Waves and instability at the interface of two flows of miscible magnetic and non-magnetic fluids (original) (raw)
Related papers
Journal of Magnetism and Magnetic Materials, 2011
The interfacial instability of miscible magnetic fluids in a Hele-Shaw Cell is studied experimentally, with different magnitudes and sweep rates of the external magnetic field. The initial circular oil-based magnetic fluid drop is surrounded by the miscible fluid, diesel. The external uniform magnetic fields induce small fingerings around the initial circular interface, so call labyrinthine fingering instability, and secondary waves. When the magnetic field is applied at a given sweep rate, the interfacial length grows significantly at the early stage. It then decreases when the magnetic field reaches the preset values, and finally approaches a certain asymptotic value. In addition, a dimensionless parameter, Pe, which includes the factors of diffusion and sweep rate of the external magnetic field, is found to correlate the experimental data. It is shown that the initial growth rate of the interfacial length is linearly proportional to Pe for the current experimental parameter range and is proportional to the square root of the sweep rate at the onset of labyrinthine instability.
Magnetohydrodynamic instability of a two fluid interface
Journal of Magnetism and Magnetic Materials, 1992
The stability of a gas cylinder (density p) immersed in a liquid (density p') subjected to capillary, pressure gradient, inertia and electro-magnetic forces has been developed analytically and numerically. A general hydromagnetic eigenvalue relation describing the characteristics of that model is deri,,ed based on the linearized perturbation technique, in the abscence of a magnetic field, the model is only unstable to axisymmetric disturbances whose wavelength is longer than the circumference of the gas cylinder and stable in all other disturbance states. The instability of the model rapidly decreases with increasing (if~p) but can never be suppressed, however large the (if~p) value is. The magnetic field has a strong stabilizing effect on all perturbation modes for all wavelengths. Its influence is to decrease the wavelength at which the capillary instability occurs. The latter could be completely suppressed above a certain value of the applied magnetic field strength, independent of (if~p) values, then the stability arises. However, in a two-dimensional perturbation (k = 0, k is the axial wavenumber) it is found that the capillary force remains unaffected by such a magnetic field. The present resulls coincide with our results [A.E. Radwan, J. Magn. Magn. Mater. 72 (1988) 219] if we neglect here the gas inertia force and with some Chandrasekhar's results [S. Chandrasekh,~,, Hydrodynamic and Hydromagnetic Stability (Dover. New York, 1981)] with appropriate choices. 0304-8853/92/$05.00
Acta Mechanica Sinica, 2008
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 Schrödinger equations (l-NLS) with complex coefficients. These equations generally describe the competition between nonlinearity and dispersion. The stability criteria are theoretically 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.
Astrophysics and Space Science
This study investigates the combined effect of density, velocity and magnetic field gradients on the Kelvin-Helmholtz instability of two viscous fluid layers. For the linear phase of instability that refers to the early stage of development of Kelvin-Helmholtz instability, the linear growth rate and frequency are presented. With respect to our selected variables and the Atwood number, the behaviour of growth rate and frequency are analysed. It is found that, the behaviour of frequency is not affected by the magnetic field and viscous term. The velocity gradient with the small Atwood numbers tends to stabilize KHI flows, while the velocity gradient with the large Atwood numbers has destabilizing effect on KHI. The growth rate reduces with the constant magnetic field and viscous term, while it enhances with magnetic field gradient.
Stability analysis of magnetic fluids in the presence of an oblique field and mass and heat transfer
MATEC Web of Conferences
In this paper, we investigate an analysis of the stability of a basic flow of streaming magnetic fluids in the presence of an oblique magnetic field is made. We have use the linear analysis of modified Kelvin-Helmholtz instability by the addition of the influence of mass transfer and heat across the interface. Problems equations model is presented where nonlinear terms are neglected in model equations as well as the boundary conditions. In the case of a oblique magnetic field, the dispersion relation is obtained and discussed both analytically and numerically and the stability diagrams are also obtained. It is found that the effect of the field depends strongly on the choice of some physical parameters of the system. Regions of stability and instability are identified. It is found that the mass and heat transfer parameter has a destabilizing influence regardless of the mechanism of the field.
