partially miscible system induces fingering patterns while stable circular patterns are made at fully miscible and immiscible systems. The fingering instability in the partially miscible system results from complex and entangled elements involving viscous dissipation, molecular diffusion, and phase separation. The analyzing mechanism requires a quantitative relationship between the hydrodynamic interfacial fingering patterns and underlying physicochemical properties. Here, we experimentally investigated the change in fluid patterns formed by the progression of phase separation in the partially miscible systems and categorized them into three patterns: finger-like pattern, annular-like pattern, and circular pattern. Moreover, we propose the mechanism of the pattern formation by an interfacial tension measurement and evaluate the patterns by modified capillary number and newly defined body force ratio, Bf. Our analysis revealed that the deformation index of the pattern can be expressed as a function of Bf on a single curve regardless of the miscibility.
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Zhu, Dawei, Yunjin Wang, Mingyue Cui, Fujian Zhou, Yaocong Wang, Chong Liang, Honglan Zou, and Fei Yao. "Acid System and Stimulation Efficiency of Multistage Acid Fracturing in Porous Carbonate Reservoirs." Processes 10, no. 9 (September 17, 2022): 1883. http://dx.doi.org/10.3390/pr10091883.
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With little to no natural fracture development and the high calcite content in porous carbonate reservoirs, for multistage acid fracturing, different fluids are used to form a viscous fingering in the fracture, thus enhancing the degree of nonuniform etching. However, existing studies on multistage acid fracturing mainly focused on the combination of fracturing fluid and acid, which is less specific for porous carbonate rocks. Here, the rheological properties of five fluids, including guar-based fluid, cross-linked guar, gelled acid, cross-linked acid, and diverting acid, were studied at each temperature condition, and the viscosity relationship between each fluid was clarified. Based on the rheological properties, the differences between the seven liquid combinations on the etched morphology of the fracture walls were studied and analyzed. The conductivity of the seven acid-etched fractures under different closure stress was simulated. The experimental results showed that the viscosity relationships between the fluids at different temperatures were cross-linked guar > cross-linked acid > diverting acid (spent acid) > gelled acid > guar-based liquid > diverting acid (fresh acid). Because cross-linked acid has higher viscosity than gelled acid, it can form more obvious viscous fingering with a variety of liquids, which is more suitable for acid fracturing stimulation of porous carbonate reservoirs. In addition, the combination of cross-linked and diverting acids was screened out. The multistage alternate injection of this fluid combination could form tortuous and complex etching channels, and its acid-etching fracture conductivity was significantly higher than that of other fluid combinations at different closure stress. In this study, we optimized the fluid combination of porous carbonates and clarified the effect and mechanism of nonuniform etching to provide guidance for the fluid combination selection of multistage alternate acid fracturing process for porous carbonate reservoirs.
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Shiri, Yousef, and Hossein Hassani. "TWO-COMPONENT FLUID FRONT TRACKING IN FAULT ZONE AND DISCONTINUITY WITH PERMEABILITY HETEROGENEITY." Rudarsko-geološko-naftni zbornik 36, no. 3 (2021): 19–30. http://dx.doi.org/10.17794/rgn.2021.3.2.
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Fluid front tracking is important in two-phase/component fluid flow in porous media with different heterogeneities, especially in the improved recovery of oil. Three different flow patterns of stable, viscous fingering, and capillary fingering exist based on the fluids’ viscosity and capillary number (CA). In addition, fluid front and sweep efficiency are affected by the heterogeneity of the porous medium. In the current study, the heterogeneous porous media are: (1) normal fault zone or cross-bedding with heterogeneity in permeability, and (2) a fracture or discontinuity between two porous media consisting of two homogeneous layers with very low and high permeabilities, in which immiscible water flooding is performed for sweep efficiency and streamlines tracking purposes. By considering the experimental glass micromodel and the simulation results of discontinuity, a crack is the main fluid flow path. After the breakthrough, fluid inclines to penetrate the fine and coarse grains around the crack. Moreover, an increase in flow rate from 1 and 200 (ml/h) in both the experimental and simulation models causes a reduction in the sweep efficiency from 14% to 7.3% and 15.6% to 10% by the moment of breakthrough, respectively. In the fault zone, the sweep efficiency and the streamline of the injected fluid showed a dependency on the interface incident angle, and the layers’ permeability. The presented glass micromodel and Lattice Boltzmann Method were consistent with fluid dynamics, and both of them were suitable for a precise evaluation of sweep efficiency and visualization of preferential pathway of fluid flow through cross-bedding and discontinuity for enhanced oil recovery purposes.
