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Journal articles on the topic 'Flow of immiscible fluids'

Author: Grafiati

Published: 28 June 2021

Last updated: 3 February 2022

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1

Mateen, Abdul. "Transient Magnetohydrodynamic flow of two immiscible Fluids through a horizontal channel." International Journal of Engineering Research 3, no. 1 (January 1, 2014): 13–17. http://dx.doi.org/10.17950/ijer/v3s1/104.

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2

Deng, Yongbo, Zhenyu Liu, and Yihui Wu. "Topology Optimization of Capillary, Two-Phase Flow Problems." Communications in Computational Physics 22, no. 5 (October 31, 2017): 1413–38. http://dx.doi.org/10.4208/cicp.oa-2017-0003.

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AbstractThis paper presents topology optimization of capillary, the typical two-phase flow with immiscible fluids, where the level set method and diffuse-interface model are combined to implement the proposed method. The two-phase flow is described by the diffuse-interface model with essential no slip condition imposed on the wall, where the singularity at the contact line is regularized by the molecular diffusion at the interface between two immiscible fluids. The level set method is utilized to express the fluid and solid phases in the flows and the wall energy at the implicit fluid-solid interface. Based on the variational procedure for the total free energy of two-phase flow, the Cahn-Hilliard equations for the diffuse-interface model are modified for the two-phase flow with implicit boundary expressed by the level set method. Then the topology optimization problem for the two-phase flow is constructed for the cost functional with general formulation. The sensitivity analysis is implemented by using the continuous adjoint method. The level set function is evolved by solving the Hamilton-Jacobian equation, and numerical test is carried out for capillary to demonstrate the robustness of the proposed topology optimization method. It is straightforward to extend this proposed method into the other two-phase flows with two immiscible fluids.

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3

Hasnain, A., E. Segura, and K. Alba. "Buoyant displacement flow of immiscible fluids in inclined pipes." Journal of Fluid Mechanics 824 (July 10, 2017): 661–87. http://dx.doi.org/10.1017/jfm.2017.367.

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We experimentally study the iso-viscous displacement flow of two immiscible Newtonian fluids in an inclined pipe. The fluids have the same viscosity but different densities. The displacing fluid is denser than the displaced fluid and is placed above the displaced fluid (i.e. a density-unstable configuration) in a pipe with small diameter-to-length ratio ($\unicode[STIX]{x1D6FF}\ll 1$). In the limit considered, six dimensionless groups describe these flows: the pipe inclination angle, $\unicode[STIX]{x1D6FD}$, an Atwood number, $At$, a Reynolds number, $Re$, a densimetric Froude number, $Fr$, a capillary number, $Ca$, and the fluids static contact angle, $\unicode[STIX]{x1D703}$. Our experiments, carried out in an acrylic pipe using wetting salt-water solutions displacing non-wetting oils, cover a fairly broad range of these parameters. Completely different patterns than those of miscible flows have been observed, governed by distinct dynamics. The wetting properties of the displacing liquid and fluids immiscibility are found to significantly increase the efficiency of the displacement. During the early stage of the displacement, strong shearing is observed between the heavy and light layers, promoting Kelvin–Helmholtz instabilities. At later stages, the intensity of Kelvin–Helmholtz instabilities is reduced. However, surface-tension-driven Rayleigh-type instabilities will remain active causing droplet shedding (pearling) at displaced fluid receding contact lines. The speed of the advancing displacing front (inversely related to the displacement efficiency) is measured and characterized in dimensionless maps suggesting high values at low ranges of $Re$ and $Ca$. Depending on the degree of flow stability and droplet formation, three major flow regimes namely viscous, transitionary and dispersed are characterized and classified in dimensionless maps. In the absence of a mean imposed velocity (exchange flow), it is found that capillary blockage may occur hindering Rayleigh–Taylor instabilities.

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4

Yadav, Pramod Kumar, and Sneha Jaiswal. "Influence of an inclined magnetic field on the Poiseuille flow of immiscible micropolar–Newtonian fluids in a porous medium." Canadian Journal of Physics 96, no. 9 (September 2018): 1016–28. http://dx.doi.org/10.1139/cjp-2017-0998.

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The present problem is concerned with two-phase fluid flow through a horizontal porous channel in the presence of uniform inclined magnetic field. The micropolar fluid or Eringen fluid and Newtonian viscous fluid are flowing in the upper and lower regions of the horizontal porous channel, respectively. In this paper, the permeability of each region of the horizontal porous channel has been taken to be different. The effects of various physical parameters like angles of inclination of magnetic field, viscosity ratio, micropolarity parameter, etc., on the velocities, micro-rotational velocity of two immiscible fluids in horizontal porous channel, wall-shear stress, and flow rate have been discussed. The result obtained for immiscible micropolar–Newtonian fluids are compared with the results of two immiscible Newtonian fluids. The obtained result may be used in production of oil from oil reservoirs, purification of contaminated ground water, etc.

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5

Salin, D., and L. Talon. "Revisiting the linear stability analysis and absolute–convective transition of two fluid core annular flow." Journal of Fluid Mechanics 865 (February 26, 2019): 743–61. http://dx.doi.org/10.1017/jfm.2019.71.

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Numerous experimental, numerical and theoretical studies have shown that core annular flows can be unstable. This instability can be convective or absolute in different situations: miscible fluids with matched density but different viscosities, creeping flow of two immiscible fluids or buoyant flow along a fibre. The analysis of the linear stability of the flow equation of two fluids injected in a co-current and concentric manner into a cylindrical tube leads to a rather complex eigenvalue problem. Until now, all analytical solution to this problem has involved strong assumptions (e.g. lack of inertia) or approximations (e.g. developments at long or short wavelengths) even for axisymmetric disturbances. However, in this latter case, following C. Pekeris, who obtained, almost seventy years ago, an elegant explicit solution for the dispersion relationship of the flow of a single fluid, we derive an explicit solution for the more general case of two immiscible fluids of different viscosity, density and inertia separated by a straight interface. This formulation is well adapted to commercial software. First, we review the creeping flow limit (zero Reynolds number) of two immiscible fluids as it is used in microfluidics. Secondly, we consider the case of two fluids of different viscosities but of the same density in the absence of surface tension and also without diffusion (i.e. miscible fluids with infinite Schmidt number). In both cases, we study the transition from convective to absolute instability according to the different control parameters.

