Structure and stability of the interface between magnetic and conventional fluids. Model of a three-component medium

The structure of a flat interphase boundary between a magnetic suspension and a conventional immiscible fluid is investigated within the framework of the model of a three-component medium taking the dependence of the free energy of the system on the concentration gradients into account. It is shown that for certain values of the constitutive parameters the bulk magnetic particle concentration increases significantly inside the interfacial layer, i.e., the particles are significantly adsorbed on the interface. The dependence of the surface tension on the magnetic field strength is determined. It is shown that for certain problem parameters this dependence qualitatively corresponds to that obtained experimentally and described in the phenomenological theory developed by Golubyatnikov and Subkhankulov in 1986. In the case of strong particle adsorption the dependence of the surface tension on the magnetic particle concentration on the phase interface is significantly nonlinear. A refined model of the interface as a two-dimensional continuum with surface magnetization is constructed. Constitutive equations, conditions on the interface, and necessary stability conditions are obtained.     

Evolution of perturbations of a charged interface between immiscible inviscid fluids in the interelectrode gap

Perturbations of the interface between two immiscible ideal fluids of finite thickness (the lower and upper fluids are the conductor and the dielectric, respectively) located in the gap between two electrodes are considered. In the cases of the “shallow” and “deep” upper fluid the dispersion relations of linear waves and their longwave expansions are found. The methods of determining the space-time evolution of an initial surface perturbation are developed on the basis of the linear approximation. In the cases of the “shallow” and “deep” upper fluid examples of the development of an initial perturbation of the “step” type are given. The development of an initial perturbation of the “step” type are also considered in the near-critical electric fields and in the case of degeneration of cubic dispersion.     

Exact solutions of the problem of the motion of the interface between immiscible fluids in a porous medium

Translated from Zhurnal Prikladnoi Mekhaniki i Tekhnicheskoi Fiziki, No. 1, pp. 68–71, January–February, 1991.     

Instability of a plane interface between two immiscible conducting viscous fluids in a normal electrostatic field

The dispersion relation for motions of a charged plane interface between two viscous incompressible immiscible conducting fluids is analyzed numerically for finite values of all the parameters involved. It is shown that in addition to the well-known aperiodic (Tonkes-Frenkel’ type) instability for certain values of the physical parameters an oscillatory instability with periodically growing amplitude may be realized in the system. Yaroslavl’. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 6, pp. 116–123, November–December, 1998.     

A Level Set method for capturing interface deformation in immiscible stratified fluids

The interface behavior between two stratified fluids showing a large difference in viscosity was investigated numerically. A three-dimensional numerical method for the simulation of the deformation of the interface in a stirred vessel is presented. In such a systems, the interface is distorted by hydrodynamic stresses and pressure changes. Different regimens of agitation were employed to explore the response of the interface, where the boundary between them is preserved and break up is avoided. The numerical scheme presented explicitly solves the Navier–Stokes equations for an incompressible fluid whilst the convection-diffusion part is treated through a Level-Set method along a moving and deforming interface. The spatial discretization was carried out by implementing a Runge–Kutta method in a second order scheme, along as a Weighted Essentially Non-Oscillatory approach. In addition, surface tension effects were included to observe its influence on the interface response. It was found that due the effect of inertia the interface is reshaped towards the vertical direction, in this process the interface experiences high-pressure gradients, which drag the interface in the upward direction. The numerical methodology was validated by comparison of simulations and experimental measurements of an interface deforming at two low Reynolds number. The results shown that the algorithm is able to resolve accurately the detailed features of the distorted fluid interfaces.     

Diffuse interface tracking of immiscible fluids: Improving phase continuity through free energy density selection

Diffuse interface (DI) tracking methods frequently adopt the double-well energy density function to describe the free energy variation across an interface, leading to phase interpenetration and spontaneous drop shrinkage when applied to immiscible two-phase systems. While the observed continuity losses can be limited by constraints placed on the interfacial width and mobility parameter, the associated increase in computational cost and mesh requirements has limited DI methods to 2D planar and axi-symmetric flow.     

The flow of incompressible immiscible fluids between two plates

Summary The flow of layers of different heights of n incompressible immiscible fluids between two plates has been considered and it has been shown that whatever be the number of fluids and whatever be their heights, a unique velocity maximum always exists and a formula for finding the layer in which this maximum occurs has been given. For the particular case of two layers it has been shown that the curve of total flux against the ratio of the heights of the fluids has always a point of inflexion. Further this ratio has been determined so that the fluxes of the two fluids are equal.     