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BALMFORTH, N. J., and R. V. CRASTER. "Dynamics of cooling domes of viscoplastic fluid." Journal of Fluid Mechanics 422 (November 3, 2000): 225–48. http://dx.doi.org/10.1017/s002211200000166x.
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A non-isothermal viscoplastic thin-layer theory is developed to explore the effects of surface cooling, yield stress, and shear thinning on the evolution of non-isothermal domes of lava and laboratory fluids. The fluid is modelled using the Herschel–Bulkley constitutive relations, but modified to have temperature-dependent viscosity and yield stress. The thin-layer equations are solved numerically to furnish models of expanding, axisymmetrical domes. Linear stability theory reveals the possibility of non-axisymmetrical, fingering-like instability in these domes. Finally, the relevance to lava and experiments is discussed.
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John, M. O., R. M. Oliveira, F. H. C. Heussler, and E. Meiburg. "Variable density and viscosity, miscible displacements in horizontal Hele-Shaw cells. Part 2. Nonlinear simulations." Journal of Fluid Mechanics 721 (March 13, 2013): 295–323. http://dx.doi.org/10.1017/jfm.2013.64.
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AbstractDirect numerical simulations of the variable density and viscosity Navier–Stokes equations are employed, in order to explore three-dimensional effects within miscible displacements in horizontal Hele-Shaw cells. These simulations identify a number of mechanisms concerning the interaction of viscous fingering with a spanwise Rayleigh–Taylor instability. The dominant wavelength of the Rayleigh–Taylor instability along the upper, gravitationally unstable side of the interface generally is shorter than that of the fingering instability. This results in the formation of plumes of the more viscous resident fluid not only in between neighbouring viscous fingers, but also along the centre of fingers, thereby destroying their shoulders and splitting them longitudinally. The streamwise vorticity dipoles forming as a result of the spanwise Rayleigh–Taylor instability place viscous resident fluid in between regions of less viscous, injected fluid, thereby resulting in the formation of gapwise vorticity via the traditional, gap-averaged viscous fingering mechanism. This leads to a strong spatial correlation of both vorticity components. For stronger density contrasts, the streamwise vorticity component increases, while the gapwise component is reduced, thus indicating a transition from viscously dominated to gravitationally dominated displacements. Gap-averaged, time-dependent concentration profiles show that variable density displacement fronts propagate more slowly than their constant density counterparts. This indicates that the gravitational mixing results in a more complete expulsion of the resident fluid from the Hele-Shaw cell. This observation may be of interest in the context of enhanced oil recovery or carbon sequestration applications.
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Logvinov, Oleg A. "Viscous fingering in poorly miscible power-law fluids." Physics of Fluids 34, no. 6 (June 2022): 063105. http://dx.doi.org/10.1063/5.0088487.
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A renowned problem of a viscous fluid displacement by a less viscous one from a Hele–Shaw cell is considered. Both fluids exhibit non-Newtonian properties: a power-law viscosity dependence on strain rates (Ostwald–de Waele rheology). A unified approach independent of particular rheology is applied to derive averaged two-dimensional equations of motion (so-called Hele–Shaw models). The equations are based on Reynolds class averaging procedure. Under these governing equations, linear stability analysis of the radial interface is conducted with a new key idea—possibility of characteristic size selection even in the absence of stabilizing factors such as surface tension and molecular diffusion. For proving this, proper boundary conditions are set on the interface, namely, the equality of full normal stresses including viscous ones, instead of the simple equality of pressures.
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Jangir, Pooja, Anushka Herale, Ratan Mohan, and Paresh Chokshi. "Role of viscoelastic fluid rheology in miscible viscous fingering." International Journal of Engineering Science 179 (September 2022): 103733. http://dx.doi.org/10.1016/j.ijengsci.2022.103733.
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Bogdan, Michał J., and Thierry Savin. "Fingering instabilities in tissue invasion: an active fluid model." Royal Society Open Science 5, no. 12 (December 2018): 181579. http://dx.doi.org/10.1098/rsos.181579.
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Metastatic tumours often invade healthy neighbouring tissues by forming multicellular finger-like protrusions emerging from the cancer mass. To understand the mechanical context behind this phenomenon, we here develop a minimalist fluid model of a self-propelled, growing biological tissue. The theory involves only four mechanical parameters and remains analytically trackable in various settings. As an application of the model, we study the evolution of a two-dimensional circular droplet made of our active and expanding fluid, and embedded in a passive non-growing tissue. This system could be used to model the evolution of a carcinoma in an epithelial layer. We find that our description can explain the propensity of tumour tissues to fingering instabilities, as conditioned by the magnitude of active traction and the growth kinetics. We are also able to derive predictions for the tumour size at the onset of metastasis, and for the number of subsequent invasive fingers. Our active fluid model may help describe a wider range of biological processes, including wound healing and developmental patterning.