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6

Abd Elmaboud, Y., Sara I. Abdelsalam, Kh S. Mekheimer, and Kambiz Vafai. "Electromagnetic flow for two-layer immiscible fluids." Engineering Science and Technology, an International Journal 22, no. 1 (February 2019): 237–48. http://dx.doi.org/10.1016/j.jestch.2018.07.018.

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7

Sahu, Kirti Chandra, and Rama Govindarajan. "Linear stability analysis and direct numerical simulation of two-layer channel flow." Journal of Fluid Mechanics 798 (June 13, 2016): 889–909. http://dx.doi.org/10.1017/jfm.2016.346.

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We study the stability of two-fluid flow through a plane channel at Reynolds numbers of 100–1000 in the linear and nonlinear regimes. The two fluids have the same density but different viscosities. The fluids, when miscible, are separated from each other by a mixed layer of small but finite thickness, across which the viscosity changes from that of one fluid to that of the other. When immiscible, the interface is sharp. Our study spans a range of Schmidt numbers, viscosity ratios and locations and thicknesses of the mixed layer. A region of instability distinct from that of the Tollmien–Schlichting mode is obtained at moderate Reynolds numbers. We show that the overlap of the layer of viscosity-stratification with the critical layer of the dominant disturbance provides a mechanism for this instability. At very low values of diffusivity, the miscible flow behaves exactly like the immiscible one in terms of stability characteristics. High levels of miscibility make the flow more stable. At intermediate levels of diffusivity however, in both linear and nonlinear regimes, miscible flow can be more unstable than the corresponding immiscible flow without surface tension. This difference is greater when the thickness of the mixed layer is decreased, since the thinner the layer of viscosity stratification, the more unstable the miscible flow. In direct numerical simulations, disturbance growth occurs at much earlier times in the miscible flow, and also the miscible flow breaks spanwise symmetry more readily to go into three-dimensionality. The following observations hold for both miscible and immiscible flows without surface tension. The stability of the flow is moderately sensitive to the location of the interface between the two fluids. The response is non-monotonic, with the least stable location of the layer being mid-way between the wall and the centreline. As expected, flow at higher Reynolds numbers is more unstable.

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8

Kozubková, Milada, Jana Jablonská, Marian Bojko, František Pochylý, and Simona Fialová. "Multiphase Flow in the Gap Between Two Rotating Cylinders." MATEC Web of Conferences 328 (2020): 02017. http://dx.doi.org/10.1051/matecconf/202032802017.

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The research of liquids composed of two (or more) mutually immiscible components is a new emerging area. These liquids represent new materials, which can be utilized as lubricants, liquid seals or as fluid media in biomechanical devices. The investigation of the problem of immiscible liquids started some years ago and soon it was evident that it will have a great application potential. Recently, there has been an effort to use ferromagnetic or magnetorheological fluids in the construction of dumpers or journal bearings. Their advantage is a significant change in dynamic viscosity depending on magnetic induction. In combination with immiscible liquids, qualitatively new liquids can be developed for future technologies. In our case, immiscible fluids increase the dynamic properties of the journal hydrodynamic bearing. The article focuses on the stability of single-phase and subsequently multiphase flow of liquids in the gap between two concentric cylinders, one of which rotates. The aim of the analysis was to study the effect of viscosity and density on the stability/instability of the flow, which is manifested by Taylor vortices. Methods of experimental and mathematical analysis were used for the analysis in order to verify mathematical models of laminar and turbulent flow of immiscible liquids.

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9

Lemenand, Thierry, Pascal Dupont, Dominique Della Valle, and Hassan Peerhossaini. "Turbulent Mixing of Two Immiscible Fluids." Journal of Fluids Engineering 127, no. 6 (June 10, 2005): 1132–39. http://dx.doi.org/10.1115/1.2073247.

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The emulsification process in a static mixer HEV (high-efficiency vortex) in turbulent flow is investigated. This new type of mixer generates coherent large-scale structures, enhancing momentum transfer in the bulk flow and hence providing favorable conditions for phase dispersion. We present a study of the single-phase flow that details the flow structure, based on LDV measurements, giving access on the scales of turbulence. In addition, we discuss the liquid-liquid dispersion of oil in water obtained at the exit of the mixer/emulsifier. The generation of the dispersion is characterized by the Sauter diameter and described via a size-distribution function. We are interested in a local turbulence analysis, particularly the spatial structure of the turbulence and the turbulence spectra, which give information about the turbulent dissipation rate. Finally, we discuss the emulsifier efficiency and compare the HEV performance with existing devices.

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10

IWATSUKI, HIROKI, NAOTO GOHKO, HIROSHI KIMURA, YUICHI MASUBUCHI, JUN-ICHI TAKIMOTO, and KIYOHITO KOYAMA. "MOLECULAR ORIENTATION AND ELECTROHYDRODYNAMIC FLOW IN HOMOGENEOUS ER FLUIDS." International Journal of Modern Physics B 15, no. 06n07 (March 20, 2001): 973–79. http://dx.doi.org/10.1142/s0217979201005490.

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Homogeneous ER fluid is an ER fluid which consists of a homogeneous fluid only; it is neither a suspension nor a blend of immiscible liquids. Various liquid crystals are typical examples of homogeneous ER fluids. Recently, we have found that urethane-modified polypropylene glycol (UPPG) is one of the very few examples of homogeneous ER fluids which show no liquid crystalline order. In order to clarify the mechanism of the ER effect in this fluid, we have studied, in this paper, electrohydrodynamic flow under shear and electric field.

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11

LIN, CHENFANG. "MODELING THE FLOW OF IMMISCIBLE FLUIDS IN SOILS." Soil Science 143, no. 4 (April 1987): 293–300. http://dx.doi.org/10.1097/00010694-198704000-00006.

