Stability of magnetic fluid penetration through a porous medium with uniform magnetic field oblique to the interface

Recent work has shown that the fingering instability, which develops when a more viscous fluid is pushed through the voids of a porous medium or through a Hele-Shaw cell by a less viscous fluid, can be prevented if a magnetic field is applied tangential to a flat fluid interface separating magnetizable and non-magnetizable fluids. This earlier work is extended here by considering equilibrium magnetic field components both perpendicular and parallel to the flat interface. The tangential field component stabilizes those waves traveling along the field lines while the normal field is destabilizing. The analysis is developed through a general set of relations for perturbation field and flow interfacial variables defined for a "prototype" magnetizable fluid layer which can be used to describe the small signal stability characteristics of layered fluid systems. In a uniform tangential magnetic field geometry, experimental results of the most unstable wavelength in a Hele-Shaw cell are shown to agree well with theory.     

Kinematic instabilities in two-layer eccentric annular flows,part 1: Newtonian fluids

Primary-cementing displacement flows occur in long narrow eccentric annuli during the construction of oil and gas wells. A common problem is that the displacing fluid fingers up the upper wide side of the annulus, leaving behind a “mud channel” of displaced fluid on the lower narrow side of the annulus. Tehrani et al. report that the interface between displacing fluid and mud channel can in certain circumstances become unstable, and a similar phenomenon has been observed in our ongoing experiments. Here an explanation for these instabilities is provided via analysis of the stability of two-layer eccentric annular Hele-Shaw flows, using a transient version of the usual Hele-Shaw approach, in which fluid acceleration terms are retained. Two Newtonian fluids are considered, as a simplification of the general case in which the fluids are shear-thinning yield-stress fluids. It is shown that negative azimuthal buoyancy gradients are in general stabilizing in inclined wells, but that buoyancy may also have a destabilizing effect via axial buoyancy forces that influence the base-flow interfacial velocity. In a variety of special cases where buoyancy is not dominant, it is found that instability is suppressed by a positive product of interfacial velocity difference and reduced Reynolds-number difference between fluids. Even a small positive azimuthal buoyancy gradient, (heavy fluid over light fluid), can be stabilized in this way. Eccentricity of the annulus seems to amplify the effect of buoyancy on stability or instability, e.g. stably stratified fluid layers become more stable as the eccentricity is increased.     

A numerical study on radial Hele-Shaw flow: influence of fluid miscibility and injection scheme

Fingering instability triggered by injection of a less viscous fluid in a Hele-Shaw cell is numerically investigated. Simulations are based on a diffuse-interface method, and the formulation, capable of dealing with immiscible and miscible interfaces, is presented in details. Three miscibility conditions, including immiscible with surface tension, partially miscible with effective interfacial tension and fully miscible without interfacial stresses, are simulated to verify generality of an optimal linear injection scheme proposed by Dias et al. (Phys Rev Lett 109:144502, 2012) in the limit of infinite viscosity contrast. stabilizing effects of this linear injection scheme are universally confirmed for the interfaces with the presence of interfacial stresses, such as immiscible and partially miscible conditions. On the other hand, the linear injection scheme in a fully miscible interface leads to contradictory results. Even the fingering pattern appears qualitatively more stable without the secondary phenomenon of finger merging, relevant quantitative measurements, such as longer channeling zone and interfacial length, indicate enhancement of fingering prominence. The inconsistent behaviors suggest that the coupling effects with the interfacial stresses are crucial in the applications of the optimal linear injection scheme.     