Rayleigh-Taylor instability of the interface between conducting and nonconducting fluids in an alternating magnetic field

The influence of an alternating magnetic field on the Rayleigh-Taylor instability of a conducting fluid has been investigated [1, 2] in the limiting cases of long- and short-wave (compared with the skin-layer thickness) perturbations. Garnier [3] has reported a new mechanism of instability of the interface between conducting and nonconducting fluids which differs not only from the classical Rayleigh-Taylor instability but also from parametric excitation of perturbations. From the instability criterion obtained in [3] without restriction on the spatial scale of the perturbation a paradoxical result follows: An increase in the frequency of the field leads to instability, whereas the practical results of metal casting in an electromagnetic crystallizing tank [4] indicate the opposite effect. In the present paper, it is shown that a plane-polarized high-frequency field effectively stabilizes part of the spectrum of three-dimensional perturbations of an interface but does not completely suppress the Rayleigh-Taylor instability mechanism. The instability generated by the self-field has the nature of parametric resonance.     

Stability of the wave motion on the charged interface between two immiscible fluids in the presence of a tangential velocity field discontinuity

In the second-order approximation in the dimensionless wave amplitude, the problem of nonlinear periodic capillary-gravity wave motion of the uniformly charged interface between two immiscible ideal incompressible fluids, the lower of which is perfectly electroconductive and the upper, dielectric, moves translationally at a constant velocity parallel to the interface, is solved analytically. It is shown that on the uniformly charged surface of an electroconductive ideal incompressible fluid the positions of internal nonlinear degenerate resonances depend of the medium density ratio but are independent of the upper medium velocity and the surface charge density on the interface. All resonances are realized at densities of the upper medium smaller than the density of the lower medium. In the region of Rayleigh-Taylor instability with respect to density there is no resonant wave interaction.     

Magnetohydrodynamics instability of interfacial waves between two immiscible incompressible cylindrical fluids

The problem of nonlinear instability of interfacial waves between two immiscible conducting cylindrical fluids of a weak Oldroyd 3-constant kind is studied. The system is assumed to be influenced by an axial magnetic field, where the effect of surface tension is taken into account. The analysis, based on the method of multiple scale in both space and time, includes the linear as well as the nonlinear effects. This scheme leads to imposing of two levels of the solvability conditions, which are used to construct like-nonlinear Schr6dinger equations （1-NLS） with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoret- ically discussed and thereby stability diagrams are obtained for different sets of physical parameters. Proceeding to the nonlinear step of the problem, the results show the appearance of dual role of some physical parameters. Moreover, these effects depend on the wave kind, short or long, except for the ordinary viscosity parameter. The effect of the field on the system stability depends on the existence of viscosity and differs in the linear case of the problem from the nonlinear one. There is an obvious difference between the effect of the three Oldroyd constants on the system stability. New instability regions in the parameter space, which appear due to nonlinear effects, are shown.     

Slip at the interface between immiscible polymer melts I: method to measure slip

Slip at the interface between immiscible polymer melts remains poorly understood. A method that relies solely on rheological measurements to obtain the interfacial slip velocity uses the slip-induced deviation in the flow variables. To use the method, accurate estimates of the flow variables under the assumption of no-slip are necessary. Although such estimates can be easily derived under some cases, in general, this is not straightforward. Therefore, methods to determine the interfacial slip velocity without using estimates for the flow variables under no-slip conditions are desirable. In this work, we focus on investigations of slip at the interface between two immiscible polymer melts undergoing two-phase coaxial flow. To enable such investigations, we have adapted the Mooney method, usually used to investigate wall slip, to investigate polymer/polymer interfacial slip. Using this method, we have measured the slip velocity at the interface between polypropylene and polystyrene as a function of the interfacial stress. To determine the validity of the modified Mooney method, we also determine the slip velocity using the slip-induced deviation in the flow variables. To enable this determination, we use polypropylene and polystyrene with almost identical shear rate-dependent viscosities over a range of shear rates. The slip velocity obtained from the modified Mooney method displayed excellent agreement with that determined using the deviation from no-slip. In agreement with prior work, the dependence of the slip velocity on the interfacial stress is a power-law. Our investigation spans a sufficiently wide range of interfacial stress to enable the direct observation of two power-law regimes and also the transition between the two regimes. We also find that the power-law exponent of approximately 3 at low stresses decreases to approximately 2 at high stresses.     