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12

Hamza, F., A. M. Abd El-Latief, and W. Khatan. "Thermomechanical Fractional Model of Two Immiscible TEMHD." Advances in Materials Science and Engineering 2015 (2015): 1–16. http://dx.doi.org/10.1155/2015/391454.

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We introduce a mathematical model of unsteady thermoelectric MHD flow and heat transfer of two immiscible fractional second-grade fluids, with thermal fractional parametersαiand mechanical fractional parametersβi,i=1,2. The Laplace transform with respect to time is used to obtain the solution in the transformed domain. The inversion of Laplace transform is obtained by using numerical method based on a Fourier-series expansion. The numerical results for temperature, velocity, and the stress distributions are represented graphically for different values ofαiandβi. The graphs describe the fractional thermomechanical parameters effect on the case of two immiscible fluids and the case of a single fluid.

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13

Ahn, Haejin, Seon-Ok Kim, Minhee Lee, and Sookyun Wang. "Migration and Residual Trapping of Immiscible Fluids during Cyclic Injection: Pore-Scale Observation and Quantitative Analysis." Geofluids 2020 (July 16, 2020): 1–13. http://dx.doi.org/10.1155/2020/4569208.

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Geological CO2 sequestration (GCS) is one of the most promising technologies for mitigating greenhouse gas emission into the atmosphere. In GCS operations, residual trapping is the most favorable form of a trapping mechanism because of its storage security and capacity. In this study, the effects of cyclic injection of CO2-water on the immiscible displacement and residual trapping in pore networks were examined. For the purpose, a series of injection experiments with five sets of drainage-imbibition cycles were performed using 2D transparent micromodels and a pair of proxy fluids, n-hexane, and deionized water. The multiphase flow and immiscible displacement phenomena during drainage and imbibition processes in pore networks were visually observed, and the temporal and spatial changes in distribution and saturation of the two immiscible fluids were quantitatively estimated at the pore scale using image analysis techniques. The results showed that the mobile region of invading fluids decreased asymptotically as the randomly diverged flow paths gradually converged into less ramified ones over multiple cycles. Such decrease was accompanied by a gradual increase of the immobile region, which consists of tiny blobs and clusters of immiscible fluids. The immobile region expanded as streams previously formed by the insertion of one fluid dispersed into numerous isolated, small-scale blobs as the other fluid was newly injected. These processes repeated until the immobile region approached the main flow channels. The observations and analyses in this study implied that the application of cyclic injection in GCS operations may be used to store large-scale CO2 volume in small-scale dispersed forms, which may significantly improve the effectiveness and security of geological CO2 sequestration.

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14

El-Khatib, Noaman A. F. "Immiscible Displacement of Non-Newtonian Fluids in Communicating Stratified Reservoirs." SPE Reservoir Evaluation & Engineering 9, no. 04 (August 1, 2006): 356–65. http://dx.doi.org/10.2118/93394-pa.

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Summary The displacement of non-Newtonian power-law fluids in communicating stratified reservoirs with a log-normal permeability distribution is studied. Equations are derived for fractional oil recovery, water cut, injectivity ratio, and pseudorelative permeability functions, and the performance is compared with that for Newtonian fluids. Constant-injection-rate and constant-total-pressure-drop cases are studied. The effects of the following factors on performance are investigated: the flow-behavior indices, the apparent mobility ratio, the Dykstra-Parsons variation coefficient, and the flow rate. It was found that fractional oil recovery increases for nw > no and decreases for nw < no, as compared with Newtonian fluids. For the same ratio of nw /no, oil recovery increases as the apparent mobility ratio decreases. The effect of reservoir heterogeneity in decreasing oil recovery is more apparent for the case of nw > no . Increasing the total injection rate increases the recovery for nw > no, and the opposite is true for nw < no . It also was found that the fractional oil recovery for the displacement at constant total pressure drop is lower than that for the displacement at constant injection rate, with the effect being more significant when nw < no. Introduction Many of the fluids injected into the reservoir in enhanced-oil-recovery (EOR)/improved-oil-recovery (IOR) processes such as polymer, surfactant, and alkaline solutions may be non-Newtonian; in addition, some heavy oils exhibit non-Newtonian behavior. Flow of non-Newtonian fluids in porous media has been studied mainly for single-phase flow. Savins (1969) presented a comprehensive review of the rheological behavior of non-Newtonian fluids and their flow behavior through porous media. van Poollen and Jargon (1969) presented a finite-difference solution for transient-pressure behavior, while Odeh and Yang (1979) derived an approximate closed-form analytical solution of the problem. Chakrabarty et al. (1993) presented Laplace-space solutions for transient pressure in fractal reservoirs. For multiphase flow of non-Newtonian fluids in porous media, the problem was considered only for single-layer cases. Salman et al. (1990) presented the modifications for the Buckley-Leverett frontal-advance method and for the JBN relative permeability method for non-Newtonian power-law fluid displacing a Newtonian fluid. Wu et al. (1992) studied the displacement of a Bingham non-Newtonian fluid (oil) by a Newtonian fluid (water). Wu and Pruess (1998) introduced a numerical finite-difference solution for displacement of non-Newtonian fluids in linear systems and in a five-spot pattern. Yi (2004) developed a Buckley-Leverett model for displacement by a Newtonian fluid of a fracturing fluid having a Herschel-Bulkley rheological behavior. An iterative procedure was used to obtain a solution of the model. The methods available in the literature to predict linear waterflooding performance in stratified reservoirs are grouped into two categories depending on the assumption of communication or no communication between the different layers. In the case of noncommunicating systems, no vertical crossflow is permitted between the adjacent layers. The Dykstra-Parsons (1950) method is the basis for performance prediction in noncommunicating stratified reservoirs.

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15

Zeybek, M., and Y. C. Yortsos. "Parallel flow in Hele-Shaw cells." Journal of Fluid Mechanics 241 (August 1992): 421–42. http://dx.doi.org/10.1017/s0022112092002106.

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We consider the parallel flow of two immiscible fluids in a Hele-Shaw cell. The evolution of disturbances on the fluid interfaces is studied both theoretically and experimentally in the large-capillary-number limit. It is shown that such interfaces support wave motion, the amplitude of which for long waves is governed by a set of KdV and Airy equations. The waves are dispersive provided that the fluids have unequal viscosities and that the space occupied by the inner fluid does not pertain to the Saffman-Taylor conditions (symmetric interfaces with half-width spacing). Experiments conducted in a long and narrow Hele-Shaw cell appear to validate the theory in both the symmetric and the non-symmetric cases.