亚临界流体挤出法制备高密度聚乙烯/木粉复合材料

采用亚临界流体挤出法制备高密度聚乙烯(HDPE)/木粉复合材料,研究了亚临界流体种类(去离子水、正丙醇和乙醇)与温度对木塑复合材料(WPC)综合力学性能的影响。实验利用傅立叶变换红外光谱、差示扫描量热分析和扫描电镜分别对复合材料的化学组成、热变形温度和界面形貌作了相应的研究。结果表明,亚临界流体的高温高压可以对木纤维起到很好的溶胀作用,一定程度上打破了木素、半纤维素对纤维素的包裹作用,明显促进基体与木纤维之间的机械捏合与酯化反应,增加界面强度。在亚临界流体条件下,尤其在亚临界乙醇条件下,木粉在HDPE树脂基体中具有优异的分散性,拉伸断面处的断裂形式主要以基体与纤维断裂为主,说明HDPE/木粉的WPC具有较好的界面结合强度。     

Asymptotics for the Muskat problem

The Muskat problem is a simple model for the displacement of one fluid by another in a porous medium or Hele-Shaw cell. Solutions of the problem are unstable to small-wavelength disturbances, and there is evidence that the problem is ill-posed. A well-posed problem may be developed by including additional regularising physical effects, primarily surface tension. In practical situations involving oil recovery, one can engineer for there to be a gradual change in the viscosity of the fluids, either by the gradual introduction of a polymer capable of altering the viscosity of water, or by gradual diffusion between two miscible fluids. The regularising effect of smoothing the initial data is investigated. Thus rather than a sharp interface between the two fluids, and therefore a sharp jump in viscosity, there is a smooth transition from one viscosity to another. It is shown how the standard Muskat problem may be recovered as an asymptotic limit and the effective free-surface model that may be recovered is discussed. The stability of solutions to the smoothed Muskat problem is investigated, and the important effect of smoothing for disturbances with a large wavenumber is demonstrated.     

Stretching of a liquid layer underneath a semi-infinite fluid

Exact similarity solutions of the Navier–Stokes equation are derived describing the flow of a liquid layer coated on a stretching surface underneath another semi-infinite fluid. In the absence of hydrodynamic instability, the interface remains flat as the layer thickness decreases in time. When the physical properties of the fluids are matched, we obtain Crane’s analytical solution for two-dimensional (2D) flow and a corresponding numerical solution for axisymmetric flow. When the rate of stretching of the surface is constant in time, the temporal evolution of the interface between the layer and the overlying fluid is computed by integrating in time a system of coupled partial differential equations for the velocity in each fluid together with an ordinary differential equation expressing kinematic compatibility at the interface, subject to appropriate boundary, interfacial, and far-field conditions. Multiple solutions are found in certain ranges of the density and viscosity ratios. Additional similarity solutions are presented for accelerated 2D and axisymmetric stretching. The numerical prefactors that appear in the analytical expressions for the interface location and wall shear stress are presented for different ratios of the densities and viscosities of the two fluids.     

Surface tension effects on the nonlinear behavior of long waves in a two layer flow

 The propagation of long waves of finite amplitude at the interface of two viscous fluids in the presence of interfacial tension is examined. The effect of capillarity on the shape of the waves at the interface of two superposed fluids is investigated for a wide range of density differences, viscosity ratios and imposed pressure gradients. It is found that in planar geometry surface tension stabilizes the interfacial disturbances. Attention is given to the case in which the upper fluid is more dense and comprises a thin film above the lower fluid. With the heavier fluid on the top the flow pattern is always unstable when surface tension effects are neglected. In this case the interfacial waves do not grow forever and reach a finite amplitude only when the interfacial tension is greater than a critical value.     

Modeling method for the crack problem of a functionally graded interfacial zone with arbitrary material properties

A new multi-layered model is developed for the fracture analysis of a functionally graded interfacial zone with arbitrary material properties. It is assumed that the interfacial zone is divided into sub-layers with the material properties of each sub-layer varying in a power-law function. The model is used to study the crack problem in the functionally graded interfacial zone between two homogeneous half-planes under a dynamic anti-plane load. Using Fourier–Laplace transforms and the transfer matrix method, the mixed boundary value problem is reduced to a Cauchy singular integral equation, which is solved numerically in the Laplace transform domain. Laplace numerical inversion transform is employed to obtain the stress intensity factors. The results show that the new model is general and effective for the crack problem of the functionally graded interfacial zone with arbitrary properties.     