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Biggins, John S., Z. Wei, and L. Mahadevan. "Fluid-driven fingering instability of a confined elastic meniscus." EPL (Europhysics Letters) 110, no. 3 (May 1, 2015): 34001. http://dx.doi.org/10.1209/0295-5075/110/34001.
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Zhang, Qing, Amin Amooie, Martin Z. Bazant, and Irmgard Bischofberger. "Growth morphology and symmetry selection of interfacial instabilities in anisotropic environments." Soft Matter 17, no. 5 (2021): 1202–9. http://dx.doi.org/10.1039/d0sm01706j.
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Patel, Shailesh. "SINGULAR PERTURBATION SOLUTION OF THE PROBLEM VISCOUS FINGERING PHENOMENON IN MULTIFLUID IMMISCIBLE FLOW." International Journal of Engineering Technologies and Management Research 5, no. 4 (February 26, 2020): 57–61. http://dx.doi.org/10.29121/ijetmr.v5.i4.2018.208.
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In this paper the phenomenon namely fingering which occurs in the flow problems of oil reservoir engineering has been discussed. The effects arises due to the fingering have been studied by using the Darcy’s law together with different kinds of suitable assumptions and conditions. The problem is then modeled into mathematical form which yields second order partial differential equation. The equation is then solved by using singular perturbation technique together with initial and boundary conditions. The solution is then interpreted in terms of fluid flow terms.
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Nasir, Muhammad, Ryuhei Yamaguchi, Yun She, Anindityo Patmonoaji, Mohammad Azis Mahardika, Weicen Wang, Zijing Li, Shintaro Matsushita, and Tetsuya Suekane. "Hydrodynamic Fingering Induced by Gel Film Formation in Miscible Fluid Systems: An Experimental and Mathematical Study." Applied Sciences 12, no. 10 (May 17, 2022): 5043. http://dx.doi.org/10.3390/app12105043.
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Hydrodynamic fingering induced by gel formation shares common features with growing biofilms, bacterial colonies, and the instability of a confined chemical garden. Fluid displacement with gel formation is also essential in various engineering applications, including CO2 leakage remediation from storage reservoirs and enhanced oil recovery. We conducted Hele-Shaw cell displacement experiments for a miscible fluid system using skim milk and aqueous citric acid solution. This study aimed to investigate the effects of gel film formation on the fingering instability of a miscible fluid system and develop a mathematical model of the sequential growth of gel film formation at the fingertip. We found that the gel film formation thickens with time, resulting in instability at the interface. A distinctive fingering pattern, resembling tentacles, appears where miscibility is suppressed, and the growth of the finger is localized at the fingertip. The finger width remains constant with increasing flow rate, whereas the number of fingers increases linearly before the fingers merge. The gap width significantly limits the finger width. Finally, a mathematical model of sequential film thickness growth for a bubble-like fingertip structure was developed. This model is based upon the interplay between the diffusion of citric acid through the existing gel film formation and elongation of the fingertip. The model provides an understanding of the fundamental mechanism of the growth of the bubble-like fingertip.
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An, Baizheng, Daniel Solorzano, and Qingwang Yuan. "Viscous Fingering Dynamics and Flow Regimes of Miscible Displacements in a Sealed Hele-Shaw Cell." Energies 15, no. 16 (August 10, 2022): 5798. http://dx.doi.org/10.3390/en15165798.
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Miscible viscous fingering occurs when a less viscous fluid displaces a more viscous one in porous media or a Hele–Shaw cell. Such flow instabilities are of particular interest in a variety of applications in flows and displacements in subsurface energy and environment systems. In this study, we investigate the miscible viscous fingering dynamics experimentally using water to displace glycerol in a sealed Hele–Shaw cell with two wells located in it instead of at the boundary or corners. We comprehensively examine the spatial and temporal variations of fingering dynamics, different flow regimes, and how they are affected by the water injection rate and control of pressure or rate at the outlet. Alongside the widely recognized diffusion-dominated and convection-dominated flow regimes, we identify three new regimes: a slow expansion regime prior to breakthrough, a rapid shrinkage regime immediately after breakthrough, and a uniform, slow expansion regime without fingering instability. Each regime is characterized by interesting flow dynamics, which has not been reported previously. The duration of each regime depends on the water injection rate and whether constant pressure or a constant production rate is applied at the outlet. The variations of swept area, interfacial length, and count of fingers are also quantitatively examined. This study provides new insights into the fundamental mechanisms for miscible fluid displacements in a variety of applications such as CO2 sequestration, hydrogen storage, enhanced oil recovery, and groundwater contaminate remediation.