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16

Srinivas, J., J. V. Ramana Murthy, and Ali J. Chamkha. "Analysis of entropy generation in an inclined channel flow containing two immiscible micropolar fluids using HAM." International Journal of Numerical Methods for Heat & Fluid Flow 26, no. 3/4 (May 3, 2016): 1027–49. http://dx.doi.org/10.1108/hff-09-2015-0354.

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Purpose – The purpose of this paper is to examine the flow, heat transfer and entropy generation characteristics for an inclined channel of two immiscible micropolar fluids. Design/methodology/approach – The flow region consists of two zones, the flow of the heavier fluid taking place in the lower zone. The flow is assumed to be governed by Eringen’s micropolar fluid flow equation. The resulting governing equations are then solved using the homotopy analysis method. Findings – The following findings are concluded: first, the entropy generation rate is more near the plates in both the zones as compared to that of the interface. This indicates that the friction due to surface on the fluids increases entropy generation rate. Second, the entropy generation rate is more near the plate in Zone I than that of Zone II. This may be due to the fact that the fluid in Zone I is more viscous. This indicates the more the viscosity of the fluid is, the more the entropy generation. Third, Bejan number is the maximum at the interface of the fluids. This indicates that the amount of exergy (available energy) is maximum and irreversibility is minimized at the interface between the fluids. Fourth, as micropolarity increases, entropy generation rate near the plates decreases and irreversibility decreases. This indicates an important industrial application for micropolar fluids to use them as a good lubricant. Originality/value – The problem is original as no work has been reported on entropy generation in an inclined channel with two immiscible micropolar fluids.

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17

Siddiqui, A. M., Q. A. Azim, and M. Imran. "Exact solutions for n-layer concentric flow of PTT fluids through a cylindrical pipe." Canadian Journal of Physics 98, no. 2 (February 2020): 134–41. http://dx.doi.org/10.1139/cjp-2019-0068.

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Flows of multiple layers of fluids are encountered in many industrial and manufacturing processes. This paper investigates the concentric n-layer flow for Phan–Thien–Tanner (PTT) fluids through a cylindrical pipe. Finitely many immiscible non-Newtonian fluids are considered to be flowing concentrically in a tube. The flow is modelled using the exponential PTT fluid model and exact solutions for velocity fields and volume flow rates are computed. It has been shown that the corresponding results for linear PTT fluid model as well as Newtonian fluids can be deduced from the obtained expressions, and that they match with the present literature. It has also been observed that for such layered flow, the non-Newtonian parameters significantly affect the flow of fluids in adjacent layers. The effects of involved parameters on the velocity profiles are also shown graphically. We show that a unique velocity maximum exists along the axis of the pipe. Moreover, it is observed with the help of an example that layer thickness can be adjusted to obtain maximal flow rate with a given pressure gradient.

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18

Srinivasu, M., Devulapalli R.V.S.R.K.Sastry, and G. V.S.R.Deekshitulu. "Ohmic Heating Effect on Magneto Hydrodynamic Marangoni Mixed Convection Boundary Layer Nanofluid Flow." International Journal of Engineering & Technology 7, no. 4.10 (October 2, 2018): 666. http://dx.doi.org/10.14419/ijet.v7i4.10.21308.

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In surface driven flows, dissipative layers which occur along the surface of two immiscible fluids are known as marangoni boundary layers. Mixed connection takes place when buoyancy forces act beside marangoni effect. Consider a nanofluid flow along a flat surface experiencing marangoni convection with ohmic dissipation and magnetic field. Copper and Alumina are the nanoparticles with water as base fluid. The similarity equations are solved numerically by BVP solver ‘bcp4c”. The flow characteristics are analyzed graphically and discussed.

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19

Chamkha, Ali J., J. C. Umavathi, and Abdul Mateen. "Oscillatory Flow and Heat Transfer in Two Immiscible Fluids." International Journal of Fluid Mechanics Research 31, no. 1 (2004): 13–36. http://dx.doi.org/10.1615/interjfluidmechres.v31.i1.20.

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20

Murthy, J. V. Ramana, J. Srinivas, and K. S. Sai. "FLOW OF IMMISCIBLE MICROPOLAR FLUIDS BETWEEN TWO POROUS BEDS." Journal of Porous Media 17, no. 4 (2014): 287–300. http://dx.doi.org/10.1615/jpormedia.v17.i4.20.

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21

Misztal, Marek Krzysztof, Kenny Erleben, Adam Bargteil, Jens Fursund, Brian Bunch Christensen, Jakob Andreas Baerentzen, and Robert Bridson. "Multiphase Flow of Immiscible Fluids on Unstructured Moving Meshes." IEEE Transactions on Visualization and Computer Graphics 20, no. 1 (January 2014): 4–16. http://dx.doi.org/10.1109/tvcg.2013.97.

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22

Tigrine, Z., F. Mokhtari, A. Bouabdallah, and M. Mahloul. "Experiments on two immiscible fluids in spherical Couette flow." Acta Mechanica 225, no. 1 (August 29, 2013): 233–42. http://dx.doi.org/10.1007/s00707-013-0960-9.

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Chamkha, Ali J. "Flow of Two-Immiscible Fluids in Porous and Nonporous Channels." Journal of Fluids Engineering 122, no. 1 (December 6, 1999): 117–24. http://dx.doi.org/10.1115/1.483233.