Development of Concentration-Dependent Diffusion Instability in Reactive Miscible Fluids Under Influence of Constant or Variable Inertia

In this work, we focus on the processes which accompany a frontal neutralization reaction occurring between two miscible fluids filling a vertical Hele-Shaw cell. We have found that chemically-induced changes of reagent concentrations coupled with concentration- dependent diffusion (CDD) can produce spatially localized low density areas which are sensitive to the external inertial field. In the case of static gravity we have demonstrated both experimentally and theoretically that it can give rise to the development of perfectly periodic convective structure. This scenario is strikingly different from the irregular density fingering, which is typically observed in the miscible systems. When the system is under the influence of the periodic low-frequency vibrations perpendicular to the reaction front, we found numerically the excitation of a mixed-mode instability combining the double-diffusion instabilities and the Rayleigh-Taylor mechanism of the convection within the low density areas.     

Interfacial capillary–gravity waves due to a fundamental singularity in a system of two semi-infinite fluids

The interfacial capillary–gravity waves due to a transient fundamental singularity immersed in a system of two semi-infinite immiscible fluids of different densities are investigated analytically for two- and three- dimensional cases. The two-fluid system, which consists of an inviscid fluid overlying a viscous fluid, is assumed to be incompressible and initially quiescent. The two fluids are each homogeneous, and separated by a sharp and stable interface. The Laplace equation is taken as the governing equation for the inviscid flow, while the linearized unsteady Navier–Stokes equations are used for the viscous flow. With surface tension taken into consideration, the kinematic and dynamic conditions on the interface are linearized for small-amplitude waves. The singularity is modeled as a simple mass source when immersed in the inviscid fluid above the interface, or as a vertical point force when immersed in the viscous fluid beneath the interface. Based on the integral solutions for the interfacial waves, the asymptotic wave profiles are derived for large times with a fixed distance-to-time ratio by means of the generalized method of stationary phase. It is found that there exists a minimum group velocity, and the wave system observed will depend on the moving speed of the observer. Two schemes of expansion of the phase function are proposed for the two cases when the moving speed of an observer is larger than, or close to the minimum group velocity. Explicit analytical solutions are presented for the long gravity-dominant and the short capillary-dominant wave systems, incorporating the effects of density ratio, surface tension, viscosity and immersion depth of the singularity.     

Microgravity investigations of instability and mixing flux in frontal displacement of fluids

The goal of the present study is to investigate analytically, numerically and experimentally the instability of the displacement of viscous fluid by a less viscous one in a two-dimensional channel, and to determine characteristic size of entrapment zones. Experiments on miscible displacement of fluids in Hele-Shaw cells were conducted under microgravity conditions. Extensive direct numerical simulations allowed to investigate the sensitivity of the displacement process to variation of values of the main governing parameters. Validation of the code was performed by comparing the results of model problems simulations with experiments and with the existing solutions published in literature. Taking into account non-linear effects in fluids displacement allowed to explain new experimental results on the pear-shape of fingers and periodical separation of their tip elements from the main body of displacing fluid. Those separated blobs of less viscous fluid move much faster than the mean flow of the displaced viscous fluid. The results of numerical simulations processed based on the dimensions analysis allow to introduce criteria characterizing the quality of displacement. The functional dependence of the dimensionless criteria on the values of governing parameters needs further investigations.     

Bubble Meets Droplet: Particle‐Assisted Reconfiguration of Wetting Morphologies in Colloidal Multiphase Systems

Wetting phenomena are ubiquitous in nature and play key functions in various industrial processes and products. When a gas bubble encounters an oil droplet in an aqueous medium, it can experience either partial wetting or complete engulfment by the oil. Each of these morphologies can have practical benefits, and controlling the morphology is desirable for applications ranging from particle synthesis to oil recovery and gas flotation. It is known that the wetting of two fluids within a fluid medium depends on the balance of interfacial tensions and can thus be modified with surfactant additives. It is reported that colloidal particles, too, can be used to promote both wetting and dewetting in multifluid systems. This study demonstrates the surfactant‐free tuning and dynamic reconfiguration of bubble‐droplet morphologies with the help of cellulosic particles. It further shows that the effect can be attributed to particle adsorption at the fluid interfaces, which can be probed by interfacial tensiometry, making particle‐induced transitions in the wetting morphology predictable. Finally, particle adsorption at different rates to air–water and oil–water interfaces can even lead to slow, reentrant wetting behavior not familiar from particle‐free systems.     