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Araque-Martinez, Aura N., and Larry W. Lake. "The Effect of Compressibility and Outer Boundaries on Incipient Viscous Fingering." SPE Reservoir Evaluation & Engineering 24, no. 03 (April 7, 2021): 619–38. http://dx.doi.org/10.2118/201310-pa.
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Summary The knowledge of the effects of instability and heterogeneity on displacements, primarily enhanced oil recovery, and carbon dioxide storage are well known, although they remain difficult to predict. The usual recourse to modeling these effects is through numerical simulation. Simulation remains the gold standard for prediction; however, its results lack generality, being case-specific. There are also several analytic models for displacements that are usually more informative than simulation results. However, these methods apply to steady-state, incompressible flow. Carbon dioxide injection for storage uses compressible fluids and, in the absence of producers, will not approach steady-state flow (Wu et al. 2017). Consequently, it is unlikely that storage will be in reservoirs of open boundaries (steady-state flow). Flow of compressible fluid necessitates the use of closed or partially sealed boundaries, a factor that is consistent with compressible flow. This work deals with the conditions that cause the onset of incipient viscous fingering or Saffman-Taylor (ST) instability. The actual growth and propagation of fingers, a subject of much recent literature, is not discussed here. The original ST formalism of M > 1 for gravity-free flow is highly restrictive: it is for linear flow of nonmixing incompressible fluids in steady-state flow. In this work, we relax the incompressible flow restriction and thereby broaden the ST criterion to media that have sealing and/or partially sealing outer boundaries. We use the nonlinear partial differential equation for linear flow and developed analytic solutions for a tracer flow analog and also for a two-fluid compressible flow. The analysis is restricted to stabilized flow and to constant compressibility fluids, but we are not restricted to small compressibility fluids. There is no transition (mixing) zone between displacing and displaced fluids; the displacement is piston-like. The absence of a transition zone means that the results apply to both miscible and immiscible displacements, absent dispersion, or local capillary pressure. The assumption of a sharp interface is to focus on the combined effect of mobility ratio and compressibility. We use the product of the fluid compressibility and pressure drop (cfΔP) to differentiate the compressibility groups (Dake 1978; Dranchuk and Quon 1967), where ΔP is defined as the pressure drop within the specific fluid region. The results will be based on proposed analytical solutions compared to numerical simulation. The proposed formulation is less restrictive than the original ST formalism of M > 1 and allows evaluation of viscous fingering initiation or ST stability criterion in the presence of different boundary conditions (open vs. closed boundaries) with compressible fluids under the stated assumptions, which is the scope of this work. The key contribution here is the effect of external boundaries, which consequently makes necessary the use of compressible fluids. Absent compressibility, the necessary condition for the growth of a viscous finger is simply the mobility ratio, M > 1. It is the objective of this work to study how the ST criterion is affected by the presence of sealing and partially sealing outer boundaries with the consequent inclusion of compressible flows as in carbon dioxide storage and enhanced oil recovery by gas injection. The results show that adding compressibility always makes displacements more unstable for stabilized background flow, even for a favorable mobility ratio (M < 1) at extremely large compressibility (e.g., cf > 5×10−3 1/psi). For a sealed external boundary (no production or leakage), displacements will become more stable as a front approaches an external boundary for all mobility ratios (M) investigated.
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Austin-Adigio, Maureen, and Ian D. Gates. "Thermal Viscous Fingering in Thermal Recovery Processes." Energies 13, no. 18 (September 22, 2020): 4986. http://dx.doi.org/10.3390/en13184986.
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Heat and fluid flow at the edge of steam chambers found in thermal recovery processes such as steam-assisted gravity drainage and cyclic steam stimulation remain unresolved. Given the multiple phases present and contrast of thermophysical properties, it remains unclear where instabilities occur within this thin, yet critical, zone of the process. In the research reported here, heat and fluid flow are examined in vertical and horizontal sections of a steam chamber to understand the differences between the two orientations by using detailed and fine-gridded thermal reservoir simulation models. The results show that heat transfer in vertical and horizontal directions are different with greater heat transfer found in the vertical orientation. In the vertical direction, heat transfer occurs with mobilized bitumen draining with subsequent steam moving into the emptied pore space. Conduction beyond the edge of the chamber dominates and heated, low viscosity bitumen fingers into cold, higher viscosity bitumen at the edge of the chamber. Relative permeability effects are observed which can interfere with enhanced oil mobility.