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This study considers steady, laminar flow of two viscous, incompressible, electrically-conducting and heat-generating or absorbing immiscible fluids in an infinitely-long, impermeable parallel-plate channel filled with a uniform porous medium. A magnetic field of uniform strength is applied normal to the flow direction. The channel walls are assumed to be electrically nonconducting and are maintained at two different temperatures. When present, the porous medium is assumed to act as an electrical insulator and that it is in local thermal equilibrium with the fluid. The transport properties of both fluids are assumed to be constant. This study is expected to be useful in understanding the influence of the presence of slag layers on the flow and heat transfer aspects of coal-fired Magnetohydrodynamic (MHD) generators when the porous medium is absent and the effects of thermal buoyancy and a magnetic field on enhanced oil recovery and filtration systems where the porous medium is present. The problem is formulated by employing the balance laws of mass, linear momentum, and energy for both phases. Continuous conditions for the velocity and temperature as well as the shear stress and heat flux of both phases at the interface are employed. The resulting governing ordinary differential equations are solved numerically subject to the boundary and interface conditions for the velocity and temperature distributions of both fluids in the channel. Analytical solutions for a special case of the problem where the porous medium is absent or only its inertia effect is neglected are obtained. Comparisons with previously reported velocity profiles are performed and excellent agreements are obtained. A parametric study illustrating the influence of the physical parameters involved in the problem is conducted and the results are presented graphically and discussed. [S0098-2202(00)02101-5]

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OZTEKIN, A., B. R. SEYMOUR, and E. VARLEY. "Self-similar flows of multi-phase immiscible fluids." European Journal of Applied Mathematics 11, no. 6 (December 2000): 529–59. http://dx.doi.org/10.1017/s0956792500004289.

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Exact analytical representations are obtained describing self-similar unsteady flows of multi-phase immiscible fluids in the vicinity of non-circular, but constant strength, fronts. It is assumed that Darcy's law holds for each phase and that the mobilities are known functions of the saturations. Equivalent representations are obtained for Hele-Shaw cell flows that are produced when a viscous fluid is injected into a region containing some other viscous fluid. The fluids may be Newtonian fluids or non-Newtonian fluids for which the coefficients of viscosity depend on the shear stress. Even though the flows are unsteady and two dimensional, the representations are obtained by using hodograph techniques.

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WANG, AN-LIN, RUO-FAN QIU, and QIANG CHEN. "AN LBM-BASED INVESTIGATION METHOD FOR THERMAL IMMISCIBLE MIXTURE FLUID FLOW IN RECTANGULAR MULTI-JET CAVITY." International Journal of Modern Physics B 28, no. 01 (December 11, 2013): 1350198. http://dx.doi.org/10.1142/s0217979213501981.

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An investigation method for thermal immiscible mixture fluid flow in rectangular multi-jet cavity using lattice Boltzmann method (LBM) is presented to study influence of controllable factors on quality of mixture generated from the cavity. For immiscible mixture flow, contact area of fluids has great effect on generated mixture. The basic idea is to investigate the relationship between controllable factors and contact area of key components. The contact area is obtained through numerical simulation by an improved LBM, in which temperature equation is extended to multicomponent system. A case study of thermal mixture flow in three-jet cavity using the present method is shown.

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Coveney, P. V., J. B. Maillet, J. L. Wilson, P. W. Fowler, O. Al-Mushadani, and B. M. Boghosian. "Lattice-Gas Simulations of Ternary Amphiphilic Fluid Flow in Porous Media." International Journal of Modern Physics C 09, no. 08 (December 1998): 1479–90. http://dx.doi.org/10.1142/s0129183198001345.

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We develop our existing two-dimensional lattice-gas model to simulate the flow of single phase, binary immiscible and ternary amphiphilic fluids. This involves the inclusion of fixed obstacles on the lattice, together with the inclusion of "no-slip" boundary conditions. Here we report on preliminary applications of this model to the flow of such fluids within model porous media. We also construct fluid invasion boundary conditions, and the effects of invading aqueous solutions of surfactant on oil-saturated rock during imbibition and drainage are described.

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Coskun, S. B., and T. Tokdemir. "Modelling of Permeation Grouting Through Soils." Journal of Applied Engineering Sciences 10, no. 1 (May 1, 2020): 11–16. http://dx.doi.org/10.2478/jaes-2020-0003.

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AbstractIn this study, mathematical modeling of permeation grouting through fully saturated soil is proposed based on immiscible multiphase flow theory. Grout flow in the medium is modeled together with the existing water as the simultaneous flow of two immiscible fluids. In the model, the porous medium is assumed as isotropic and rigid, fluids are assumed as incompressible and capillary pressure is assumed as negligible. Governing equations are discretized using upstream weighted finite element technique and results show that, proposed models give good results and may be used in the numerical simulation of grouting through fully saturated soils.

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Xu, Peng, Ming-Zhou Yu, Shu-Xia Qiu, and Bo-Ming Yu. "Monte Carlo simulation of a two-phase flow in an unsaturated porous media." Thermal Science 16, no. 5 (2012): 1382–85. http://dx.doi.org/10.2298/tsci1205382x.

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Relative permeability is a significant transport property which describes the simultaneous flow of immiscible fluids in porous media. A pore-scale physical model is developed for the two-phase immiscible flow in an unsaturated porous media according to the statistically fractal scaling laws of natural porous media, and a predictive calculation of two-phase relative permeability is presented by Monte Carlo simulation. The tortuosity is introduced to characterize the highly irregular and convoluted property of capillary pathways for fluid flow through a porous medium. The computed relative permeabilities are compared with empirical formulas and experimental measurements to validate the current model. The effect of fractal dimensions and saturation on the relative permeabilities is also discussed

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29

Khan, Zeeshan, Nasser Tairan, Wali Khan Mashwani, Haroon Ur Rasheed, Habib Shah, and Waris Khan. "MHD and Slip Effect on Two-immiscible Third Grade Fluid on Thin Film Flow over a Vertical Moving Belt." Open Physics 17, no. 1 (October 4, 2019): 575–86. http://dx.doi.org/10.1515/phys-2019-0059.

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Abstract The present paper related to thin film flows of two immiscible third grade fluids past a vertical moving belt with slip conditions in the presence of uniform magnetic field. Immiscible fluids we mean superposed fluids of different densities and viscosities. The basic governing equations of continuity, momentum and energy are incorporated. The modeled coupled equations are solved analytically by using Adomian Decomposition Method (ADM) along with Homotopy Analysis Method (HAM). The residual errors show the authentication of the present work. For comparison, numerical method (ND-Solve) is also applied and good agreement is found. The effects of model parameters on velocity, skin friction and temperature variation have been studied. At the end, the present study is also compared with single layer flow and revealed in close agreement with the result available in the literature.