A boundary element study of the effect of surface dissolution on the evolution of immiscible viscous fingering within a Hele-Shaw cell

Fingering instabilities at the interface between two immiscible fluids can appear during the displacement of a fluid of higher viscosity by another one of lower viscosity. The evolution of the finger structures is determined by the interface kinematic and dynamic matching conditions, which describe mass and momentum conservation across the interface. In the case when the injected fluid is a gas and the resident one is a liquid, dissolution of the injected gas into the displaced liquid can occur at the interface between the two phases. In this case, the transfer velocity of the dissolved gas reduces the interface displacement velocity as described by the kinematic matching condition, delaying the evolution of the fingering. In addition, the momentum flux across the interface, due to the dissolution, modifies the dynamic matching condition with possible changes in the patterns of the fingers structures.This work studies the effects of gas dissolution on the evolution of fingering instabilities during the displacement of a viscous liquid by an immiscible injected gas in a Hele-Shaw cell. A boundary element numerical simulation of the growth of the injected gas bubble is developed and implemented. This numerical model takes into account the dissolution across a sharp interface between the two phases. Our numerical simulations suggest that the inclusion of gas dissolution can lead to the eventual breaking of the fingers. These “shed fingers” become individual bubbles, which move away from the injection source with the velocity of the surrounding fluid and eventually will dissolve into the ambient fluid. New fingers evolve, with their concurrent breaking, resulting in the possibility of a cascade of travelling and dissolving bubbles, instead of a continuous fingering structure.     

Kinematic instabilities in two-layer eccentric annular flows,part 2: shear-thinning and yield-stress effects

This paper investigates the possibility of kinematic interfacial instabilities occurring during the industrial process of primary cementing of oil and gas wells. This process involves flows in narrow eccentric annuli that are modelled via a Hele-Shaw approach. The fluids present in primary cementing are strongly non-Newtonian, usually exhibiting shear-thinning behaviour and often with a yield stress. The study is a sequel to Moyers-González and Frigaard (J Eng Math, DOI , 2007), in which the base analysis has been developed for the case of two Newtonian fluids. The occurrence of static mud channels in primary cementing has been known of since the 1960s, (see McLean et al. 1966; SPE 1488), and is a major cause of process failure. This phenomenon is quantified, which provides a simple semi-analytic expression for the maximal volume of residual fluid left behind in the annulus, f _static, and illustrate the dependency of f _static on its five dimensionless parameters. It is shown that three of the four different types of static channel flows are linearly stable. Via dimensional analysis, it is shown that the base flows depend on a minimal set of eight dimensionless parameters and the stability problem depends on an additional two dimensionless parameters. This large dimensional parameter space precludes use of the full numerical solution to the stability problem as a predictive tool or for studying the various stability regimes. Instead a semi-analytical approach has been developed based on solution of the long-wavelength limit. This prediction of instability can be evaluated via simple quadrature from the base flow and is suitable for use in process optimisation.     

Stress intensity factors for penny-shaped cracks perpendicular to graded interfacial zone of bonded bi-materials

This paper examines the stress intensity factors that are associated with a penny-shaped crack perpendicular to the interface of a bi-material bonded with a graded interfacial zone. Elastic modulus of the graded interfacial zone is assumed to be an exponential function of the depth. The stress intensity factors are calculated numerically using a so-called generalized Kelvin solution based boundary element method. Three cases of normal or shear tractions acting on the crack surfaces are examined. Values of the stress intensity factors are examined by taking into account the effects of the following four parameters: (a) the crack front position; (b) the non-homogeneity parameter of the graded interfacial zone; (c) the crack distance to the graded interfacial zone; and (d) the graded interfacial zone thickness. The numerical results are compared well with existing solutions under some degenerated conditions. These results are useful to furthering our knowledge on fracture behavior of bi-material systems with or without a graded interfacial zone.     

