Renu Bajaj

Temperature modulation in ferrofluid convection

Convective instability is suppressed by sinusoidal variation in temperature of horizontal boundaries of a ferrofluid layer subjected to vertical magnetic field. On increasing the amplitude of modulation, instability may arise in the form of oscillations which may have time period equal to that of the temperature modulation or double of it. The effect of frequency of modulation, applied magnetic field, and Prandtl number on the onset of a periodic flow in the ferrofluid layer has been investigated numerically using the Floquet theory. Some theoretical results have also been obtained to discuss the limiting behavior of the underlying instability with the temperature modulation. Depending upon the parameters, the flow patterns at the onset of instability have been found to consist of time-periodically oscillating vertical magnetoconvective rolls.

Parametric instability of the interface between two viscous magnetic fluids

Abstract The flat interface solution between two magnetic fluids can be parametrically excited by periodically oscillating magnetic field H 0 (1+m cos (ωt)) oriented in direction normal to the fluids. The stability problem for the interface of two magnetic viscous fluids has been formulated. Beyond a critical value of wave number k C and a critical value m C of amplitude of excitation, the plane interface becomes unstable and standing waves appear. The solutions for standing waves are found to exist within stability bands in ( k , m ) plane for a given value of external frequency ω and steady magnetic field H 0 .

Pattern formation in ferrofluids

The normal field instability resulting in pattern formation is examined in the presence of a general magnetic field. The stability characteristics are dependent on the magnetic permeability μ. The tangential field makes rolls stable in magnetic fluids with certain values of μ, which are otherwise unstable in the absence of such a field.

Convective instability in a ferrofluid layer with temperature-modulated rigid boundaries

Under terrestrial as well as gravity-free conditions, a time-periodic modulation in temperatures of two horizontal rigid planes containing an initially quiescent ferrofluid layer induces time-periodic oscillations in the fluid layer at the onset of instability. This results in a series of patterns of time-periodically oscillating magnetoconvective rolls, along the vertical. The onset of instability in the ferrofluid layer is either a harmonic response or a subharmonic response depending upon the modulation. The instability is found to be significantly affected by the application of magnetic field across the ferrofluid layer. Under modulation, subcritical instabilities are found to occur in the form of subharmonic response. Also, the onset of instability in the ferrofluid layer when it is driven solely by the magnetic forces alone is found to heavily depend upon the frequency of modulation, the effect being greatest for the low-frequency modulation and negligible for the case of high-frequency modulation. The gravity-free limit is also evaluated as a function of the magnetic susceptibility, under modulation. To carry out this extensive study, the classical Floquet theory is utilized.

STABILITY OF NONAXISYMMETRIC FERROFLUID FLOW IN ROTATING CYLINDERS WITH MAGNETIC FIELD

Effect of an axially applied magnetic field on the stability of a ferrofluid flow in an annular space between two coaxially rotating cylinders with nonaxisymmetric disturbances has been investigated numerically. The critical value of the ratio Ω∗ of angular speeds of the two cylinders, at the onset of the first nonaxisymmetric mode of disturbance, has been observed to be affected by the applied magnetic field.

Two-frequency parametric excitation of the surface of viscous magnetic fluid

Abstract The parametric instability of the surface of viscous magnetic fluid has been discussed in the presence of two frequency ( n 1 ω , n 2 ω ) oscillating magnetic field H 0 (t)=H 0 1+m[ cos (χ) cos (n 1 ωt)+ sin (χ) cos (n 2 ωt+φ)] . The marginal stability curves have been drawn and they divide the ( k , m ) plane into unstable and stable zones. Here k is the wave number and m is the amplitude of excitation. Also discussed is the stability of the interface of two magnetic fluids. We have studied the same two systems under gravity modulation also.

Pattern selection in magnetic fluids with surface adsorption

Abstract A magnetic fluid surface subject to normal magnetic field H , results in pattern formation when H exceeds some critical value H c . The critical value H c of a magnetic field for the onset of surface instability has been determined as a function of surface concentration. By using symmetric bifurcation theory, periodic patterns are studied in a magnetic fluid with surface adsorption. The various non-linear coefficients in the normal forms for square lattice and hexagonal lattice have been computed from the non-linear differential equations. Bifurcation diagrams have been obtained for the physical values of parameter space. The various regions of stability and instability of different patterns resulting in rolls, squares and hexagons have been identified. The phenomenon of surface adsorption makes rolls stable for a certain range of values of magnetic permeability of magnetic fluid which are otherwise unstable in the absence of surface adsorption.

Rayleigh-Bénard convection with two-frequency temperature modulation.

The response of Rayleigh-Bénard convection in a horizontal fluid layer to time-periodic heating of its horizontal boundaries with a mixture of two frequencies is analyzed numerically. The ratio of the two forcing frequencies and the mixing angle of the amplitudes of modulation provide a control on the instability of the system. In addition to the existence of well-known harmonic and subharmonic instability responses under modulation, the time-periodic oscillation of the boundary temperatures of the fluid-layer with two frequencies results in more bicritical states in comparison to the single-frequency excitation. The onset of instability depends strongly on the modulation parameters and the Prandtl number of the fluid.

Temperature Modulation in Rayleigh-Benard Convection

The stability characteristics of an infinite horizontal fluid layer excited by a time-periodic, sinusoidally varying free-boundary temperature, have been investigated numerically using the Floquet theory. It has been found that the modulation of the temperature gradient across the fluid layer affects the onset of the Rayleigh-Benard convection. Modulation can give rise to instability in the subcritical conditions and it can also suppress the instability in the supercritical cases. The instability in the fluid layer manifests itself in the form of either a harmonic or subharmonic flow, controlled by thermal modulation.

Rayleigh–Bénard convection and pattern formation in magnetohydrodynamics

A nonlinear thermal instability in a layer of electrically conducting fluid in the presence of a magnetic field is discussed. Steady-state bifurcation results in the formation of patterns: rolls, squares and hexagons. The stability of various patterns is also investigated. It is found that in the absence of a magnetic field only rolls are stable, but when the magnetic field strength exceeds a certain finite value, squares and hexagons also become stable.