Absolute instability of an interface between two magnetic fluids in the presence of a tangential velocity discontinuity and an external magnetic field

The nature of the instability of the surface of a tangential velocity discontinuity between two incompressible, inviscid, capillary, nonconducting, linearly magnetizable fluids in an external magnetic field is considered. An absolute instability criterion is obtained in analytic form. When the gravity force is negligible, this criterion does not depend on the value of the surface tension. When the surface tension is negligible, the absolute instability criterion is obtained for the region of the flow parameters in which the causality condition for the system in question is satisfied. If the magnetic field is tangential to the interface, all the criteria obtained are also applicable to the case of nonmagnetic, perfectly conducting fluids, i.e., to the case of ideal magnetohydrodynamics.Moscow. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 5, pp. 21–26, September–October, 1995.     

Blends of two immiscible and rheologically different fluids

The Doi and Ohta theory of the rheology of immiscible blends is extended by considering the field of the velocity with which the interface moves as an independent state variable. This type of generalization is needed in order to be able to take into account the difference in the rheological properties of the fluids involved. Expression for the extra stress tensor as well as equations governing the time evolution of the interfacial area, orientation of the interface and its velocity are derived.     

Vertical displacement of immiscible fluids from heterogeneous formations

The modified phase permeability model [1, 2] is extended to the case of vertical displacement with allowance for the force of gravity. It is assumed that in connection with vertical displacement a thicker dometype formation may be regarded as a stream tube of variable cross section. An exact solution of the one-dimensional displacement problem is constructed. It is shown that in vertical displacement from heterogeneous formations the gravity forces stabilize the displacement, so that at low velocities it approaches displacement of the pure piston type. It is established that a decrease in the injection and extraction rates leads to an increase in hydrocarbon output, and an increase in formation pressure to a fall in output.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 91–97, March–April, 1991.The authors wish to thank K. S. Basniev and A. K. Kurbanov for formulating the problem and taking an interest in the work.     

Capillary-gravitational separation of immiscible fluids in porous media

The redistribution of liquid phases under the action of capillary and gravitational forces determines the course of several processes in oil and gas extraction technology: the migration of hydrocarbons, and the formation of deposits, subsurface storage of oil and gas in water-saturated structures. The solution of the dynamic problem and comparison of this solution with the asymptotic solution makes it possible to determine, in addition to the detailed phase distribution, the duration of the intense segregation period, i.e., the time during which the segregation is essentially completed.We consider the problem of the dynamics of the one-dimensional segregation of immiscible liquids in a horizontal sheet-like stratum. In this case the process is described by nonlinear differential equations of the parabolic type with discontinuous coefficients and nonlinear boundary conditions. A distinctive feature of this equation is the existence of solution discontinuities at the points of discontinuity of the equation coefficients. A numerical method for solving the problem is proposed in this article and realized on a computer. We also consider dynamic segregation in a uniform stratum. The asymptotic solution for t is indicated for each of the dynamic problems. The criterion is found for the existence of contact between the phases.The authors wish to thank T. V. Startsev and L. Kh. Aminov for assistance in performing the calculations.     

Thermocapillary instability of the interface between two immiscible liquids in the presence of volume heat sources

The problem of the stability of the interface between two infinite layers of different immiscible liquids is considered. It is assumed that within the liquid a distributed volume heat source, simulating Joule heating, is given. The stability of the rest state with respect to small unsteady disturbances is investigated. The investigation is carried out using the real boundary conditions at the interface between the two liquids rather than the model boundary conditions usually employed in such problems [5]. The problem considered is related to the practical question of the stability of electrolyzer processes. In the present case a possible threshold mechanism of development of oscillations of the electrolyte-aluminum interface is examined. A numerical example with liquid parameters that coincide with those of the electrolyte and aluminum shows that the thermocapillary instability mechanism can, in fact, be the source of surface waves at the electrolyte-aluminum interface.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 156–160, September–October, 1990.     

The interface between two simple fluids between two oscillating vertical planes

The shape of the interface between two simple fluids having nearly the same densities which are contained between two oscillating vertical planes has been calculated by the method of domain perturbation pivoted about the rest state. The analysis has been carried out through second order in the amplitude of the oscillation velocity. The existence of the shearing motion on the interface has been considered by incorporating the spatial dependence of the primary motion on the vertical coordinate as well as on the transverse coordinate. This has led to an enhancement of the normal stress effect and thus results in predicting a higher rise in the interface than that in the case when no shearing motion is assumed to exist on the interface.