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30

Siddiqui, Abdul M., Maya K. Mitkova, and Ali R. Ansari. "On the Unsteady Flow of Two Incompressible Immiscible Second Grade Fluids between Two Parallel Plates." Advanced Materials Research 1016 (August 2014): 546–53. http://dx.doi.org/10.4028/www.scientific.net/amr.1016.546.

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Unsteady, pressure driven in the gap between two parallel plates flow of two non-Newtonian incompressible second grade fluids is considered. The governing equations are established for the particular two-layer flow and analytical solutions of the equations that satisfy the imposed boundary conditions are obtained. The velocity of each fluid is expressed as function of the material constants, time dependent pressure gradient and other characteristics of the fluids. As part of the solution, an expression for the interface velocity is derived. We analyze the shift of the velocity maximum from one to another fluid as a function of variety of values of fluids’ parameters.

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31

KERSWELL, R. R. "Exchange flow of two immiscible fluids and the principle of maximum flux." Journal of Fluid Mechanics 682 (July 8, 2011): 132–59. http://dx.doi.org/10.1017/jfm.2011.190.

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The steady, coaxial flow in which two immiscible, incompressible fluids of differing densities move past each other slowly in a vertical cylindrical tube has a continuum of possibilities due to the arbitrariness of the interface between the fluids. By invoking the presence of surface tension to at least restrict the shape of any interface to that of a circular arc or full circle, we consider the following question: which flow will maximise the exchange when there is only one dividing interface Γ? Surprisingly, the answer differs fundamentally from the better-known co-directional two-phase flow situation where an axisymmetric (concentric) core-annular solution always optimises the flux. Instead, the maximal flux state is invariably asymmetric either being a ‘side-by-side’ configuration where Γ starts and finishes at the tube wall or an eccentric core-annular flow where Γ is an off-centre full circle in which the more viscous fluid is surrounded by the less viscous fluid. The side-by-side solution is the most efficient exchanger for a small viscosity ratio β ≲ 4.60 with an eccentric core-annular solution optimal otherwise. At large β, this eccentric solution provides 51% more flux than the axisymmetric core-annular flow which is always a local minimiser of the flux.

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32

Huo, Y., and B. Q. Li. "Surface Deformation and Convection in Electrostatically-Positioned Droplets of Immiscible Liquids Under Microgravity." Journal of Heat Transfer 128, no. 6 (November 30, 2005): 520–29. http://dx.doi.org/10.1115/1.2188460.

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A numerical study is presented of the free surface deformation and Marangoni convection in immiscible droplets positioned by an electrostatic field and heated by laser beams under microgravity. The boundary element and the weighted residuals methods are applied to iteratively solve for the electric field distribution and for the unknown free surface shapes, while the Galerkin finite element method for the thermal and fluid flow field in both the transient and steady states. Results show that the inner interface demarking the two immiscible fluids in an electrically conducting droplet maintains its sphericity in microgravity. The free surface of the droplet, however, deforms into an oval shape in an electric field, owing to the pulling action of the normal component of the Maxwell stress. The thermal and fluid flow distributions are rather complex in an immiscible droplet, with conduction being the main mechanism for the thermal transport. The non-uniform temperature along the free surface induces the flow in the outer layer, whereas the competition between the interfacial surface tension gradient and the inertia force in the outer layer is responsible for the flows in the inner core and near the immiscible interface. As the droplet cools into an undercooled state, surface radiation causes a reversal of the surface temperature gradients along the free surface, which in turn reverses the surface tension driven flow in the outer layer. The flow near the interfacial region, on the other hand, is driven by a complimentary mechanism between the interfacial and the inertia forces during the time when the thermal gradient on the free surface has been reversed while that on the interface has not yet. After the completion of the interfacial thermal gradient reversal, however, the interfacial flows are largely driven by the inertia forces of the outer layer fluid.

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33

Balan, Catalin Mihai, Diana Broboana, and Corneliu Balan. "Mixing process of immiscible fluids in microchannels." International Journal of Heat and Fluid Flow 31, no. 6 (December 2010): 1125–33. http://dx.doi.org/10.1016/j.ijheatfluidflow.2010.06.008.

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34

Fedodeyev, V. "Emulsion formation mechanism during immiscible fluids flow in geological materials." Доклады академии наук 482, no. 3 (September 2018): 319–22. http://dx.doi.org/10.31857/s086956520003139-5.

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35

Eskin, Dmitry, and Alexander Vikhansky. "Modelling dispersion of immiscible fluids in a turbulent Couette flow." Canadian Journal of Chemical Engineering 97, no. 1 (May 21, 2018): 17–26. http://dx.doi.org/10.1002/cjce.23224.

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36

Ozen, O., N. Aubry, D. T. Papageorgiou, and P. G. Petropoulos. "Electrohydrodynamic linear stability of two immiscible fluids in channel flow." Electrochimica Acta 51, no. 25 (July 2006): 5316–23. http://dx.doi.org/10.1016/j.electacta.2006.02.002.

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37

EBMEYER, CARSTEN, and JOSÉ MIGUEL URBANO. "Quasi-steady Stokes flow of multiphase fluids with shear-dependent viscosity." European Journal of Applied Mathematics 18, no. 4 (August 2007): 417–34. http://dx.doi.org/10.1017/s0956792507006948.

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The quasi-steady power-law Stokes flow of a mixture of incompressible fluids with shear-dependent viscosity is studied. The fluids are immiscible and have constant densities. Existence results are presented for both the no-slip and the no-stick boundary value conditions. Use is made of Schauder's fixed-point theorem, compactness arguments, and DiPerna–Lions renormalized solutions.

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38

Nikodijevic, Dragisa, Zivojin Stamenkovic, Milos Jovanovic, Milos Kocic, and Jelena Nikodijevic. "Flow and heat transfer of three immiscible fluids in the presence of uniform magnetic field." Thermal Science 18, no. 3 (2014): 1019–28. http://dx.doi.org/10.2298/tsci1403019n.

