Immiscible Fluids Research Articles

Love wave along the corrugated interface between an elastic half-space and the corrugated porous layer containing two fluids

This article presents a comprehensive analysis of Love wave propagation along the interface between a porous layer saturated with two immiscible fluids and an underlying elastic half-space. The study places particular emphasis on the corrugated nature of both the interface and the upper boundary of the porous layer. A complex dispersion relation, governed by appropriate boundary conditions, is derived and subsequently simplified into four distinct subcases. The effects of corrugation parameters at the upper boundary of the porous layer and the interface between the layer and the elastic half-space are investigated. The influence of the undulation parameter, which represents the combined effects of wave number and porous layer thickness is also analyzed on the phase speed of the Love wave. In the numerical discussion, a geological structure analogous to oil-contaminated sandstone aquifers in contact with sedimentary bedrock, a common formation in coastal regions, is considered as a realistic example. The key findings reveal that the phase speed of Love waves is highly sensitive to both the corrugation and undulation parameters. Increased corrugation at the upper boundary of the layer enhances phase speed, while corrugation at the interface decreases it. An increase in the undulation parameter decreases the phase speed of the Love wave. Additionally, the presence of oil and water within the porous sandstone significantly reduces phase speed, particularly at lower frequencies, due to higher viscosity and internal friction. This study provides valuable insights into wave propagation dynamics in complex geological settings, with implications for hydrogeology, environmental monitoring, and seismic risk assessment.

Immiscible metamorphic water and methane fluids preserved in carbonated eclogite.

Subduction zones metamorphic fluids are pivotal in geological events such as volcanic eruptions, seismic activity, mineralization, and the deep carbon cycle. However, the mechanisms governing carbon mobility in subduction zones remain largely unresolved. Here we present the first observations of immiscible H2O-CH4 fluids coexisting in retrograde carbonated eclogite from the Western Tianshan subduction zone, China. We identified two types of fluid inclusions in host ankerite and amphibole, as well as in garnet and omphacite. Type-1 inclusions are water-rich with CH4 vapor, whereas Type-2 are CH4-rich, with minimal or no H2O. The coexistence of these fluid types indicates the presence of immiscible fluid phases under high-pressure conditions (P = 1.3-2.1 GPa). Carbonates in subduction zones can effectively decompose through reactions with silicates, leading to the generation of abiotic CH4. Our findings suggest that substantial amounts of carbon could be transferred from the slab to mantle wedge as immiscible CH4 fluids. This process significantly enhances decarbonation efficiency and may contribute to the formation of natural gas deposits.

Turbulent convection in emulsions: the Rayleigh–Bénard configuration

This study explores heat and turbulent modulation in three-dimensional multiphase Rayleigh–Bénard convection using direct numerical simulations. Two immiscible fluids with identical reference density undergo systematic variations in dispersed-phase volume fractions, $0.0 \leq \varPhi \leq 0.5$ , and ratios of dynamic viscosity, $\lambda _{\mu }$ , and thermal diffusivity, $\lambda _{\alpha }$ , within the range $[0.1\unicode{x2013}10]$ . The Rayleigh, Prandtl, Weber and Froude numbers are held constant at $10^8$ , $4$ , $6000$ and $1$ , respectively. Initially, when both fluids share the same properties, a 10 % Nusselt number increase is observed at the highest volume fractions. In this case, despite a reduction in turbulent kinetic energy, droplets enhance energy transfer to smaller scales, smaller than those of single-phase flow, promoting local mixing. By varying viscosity ratios, while maintaining a constant Rayleigh number based on the average mixture properties, the global heat transfer rises by approximately 25 % at $\varPhi =0.2$ and $\lambda _{\mu }=10$ . This is attributed to increased small-scale mixing and turbulence in the less viscous carrier phase. In addition, a dispersed phase with higher thermal diffusivity results in a 50 % reduction in the Nusselt number compared with the single-phase counterpart, owing to faster heat conduction and reduced droplet presence near walls. The study also addresses droplet-size distributions, confirming two distinct ranges dominated by coalescence and breakup with different scaling laws.