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Wylie, Jonathan J., and John R. Lister. "The effects of temperature-dependent viscosity on flow in a cooled channel with application to basaltic fissure eruptions." Journal of Fluid Mechanics 305 (December 25, 1995): 239–61. http://dx.doi.org/10.1017/s0022112095004617.
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A theoretical description is given of pressure-driven viscous flow of an initially hot fluid through a planar channel with cold walls. The viscosity of the fluid is assumed to be a function only of its temperature. If the viscosity variations caused by the cooling of the fluid are sufficiently large then the relationship between the pressure drop and the flow rate is non-monotonic and there can be more than one steady flow for a given pressure drop. The linear stability of steady flows to two-dimensional and three-dimensional disturbances is calculated. The region of instability to two-dimensional disturbances corresponds exactly to those flows in which an increase in flow rate leads to a decrease in pressure drop. At higher viscosity contrasts some flows are most unstable to three-dimensional (fingering) instabilities analogous, but not identical, to Saffman-Taylor fingering. A cross-channel-averaged model is derived and used to investigate the finite-amplitude evolution.
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Hong, Ting Fu, Jik Chang Leong, Long Kai Lin Liou, Chien Hsiung Tsai, and Lung Ming Fu. "Magnetic Microfluidic Mixer." Key Engineering Materials 483 (June 2011): 354–58. http://dx.doi.org/10.4028/www.scientific.net/kem.483.354.
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This paper presents a novel simple Y-type micromixer based on stable water suspensions of magnetic nanoparticles (i.e. ferrofluids). An electromagnet driven by an AC power source is used to induce transient interactive flows between a ferrofluid and DI water. The alternative magnetic field causes the ferrofluid to expand significantly and uniformly toward DI water associated with a great number of extremely fine fingering structures on the interface in the microchannel. Different magnetic strengths of the electromagnet were applied by adjusting the magnitude of AC supplied power at frequency of 45 Hz. The results show, due to the magnetic fields, two fluids mix with each other efficiently (mixing ratio can be as high as 95%). When the magnetic field is high enough, the labyrinthine fingering instability take place. This phenomenon is favorable for the fluid mixing. In addition, the increasing magnetic field enhances the efficiency of the mixing apparently.
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Sweeney, H., R. R. Kerswell, and T. Mullin. "Rayleigh–Taylor instability in a finite cylinder: linear stability analysis and long-time fingering solutions." Journal of Fluid Mechanics 734 (October 9, 2013): 338–62. http://dx.doi.org/10.1017/jfm.2013.492.
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AbstractWe consider the Rayleigh–Taylor instability problem of two initially stationary immiscible viscous fluids positioned with the denser above the less dense in a finite circular cylinder, such that their starting fluid–fluid interface is the horizontal midplane of the cylinder. The ensuing linear instability problem has a five-dimensional parameter space – defined by the density ratio, the viscosity ratio, the cylinder aspect ratio, the surface tension between the fluids and the ratio of viscous to gravitational time scales – of which we explore only part, motivated by recent experiments where viscous fluids exchange in vertical tubes (Beckett et al., J. Fluid Mech., 2011, vol. 682, pp. 652–670). We find that for these experiments, the instability is invariably ‘side-by-side’ (of azimuthal wavenumber 1 type) but we also uncover parameter regions where the preferred instability is axisymmetric. The fact that both ‘core-annular’ (axisymmetric) and ‘side-by-side’ (asymmetric) long-time flows are seen experimentally highlights the fact that the initial Rayleigh–Taylor instability of the interface does not determine the long-time flow configuration in these situations. Finally, long-time flow solutions are presented on the basis that they will be slowly varying fingering solutions.
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HE, ANDONG, and ANDREW BELMONTE. "Inertial effects on viscous fingering in the complex plane." Journal of Fluid Mechanics 668 (January 26, 2011): 436–45. http://dx.doi.org/10.1017/s0022112010005859.
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We present a nonlinear unsteady Darcy's equation which includes inertial effects for flows in a porous medium or Hele-Shaw cell and discuss the conditions under which it reduces to the classical Darcy's law. In the absence of surface tension we derive a generalized Polubarinova–Galin equation in a circular geometry, using the method of conformal mapping. The linear stability of the base-flow state is examined by perturbing the corresponding conformal map. We show that inertia always has a tendency to stabilize the interface, regardless of whether a less viscous fluid is displacing a more viscous fluid or vice versa.