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The magnetohydrodynamic flow of three immiscible fluids in a horizontal channel with isothermal walls in the presence of an applied magnetic field has been investigated. All three fluids are electrically conducting, while the channel plates are electrically insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained in three fluid regions of the channel. Separate solutions with appropriate boundary conditions for each fluid have been obtained and these solutions have been matched at the interface using suitable boundary conditions. The analytical results for various values of the Hartmann number, the ratio of fluid heights and thermal conductivities have been presented graphically to show their effect on the flow and heat transfer characteristics.

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39

Ansari, Ali R., Maya K. Mitkova, and Abdul M. Siddiqui. "Couette - Poiseuille Two-Layer Flow of a Third Grade Fluid." Applied Mechanics and Materials 390 (August 2013): 103–10. http://dx.doi.org/10.4028/www.scientific.net/amm.390.103.

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The two-layer Couette-Poiseuille flow of a third grade fluid is examined. The problem is reduced to solving nonlinear differential equations governing the motion of the two immiscible fluids in case of different thickness of layers. The solutions are used to study the effect of the third grade material parameter on the velocity profiles. The investigation focuses especially on the location of the velocity maximum as function of the viscosity and third grade material constant.

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40

Zhang, Zheng Fu, Jun Wei Wang, and Feng Bao. "Numerical Simulation of the Nozzle with Self-Oscillating Flow Using the VOF Model." Advanced Materials Research 479-481 (February 2012): 2380–82. http://dx.doi.org/10.4028/www.scientific.net/amr.479-481.2380.

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The jet water shape of the nozzle will become a self-oscillating shape, if the triangle and U shape models are made into the normal nozzle. Using the VOF model , the jet shape of the nozzle will be simulated through a commercial CFD software 'FLUENT'. The VOF model (Volume of Fluid) is a surface-tracking technique applied to a fixed Eulerian mesh. It is designed for two or more immiscible fluids where the position of the interface between the fluids is of interest. The CFD simulation results shows that the jet shape of the nozzle is oscillate in a fixed period.

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41

Renardy, Yuriko, and Daniel D. Joseph. "Couette flow of two fluids between concentric cylinders." Journal of Fluid Mechanics 150 (January 1985): 381–94. http://dx.doi.org/10.1017/s0022112085000179.

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We consider the flow of two immiscible fluids lying between concentric cylinders when the outer cylinder is fixed and the inner one rotates. The interface is assumed to be concentric with the cylinders, and gravitational effects are neglected. We present a numerical study of the effect of different viscosities, different densities and surface tension on the linear stability of the Couette flow. Our results indicate that, with surface tension, a thin layer of the less-viscous fluid next to either cylinder is linearly stable and that it is possible to have stability with the less dense fluid lying outside. The stable configuration with the less-viscous fluid next to the inner cylinder is more stable than the one with the less-viscous fluid next to the outer cylinder. The onset of Taylor instability for one-fluid flow may be delayed by the addition of a thin layer of less-viscous fluid on the inner wall and promoted by a thin layer of more-viscous fluid on the inner wall.

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42

Yagodnitsyna, Anna, Alexander Kovalev, and Artur Bilsky. "Liquid–Liquid Flows with Non-Newtonian Dispersed Phase in a T-Junction Microchannel." Micromachines 12, no. 3 (March 22, 2021): 335. http://dx.doi.org/10.3390/mi12030335.

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Immiscible liquid–liquid flows in microchannels are used extensively in various chemical and biological lab-on-a-chip systems when it is very important to predict the expected flow pattern for a variety of fluids and channel geometries. Commonly, biological and other complex liquids express non-Newtonian properties in a dispersed phase. Features and behavior of such systems are not clear to date. In this paper, immiscible liquid–liquid flow in a T-shaped microchannel was studied by means of high-speed visualization, with an aim to reveal the shear-thinning effect on the flow patterns and slug-flow features. Three shear-thinning and three Newtonian fluids were used as dispersed phases, while Newtonian castor oil was a continuous phase. For the first time, the influence of the non-Newtonian dispersed phase on the transition from segmented to continuous flow is shown and quantitatively described. Flow-pattern maps were constructed using nondimensional complex We0.4·Oh0.6 depicting similarity in the continuous-to-segmented flow transition line. Using available experimental data, the proposed nondimensional complex is shown to be effectively applied for flow-pattern map construction when the continuous phase exhibits non-Newtonian properties as well. The models to evaluate an effective dynamic viscosity of a shear-thinning fluid are discussed. The most appropriate model of average-shear-rate estimation based on bulk velocity was chosen and applied to evaluate an effective dynamic viscosity of a shear-thinning fluid. For a slug flow, it was found that in the case of shear-thinning dispersed phase at low flow rates of both phases, a jetting regime of slug formation was established, leading to a dramatic increase in slug length.

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43

Doyle, Brendon J., Frederic Morin, Jan B. Haelssig, Dominique M. Roberge, and Arturo Macchi. "Gas-Liquid Flow and Interphase Mass Transfer in LL Microreactors." Fluids 5, no. 4 (November 28, 2020): 223. http://dx.doi.org/10.3390/fluids5040223.

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This work investigates the impact of fluid (CO2(g), water) flow rates, channel geometry, and the presence of a surfactant (ethanol) on the resulting gas–liquid flow regime (bubble, slug, annular), pressure drop, and interphase mass transfer coefficient (kla) in the FlowPlateTM LL (liquid-liquid) microreactor, which was originally designed for immiscible liquid systems. The flow regime map generated by the complex mixer geometry is compared to that obtained in straight channels of a similar characteristic length, while the pressure drop is fitted to the separated flows model of Lockhart–Martinelli, and the kla in the bubble flow regime is fitted to a power dissipation model based on isotropic turbulent bubble breakup. The LL-Rhombus configuration yielded higher kla values for an equivalent pressure drop when compared to the LL-Triangle geometry. The Lockhart–Martinelli model provided good pressure drop predictions for the entire range of experimental data (AARE < 8.1%), but the fitting parameters are dependent on the mixing unit geometry and fluid phase properties. The correlation of kla with the energy dissipation rate provided a good fit for the experimental data in the bubble flow regime (AARE < 13.9%). The presented experimental data and correlations further characterize LL microreactors, which are part of a toolbox for fine chemical synthesis involving immiscible fluids for applications involving reactive gas–liquid flows.