Analytical model of small- and large-amplitude drop oscillation dynamics

The mechanical energy balance over a bulk of fluid that oscillates between prolate and oblate shapes in another immiscible fluid is solved using a general spheroidal coordinate system. The drop shape is described by a unique parameter that may continuously vary over the time, making the implementation of the model rather simple. Potential flow is assumed, and inertial and viscous effects are accounted for in both the inner and outer flow fields. The characteristics of drop oscillation for small and large amplitudes are studied, and the results are compared with theoretical, experimental, and numerical data from the open literature. The rather satisfactory validation of the model over a large variety of operating conditions allows its extension to include other physical phenomenon, like evaporation and its effect on drop oscillation.

Analytical investigation of porous medium effects on the flow of two micropolar fluids in a rotating annulus

Fluids with microstructures and microinertia play a vital role in microfluidics and nanfluidics system. One of such significant fluid is micropolar fluid. The characteristic behavior of micropolar fluid flow in conduit/pipe, etc. filled with porous medium helps us understand the flow behavior of biological fluids in porous media, groundwater flow in aquifiers, rotatory machines or viscometer. To understand such real-world problems, it is necessary to get into the mathematical model of such flow models. One such model with wide number of application is presented in this paper. This work investigated the flow of two micropolar fluids between the region formed by two concentric cylinders. Authors have considered inner cylinder to be at rest and outer cylinder rotating at a constant angular velocity. The region between two concentric cylinder is filled with an isotropic porous material. A slip condition at the outer wall and continuity conditions at interface of two fluids has been utilized to obtain an analytical solution for the proposed model. The numerical solution of the obtained solution for present problem is used to graphically analyze the motion of immisicble micropolar fluids rotating in an annulus filled with the porous medium. It is found that an outer cylinder has a notable influence on the flow behavior of immiscible micropolar fluids, contrary to the effect observed within the inner region. An analytical approach of this work not only helps us obtain precise results and analysis of the flow, but it also serves as a useful validation for future approximations within the scope of this work.

Influence of interface on nondeformable micropolar drop migration

Abstract In this article, an analytical approach is considered to study the issue of specifying Stokesian motion due to a micropolar sphere drop translating at a concentric instantaneous position within a spherical fluid-fluid interface that divides two immiscible fluids, one of which is bounded and the other is unbounded. Here, the focus is on the situation where there are two microstructure-related fluid phases (micropolar fluids) out of the three. The motion is considered to have low Reynolds numbers; thus, the drop's surface and fluid-fluid interface have insignificant deformation. For both the components of the microrotation and velocity, general solutions to the slow axisymmetric motion of the micropolar/viscous fluid in a spherical coordinate system are obtained based on a concentric position. Boundary conditions are fulfilled at the drop's surface and the fluid-fluid interface. Especially, the boundary condition for the microrotation-vorticity is utilised at the fluid-fluid interface; while the continuity of tangential couple stress and microrotation are also utilised at the drop's surface. Findings indicate that the normalised hydrodynamic force increases monotonically as the droplet-to-interface radius ratio increases, acting on a moving micropolar sphere droplet and becoming unlimited when the drop's surface touches the fluid-fluid interface. The numerical findings for the normalised force operating on the micropolar sphere droplet at different values of the suitable parameters are introduced in both graphical and tabular form. Our numerical findings are compared with the suitable data for the special cases stated in the literature. This current investigation is significant within the domains of industrial, biological, medicinal, and natural processes, for example, liquid-liquid extraction, raindrop formation, blood cells moving through a vein or artery, suspension rheology, sedimentation, and coagulation.