Hydromagnetic Instability of Streaming Viscoelastic Fluids Through Porous Media
The hydromagnetic instability of the plane interface between two uniform, superposed and streaming Rivlin-Ericksen viscoelastic fluids through porous medium is considered. The case of two uniform streaming fluids separated by a horizontal boundary is studied. It is observed, for the special case where perturbations in the direction and transverse direction of streaming are ignored, that the system is stable for stable configuration and unstable for unstable configuration. If the perturbations in the direction of streaming only one ignored, then the system is stable for stable configuration. However, the magnetic field succeeds in stabilizing certain wave-number range, which is otherwise potentially unstable. In all other directions, a minimum wave-number value has been found beyond which the system is unstable; the instability is found to be postponed by the presence of the magnetic field.
Magnetic instability between miscible fluids in a Hele-Shaw cell
2008
We show experimentally the existence of a magnetic instability between two miscible fluids. The sample is an aqueous ferrofluid. At time t = 0, the ferrofluid and water are put into contact in a Hele-Shaw cell and then submitted to a homogeneous magnetic field perpendicular to the cell. Above a threshold value of the magnetic field a fingering instability is observed at the diffuse interface, with fingers growing with time. A wavelength can be defined as the mean distance between fingers. This wavelength in the linear regime is approximatively equal to the thickness of the cell. Figs 7, Refs 19.
Research Square (Research Square), 2022
The current manuscript tackles the interaction between three viscous magnetic fluids placed on three layers and saturated in porous media. Two of them fill half the spaces above and below a thin layer that lies in the middle region. All layers are laterally extended to infinity in both horizontal directions. All fluids move in the same horizontal direction with different uniform velocities and are driven by pressure gradients. The system is stressed by tangential stationary/periodic magnetic fields. The viscous potential theory (VPT) is used to simplify the mathematical procedure. The motion of the fluids is described by the Brinkman-Darcy equations, and Maxwell equations are used for the magnetic field. The nonlinear technique is typically relying on solving linear equations of motion and presenting the nonlinear boundary conditions. The novelty of the problem concerns the nonlinear stability of the double interface under the impact of periodic magnetic fields. Therefore, the approach has resulted in two nonlinear characteristic differential equations governing the surface displacements. Accordingly, the development amplitudes of surface waves are designated by two nonlinear Schrödinger equations. Stability is theoretically analyzed; the nonlinear stability criterion is derived, and the corresponding nonlinear stability conditions are explored in detail. Approximate bounded solutions of the perturbed interfaces are estimated. Additionally, the thickness of the intermediate layer as a function of time is plotted. The impact of different parameters on the stability profile is investigated. For the middle layer, it is found that magnetic permeability, as well as viscosity, have a stabilizing effect. By contrast, the basic streaming, as well as permeability, have a destabilizing influence. The analysis of the periodic case shows that the lower interface is much more stable than the upper one. Engineering applications like petroleum products manufacturing and the electromagnetic field effect can be used to control the growth of the perturbation and then the recovery of crude oil from the pores of reservoir rocks.
Scientific Reports
The unsteady, magneto-hydrodynamic generalized Couette flows of two immiscible fluids in a rectangular channel with isothermal walls under the influence of an inclined magnetic field and an axial electric field have been investigated. Both fluids are considered electrically conducting and the solid boundaries are electrically insulated. Approximate analytical solutions for the velocity, induced magnetic, and temperature fields have been determined using the Laplace transform method along with the numerical Stehfest's algorithm for the inversion of the Laplace transforms. Also, for the nonlinear differential equation of energy, a numerical scheme based on the finite differences has been developed. A particular case has been numerically and graphically studied to show the evolution of the fluid velocity, induced magnetic field, and viscous dissipation in both flow regions.