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44

GROSFILS, PATRICK, and JEAN PIERRE BOON. "VISCOUS FINGERING IN MISCIBLE, IMMISCIBLE AND REACTIVE FLUIDS." International Journal of Modern Physics B 17, no. 01n02 (January 20, 2003): 15–20. http://dx.doi.org/10.1142/s0217979203017023.

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With the Lattice Boltzmann method (using the BGK approximation) we investigate the dynamics of Hele-Shaw flow under conditions corresponding to various experimental systems. We discuss the onset of the instability (dispersion relation), the static properties (characterization of the interface) and the dynamic properties (growth of the mixing zone) of simulated Hele-Shaw systems. We examine the role of reactive processes (between the two fluids) and we show that they have a sharpening effect on the interface similar to the effect of surface tension.

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45

Petrovic, Jelena, Zivojin Stamenkovic, Milos Kocic, and Milica Nikodijevic. "Porous medium magnetohydrodynamic flow and heat transfer of two immiscible fluids." Thermal Science 20, suppl. 5 (2016): 1405–17. http://dx.doi.org/10.2298/tsci16s5405p.

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The magnetohydordynamic flow and heat transfer of two viscous incompressible fluids through porous medium has been investigated in the paper. Fluids flow through porous medium between two parallel fixed isothermal plates in the presence of an inclined magnetic and perpendicular electric field. Fluids are electrically conducting, while the channel plates are insulated. The general equations that describe the discussed problem under the adopted assumptions are reduced to ordinary differential equations and closed-form solutions are obtained. Solutions with appropriate boundary conditions for velocity and temperature fields have been obtained. The analytical results for various values of the Hartmann number, load factor, viscosity and porosity parameter have been presented graphically to show their effect on the flow and heat transfer characteristics.

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46

Leo, J. Mara��n Di, and J. Mara��n. "Immiscible fluid flow through nanotubes." Theoretical Chemistry Accounts: Theory, Computation, and Modeling (Theoretica Chimica Acta) 110, no. 6 (December 1, 2003): 410–13. http://dx.doi.org/10.1007/s00214-003-0495-6.

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47

Devakar, M., Ankush Raje, and Shubham Hande. "Unsteady Flow of Couple Stress Fluid Sandwiched Between Newtonian Fluids Through a Channel." Zeitschrift für Naturforschung A 73, no. 7 (July 26, 2018): 629–37. http://dx.doi.org/10.1515/zna-2017-0434.

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AbstractThe aim of this article is to study the unsteady flow of immiscible couple stress fluid sandwiched between Newtonian fluids through a horizontal channel. The fluids and plates are initially at rest. At an instant of time, a constant pressure gradient is applied along the horizontal direction to generate the flow. The time-dependent partial differential equations are solved numerically using the finite difference method. The continuity of velocities and shear stresses at the fluid-fluid interfaces has been considered. The obtained results are displayed through graphs and are discussed for various fluid parameters pertaining the flow. The volume flow rate is also obtained numerically for diverse fluid parameters and is presented through a table. It is noticed that fluid velocities increased with time and reached a steady state after a certain time level. Also, the presence of couple stresses reduced the fluid velocities. Volume flow rate increased with Reynolds number and is reduced by increase of ratio of viscosities.

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48

Kumar, S. Senthil, and Y. M. C. Delauré. "An Assessment of Suitability of a SIMPLE VOF/PLIC-CSF Multiphase Flow Model for Rising Bubble Dynamics." Journal of Computational Multiphase Flows 4, no. 1 (March 2012): 65–83. http://dx.doi.org/10.1260/1757-482x.4.1.65.

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A Volume of Fluid (VOF) – Youngs' model for the solution of an incompressible immiscible two-phase flows is presented. The solver computes the flow field by solving the family of Navier Stokes equations on a fixed (Eulerian) Staggered Cartesian grid using the Finite Volume formulation of Semi-Implicit Pressure Linked Equation (SIMPLE) method and tracks the position of interface between two fluids with different fluid properties by Piecewise Linear Interface Construction (PLIC) Method. The suitability of the SIMPLE type implementation is assessed by investigating the dynamics of free rising bubbles for different fluid properties and flow parameters. The results obtained with the present numerical method for rising bubbles in viscous liquids are compared with reported numerical and experimental results.

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49

Siddiqui, Abdul, Muhammad Zeb, Tahira Haroon, and Qurat-ul-Ain Azim. "Exact Solution for the Heat Transfer of Two Immiscible PTT Fluids Flowing in Concentric Layers through a Pipe." Mathematics 7, no. 1 (January 14, 2019): 81. http://dx.doi.org/10.3390/math7010081.

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This article investigates the heat transfer flow of two layers of Phan-Thien-Tanner (PTT) fluids though a cylindrical pipe. The flow is assumed to be steady, incompressible, and stable and the fluid layers do not mix with each other. The fluid flow and heat transfer equations are modeled using the linear PTT fluid model. Exact solutions for the velocity, flow rates, temperature profiles, and stress distributions are obtained. It has also been shown that one can recover the Newtonian fluid results from the obtained results by putting the non-Newtonian parameters to zero. These results match with the corresponding results for Newtonian fluids already present in the literature. Graphical analysis of the behavior of the fluid velocities, temperatures, and stresses is also presented at the end. It is also shown that maximum velocity occurs in the inner fluid layer.

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50

Jung, Jin Ho, Ghulam Destgeer, Jinsoo Park, Husnain Ahmed, Kwangseok Park, and Hyung Jin Sung. "Microfluidic flow switching via localized acoustic streaming controlled by surface acoustic waves." RSC Advances 8, no. 6 (2018): 3206–12. http://dx.doi.org/10.1039/c7ra11194k.

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Acoustic streaming flow induced by high-frequency surface acoustic waves has been used to switch streams of two immiscible fluids flowing in parallel through a bifurcating microchannel with an H-shaped junction at the centre.

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