Well-posedness and stability for the two-phase periodic quasistationary Stokes flow

The two-phase horizontally periodic quasistationary Stokes flow in \mathbb{R}^{2} , describing the motion of two immiscible fluids with equal viscosities that are separated by a sharp interface, parameterized as the graph of a function f=f(t) , is considered in the general case when both gravity and surface tension effects are included. Using potential theory, the moving boundary problem is formulated as a fully nonlinear and nonlocal parabolic problem for the function f . Based on abstract parabolic theory, it is shown that the problem is well-posed in all subcritical spaces \mathrm{H}^{r}(\mathbb{S}) , with r\in(3/2,2) . Moreover, the stability properties of the flat equilibria are analyzed in dependence on the physical properties of the fluids.

EFFECT OF EXTERNAL HARMONIC VIBRATION ON THE FORMATION OF SOLITARY WAVES IN FALLING TWO-LAYER LIQUID FILMS

Abstract We study the influence of a low-frequency harmonic vibration on the formation of the two-dimensional rolling solitary waves in vertically co-flowing two-layer liquid films. The system consists of two adjacent layers of immiscible fluids with the first layer being sandwiched between a vertical solid plate and the second fluid layer. The solid plate oscillates harmonically in the horizontal direction inducing Faraday waves at the liquid–liquid and liquid–air interfaces. We use a reduced hydrodynamic model derived from the Navier–Stokes equations in the long-wave approximation. Linear stability of the base flow in a flat two-layer film is determined semi-analytically using Floquet theory. We consider sub-millimetre-thick films and focus on the competition between the long-wavelength gravity-driven and finite wavelength Faraday instabilities. In the linear regime, the range of unstable wave vectors associated with the gravity-driven instability broadens at low and shrinks at high vibration frequencies. In nonlinear regimes, we find multiple metastable states characterized by solitary-like travelling waves and short pulsating waves. In particular, we find the range of the vibration parameters at which the system is multistable. In this regime, depending on the initial conditions, the long-time dynamics is dominated either by the fully developed solitary-like waves or by the shorter pulsating Faraday waves.

Strong effect of often-overlooked initial spilled oil distribution on subsequent soil remediation: A pore-scale perspective

The removal of spilled oil within soil by water injection is essentially an immiscible fluid displacement process. Numerous studies have been conducted to investigate the way to achieve a higher displacement efficiency. However, these studies often assumed that the pore space was initially saturated by oil only, ignoring the effect of initial oil distribution on the remediation, which led to incorrectly computed flow field and biased analysis. This work aimed to reveal the effect of initial oil distribution on flow physics during the remediation. Based on a pore-scale model and the phase-field method, the spilled oil invasion and remediation in a heterogeneous porous media were investigated, and the dynamic evolution of the phase interface was examined in particular. Four different distribution patterns of spilled oil were obtained through various velocities during the oil invasion stage, which were considered as initial states for the subsequent remediation stage. The results showed that ignoring the oil invasion process led to a more than 10% reduction in the ultimate remediation efficiency. However, the maximum interfacial area of fluids was larger and the obtained relative permeability curve was much smoother for the scenario considering the oil invasion. Besides, a higher initial water saturation led to a lower starting pressure. This work provided new pore-scale insights into the often-overlooked roles of initial phase distribution in fluid dynamics behind the remediation of oil-contaminated soil by water injection, which was of fundamental importance to the development of effective response strategy for soil contamination.

Dramatic droplet deformation through interfacial particles jamming

Droplets of one fluid in a second, immiscible fluid are typically spherical in shape due to the interfacial tension between the two fluids. Shear forces can lead to droplet deformation when they are subjected to flow, and these effects can be further modified when the droplet is stabilized by a surfactant due to a flow-induced gradients in the surfactant concentration. An alternative method of stabilizing droplets is through the use of colloidal particles, whose stabilization behavior is intrinsically different from molecular surfactants. Under the same flow condition, a gradient of particle concentration can result in the jamming of particles in regions with a high packing density, making the interface solid-like, albeit only under compression and not tension. However, how this asymmetry in the surfactant properties alters the droplet shape under shear is unknown. Here, we show that shear of particle-stabilized droplets can lead to a remarkable array of shape deformations as the droplets flow through a constrained microchannel. The shear-induced migration of particles on the surface results in the formation of an elastic shell at the back of the droplet, which can wrinkle and invaginate, ultimately leading to a unique core-shell structure. The shapes depend on the Peclet number of the flow, reflecting the balance of shear forces that drive the particles and diffusion that randomizes them. These findings highlight the consequences of the asymmetry in the forces between the particles and provide a unique method to controllably create droplets with a vast array of different shapes.