Modeling the influence of the interfacial zone on the DC electrical conductivity of mortar

The interfacial zone separating cement paste and aggregate in mortar and concrete is believed to influence many of the properties of these composites. The available experimental evidence, obtained on artificial geometries, indicates that the DC electrical conductivity of the interfacial zone, because of its higher porosity, may be considerably larger than that of the bulk cement paste matrix. This paper presents the theoretical framework for quantitatively understanding the influence of the interfacial zone on the overall electrical conductivity of mortar, based on realistic random aggregate geometries. This understanding is also used, via an electrical analogy with Darcy's law, to make predictions about the effect of the interfacial zone on fluid permeability. The results obtained for mortar should also pertain to concrete.     

Vertically stratified flows in microchannels. Computational simulations and applications to solvent extraction and ion exchange

In this paper, we describe the conditions under which two immiscible fluids flow atop one another (viewed perpendicular to the plane on which the channel is inscribed) in a shallow microfluidic channel. First, we predict the behavior of a two-phase system using fluid dynamic simulations with water-butanol and water-chloroform as model systems. We numerically model the effect of various physical parameters, such as interfacial surface tension, density, viscosity, wall contact angle, and flow velocity on the type of flow observed and find that interfacial surface tension and viscosity are the parameters responsible for formation of vertically stratified, side-by-side, or segmented flows. As predicted by numerical simulations, a water-chloroform system never assumes a vertically stratified configuration, but a water-butanol system does when the two liquids flow at sufficiently high flow velocities. In actual experiments, we test conditions under which potentially useful two-phase systems form stable vertically stratified flows. We also demonstrate that compared to side-by-side flow schemes, shorter diffusion paths are achievable, and thus, the system can be used at higher flow rates to obtain the same performance. We then apply such findings to practical analytical problems, such as solvent extraction and ion exchange.     

Classification and general derivation of interfacial forces, acting on phases, situated in the bulk, or at the interface of other phases

In the present paper the general equation and algorithm to derive interfacial forces, acting on phases, situated in the bulk, or at the interface of other phases are given. Based on that, interfacial forces are classified into the following six major types: (i) the “curvature induced interfacial force” (due to Laplace), (ii) the “interfacial gradient force”, acting on particles in inhomogeneous fluid phases, due to composition-, temperature- and electrical potential gradient (known as Marangoni force, or thermocapillary force), (iii) the “interfacial capillary force”, acting on a phase at an interface of two large phases, including the behaviour of solid particles at the liquid/gas, fluid/fluid and solid/solid interfaces (known as the capillary force, and as the Zener pinning force), (iv) the “interfacial meniscus force,” acting between two, solid phases, situated at a curved fluid/fluid or solid/solid interface, the curvature being due to the gravitational or electric fields (known also as the lateral capillary force, or electrodipping force), (v) the “liquid bridge induced interfacial force,” acting between two, solid particles, due to the liquid bridge of small volume between them, and (vi) the “interfacial adhesion force,” acting between two particles in a homogeneous fluid phase (with the phenomenological Derjaguin- and Hamaker constants, re-visited).     

On the mechanical modeling of functionally graded interfacial zone with a Griffith crack: plane deformation

A new multi-layered model is developed for a functionally graded interfacial zone between two dissimilar elastic solids based on the fact that an arbitrary curve can be approached by a continuous but piecewise linear curve. The interfacial zone with both Young’s modulus and Poisson’s ratio varying continuously in an arbitrary manner is divided into multiple layers with the material properties varying linearly in each sub-layer and continuous at the interfaces between sub-layers. With this new model, we analyze the problem of a Griffith crack in the interfacial zone under plane stress-state deformation. The transfer matrix method and Fourier integral transform technique are used to reduce the mixed boundary-value problem to a set of Cauchy singular integral equations. The stress intensity factors are calculated. The paper compares the new model to other existing models and discusses its advantages.