Baroclinic instability in the Eady model for two coupled flows

ABSTRACT The linear instability of baroclinic flows in two superimposed and coupled, immiscible fluids is studied theoretically. These flows are westerlies, and they are thermally or mechanically coupled. The fluids are stably stratified, internally and mutually (the upper fluid is lighter than the lower fluid). In each fluid, two-level surface quasi-geostrophy governs the evolution of the perturbed westerly flow. The perturbations are horizontal normal modes. Firstly, the models are not coupled and the flow instability in each fluid is validated separately against the results of the classical Eady model of baroclinic instability. Secondly, the two fluids are thermally and/or mechanically coupled. With thermal coupling, and for meridionally uniform perturbations, a new mode of instability appears for long waves. This pair of unstable modes converges towards the modes of the uncoupled fluids at medium wavelengths. For perturbations with a non trivial meridional structure, the thermal coupling essentially damps the instability. For an upper flow with a larger deformation radius than in the lower flow, the growth rates of the perturbation are therefore more strongly altered in the former than in the latter. With mechanical coupling, the instability is essentially damped at large to medium scales, while the short-wave cut-off is extended towards smaller waves. When the fluids are both thermally and mechanically coupled, these effects add up. This very idealised study is a first step towards studying more realistic cases.

Isolation and focal treatment of brain aneurysms using interfacial fluid trapping.

Current approaches for localized intravascular treatments rely on using solid implants, such as metallic coils for embolizing aneurysms, or on direct injection of a therapeutic agent that can disperse from the required site of action. Here, we present a fluid-based strategy for localizing intravascular therapeutics that leverages surface tension and immiscible fluid interactions, to allow confined and focal treatment at brain aneurysm sites. We first show, computationally and experimentally, that an immiscible phase can be robustly positioned at the neck of human aneurysm models to seal and isolate the aneurysm's cavity for further treatment, including in wide-neck aneurysms. We then demonstrate localized delivery and confined treatment, by selective staining of cell nuclei within the aneurysm cavity as well as by hydrogel-based embolization in patient-specific aneurysm models. Altogether, our interfacial flow-driven strategy offers a potential approach for intravascular localized treatment of cardiovascular and other diseases.

An inclined magnetic field and slip effect on heat and mass transfer analysis in the peristaltic flow of immiscible fluid through an asymmetric porous channel

In this work, authors have studied peristaltic flow of immiscible type of couple stress and Newtonian fluid via an asymmetric horizontal channel filled with porous material by taking slippage into account at the channel wall which was ignored in previous published literature under the influence of thermal radiation and magnetic field. The study of peristaltic flow of considered immiscible fluids will play an important role in maximizing system efficiency, reducing energy losses, and improving performance of various fluid transport. In the present problem, the linearized form of governing equations has been solved by direct method with the use of Mathematica 14 software to obtained the closed form solutions of various flow variables. In this work, the impacts of various influencing factors on the model's flow, thermal, and concentration properties have been analyzed graphically. The work presented here leads to the significant result that large Schmidt number values in a porous filled duct reduces the mass diffusivity. Another key finding of this work is that the formation of entropy is reduced when low permeability porous material is used. Our research concludes that entropy creation in the asymmetric porous channel is decreased when the slip length increases on the channel's static borders.

Wall effects of an eccentric fluid sphere: Happel's and Kuwabara's models

AbstractIn the limit of very low Reynolds numbers, the steady translation of a fluid sphere situated at a non‐concentric position in a second immiscible fluid bounded by spherical cavity is investigated using boundary collocation technique. The flow inside and outside the fluid sphere is governed by Stokes equations. Boundary conditions at the fluid sphere are continuity of velocity and shear stress. Zero shear stress and zero vorticity are used on spherical cavity. By using superposition principle, a general solution is constructed from the basic solutions in the two spherical coordinate systems based on both the fluid sphere and spherical cavity. The normalized drag force exerted on the fluid sphere contained in a cavity is depended on the ratio of fluid sphere and cavity radii, viscosity ratio of fluid sphere and cavity, relative distance between the centers of fluid sphere and cavity. The results are in good agreement with previously published work in the limiting cases. The numerical results of the drag force are good agreement with the solutions of the translation of the fluid sphere in a concentric cavity and the translation of a solid sphere in a non‐concentric cavity. The drag force is increasing function of the viscosity ratio, volume fraction, and the relative distance. This work is extension of the previous work of Keh and Lee for the fluid sphere using Happel's and Kuwabara's models.

Bifurcation of rotating surface switching at different spin-up accelerations

It has been found, for the first time, that rotating polygons (m = 1, 2) can exist in a system of two immiscible fluids, which can be in three different steady states: stable funnel, cycling switching, and rotating twin funnel. These states are achieved due to different disk acceleration values at fixed aspect ratio (h/R) = 1 and Reynolds numbers. The acceleration time of rotating disk is found to have a significant effect on instability development.

Oscillatory excitation of Faraday waves on the interface of immiscible fluids in a slotted channel

Recent studies of the oscillatory dynamics of the interface between fluids in Hele–Shaw cells have revealed a new type of instability termed the “oscillatory Saffman instability” in the case of fluids with high-viscosity contrast. The present study is dedicated to the experimental investigation of the dynamics of the interface between low-viscosity fluids of different densities oscillating in a vertical narrow channel. It is discovered that as the amplitude of oscillations increases, a threshold excitation of parametric oscillations of the interface in the form of a standing wave is observed in the plane of the fluid layer. This phenomenon bears a resemblance to Faraday waves, but the dependence of the standing wave wavelength on the oscillation frequency does not align with the classical dispersion relation for low-viscosity fluids. The damping effect of viscous boundary layers near the cell walls and the out-of-plane curvature of the oscillating interface leads to a decrease in the natural frequency of oscillations. The experiments demonstrate a significant role of the dimensionless layer thickness. With its decrease (increase in the dimensionless out-of-plane interface curvature), the threshold oscillation acceleration rises in accordance with a power law. To the best of the authors' knowledge, this type of instability has been discovered and studied for the first time. Another important finding is the excitation of intense time-averaged vortical flows in the channel plane within the supercritical region. The physical mechanism underlying the excitation of the time-averaged vortices is clarified, and the dimensionless parameters that govern their intensity are identified.

Molecular dynamics study of the thermal radiatively pressure-driven flow of two immiscible hybrid nanofluids through a curved pipe with viscous dissipation

Hybrid nanomaterials significantly enhance thermal systems through improved thermal conductivity, efficient energy storage, and customized thermomechanical properties. Due to their superior thermophysical characteristics, hybrid nanofluids are crucial in fields such as industry, biomedicine, transportation, and pharmaceuticals. Therefore, the current article scrutinizes the characteristics of heat transfer on the thermally radiative flow of two immiscible hybrid nanofluids through a curved pipe induced due to a pressure gradient in an axial direction. The pipe is divided into two distinct regions: namely, (i) Region 1 (core) is filled with base fluid kerosene oil containing copper (Cu) and carbon nanotube (CNT) nanoparticles, while (ii) Region 2 (peripheral) is filled with base fluid water containing zinc oxide (ZnO) and aluminum oxide (Al2O3) nanoparticles. The complex curvilinear coordinates called toroidal coordinates are used to form a mathematical model for the present problem. The fluid in the core region is assumed to be more viscous than that of the peripheral region as such types of flows are observed in real life (viz. blood flow through arteries). Equations governing the flow are considered without ignoring any curvature ratio terms and are solved analytically by considering the perturbation series. The continuity of velocities and shear stresses at the fluid-fluid interface is taken into account along with no-slip, symmetric, and regularity conditions while solving the two-fluid flow problem under consideration. The effect of various fluid parameters such as curvature ratio, Reynolds number, viscosity ratio, and density ratio on the axial velocity and temperature is studied through 2-dimensional graphs, contour plots, and streamlines. The results show that the axial velocity of immiscible fluids flow decreases with an increase in the concentration of nanomaterials. Heat transport characteristics of nanofluid are increased by the addition of nanomaterials.

Analyzing Foam Injection Dynamics in Porous Media: A Combined Computational and Experimental Approach

The study of foam injection dynamics into porous media holds numerous applications, with its primary use being the optimization of the oil extraction process. Additionally, it finds utility in various other domains, including soil decontamination techniques. This study focuses on evaluating foam injection through low-cost experiments and computational models. The model integrates a classic two-phase immiscible fluid flow in a porous media framework, augmented by a mobility reduction factor to simulate foam’s impact on gas phase mobility. Simple experiments were conducted to assess water displacement using both gas and gas-foam injection methods. Results revealed that while gas injection tends to form preferential paths rapidly, leading to gas disruption, foam injection generates a more compact front, enhancing sweep efficiency by mitigating preferential path formation. The computational model successfully reproduced the experimental findings qualitatively. This research introduces a cost-effective experiment suitable for didactic purposes, illustrating complex concepts and underscoring the complementary nature of experimental and computational methodologies in advancing engineering techniques.

Demulsification of Pickering emulsions: advances in understanding mechanisms to applications.

Pickering emulsions are ultra-stable dispersions of two immiscible fluids stabilized by solid or microgel particles rather than molecular surfactants. Although their ultra-stability is a signature performance indicator, often such high stability hinders their demulsification, i.e., prevents the droplet coalescence that is needed for phase separation on demand, or release of the active ingredients encapsulated within droplets and/or to recover the particles themselves, which may be catalysts, for example. This review aims to provide theoretical and experimental insights on demulsification of Pickering emulsions, in particular identifying the mechanisms of particle dislodgment from the interface in biological and non-biological applications. Even though the adhesion of particles to the interface can appear irreversible, it is possible to detach particles via (1) alteration of particle wettability, and/or (2) particle dissolution, affecting the particle radius by introducing a range of physical conditions: pH, temperature, heat, shear, or magnetic fields; or via treatment with chemical/biochemical additives, including surfactants, enzymes, salts, or bacteria. Many of these changes ultimately influence the interfacial rheology of the particle-laden interface, which is sometimes underestimated. There is increasing momentum to create responsive Pickering particles such that they offer switchable wettability (demulsification and re-emulsification) when these conditions are changed. Demulsification via wettability alteration seems like the modus operandi whilst particle dissolution remains only partially explored, largely dominated by food digestion-related studies where Pickering particles are digested using gastrointestinal enzymes. Overall, this review aims to stimulate new thinking about the control of demulsification of Pickering emulsions for release of active ingredients associated with these ultra-stable emulsions.

On the existence, uniqueness and regularity of strong solutions to a stochastic 2D Cahn–Hilliard-Magnetohydrodynamic model

Abstract We investigate a stochastic coupled model of the Cahn–Hilliard equations and the stochastic magnetohydrodynamic equations in a bounded domain of ℝ 2 {\mathbb{R}^{2}} . The model describes the flow of the mixture of two incompressible and immiscible fluids under the influence of an electromagnetic field with stochastic perturbations. We prove the existence, uniqueness and regularity of a probabilistic strong solution. The proof of the existence is based on the Galerkin approximation, the stopping time technique and some weak convergence principles in functional analysis.