Amplitude Equation for Stationary Convection in a Rotating Binary Ferrofluid

Laroze, David; Martínez-Mardones, J.; Pérez, Laura M.; Rameshwar, Y.

doi:10.1142/s0218127409024463

Cited by 13 publications

(6 citation statements)

References 12 publications

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“…The main objective of a weakly nonlinear analysis is to obtain an evolution equation for this unknown amplitude function. This method has been applied to a number of specific examples in physics, including shear flows, shallow water waves, thermoacoustics and magnetohydrodynamics; see, for example [32][33][34][35][36][37][38]. In these examples, the nature of the equations analysed means that the algebra often becomes very complicated.…”

Section: Weakly Nonlinear Stabilitymentioning

confidence: 99%

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel

et al. 2019

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We hypothesize that dynamical systems concepts used to study the transition to turbulence in shear flows are applicable to other transition phenomena in fluid mechanics. In this paper, we consider a finite air bubble that propagates within a Hele-Shaw channel containing a depth-perturbation. Recent experiments revealed that the bubble shape becomes more complex, quantified by an increasing number of transient bubble tips, with increasing flow rate. Eventually, the bubble changes topology, breaking into multiple distinct entities with non-trivial dynamics. We demonstrate that qualitatively similar behaviour to the experiments is exhibited by a previously established, depth-averaged mathematical model and arises from the model’s intricate solution structure. For the bubble volumes studied, a stable asymmetric bubble exists for all flow rates of interest, while a second stable solution branch develops above a critical flow rate and transitions between symmetric and asymmetric shapes. The region of bistability is bounded by two Hopf bifurcations on the second branch. By developing a method for a numerical weakly nonlinear stability analysis we show that unstable periodic orbits (UPOs) emanate from the first Hopf bifurcation. Moreover, as has been found in shear flows, the UPOs are edge states that influence the transient behaviour of the system.

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Section: Weakly Nonlinear Stabilitymentioning

confidence: 99%

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel

et al. 2019

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“…For idealized boundary condition for the typical conductive state in the stationary case an analytical expression was found for the Rayleigh number as function of control parameters [30]. Recently, the weakly nonlinear analysis for stationary convection in a rotating magnetic binary mixture was studied [31]. Other effects, such as the buoyancy-surface tension effects, non-uniform thermal gradients, magnetization constitutive equations, etc., have also been studied in Refs.…”

Section: Introductionmentioning

confidence: 99%

Thermal convection thresholds in a Oldroyd magnetic fluid

Pérez

Bragard

Laroze

et al. 2011

Journal of Magnetism and Magnetic Materials

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“…For their study, the explicit expressions of stationary convection thresholds have been demonstrated according to the parameters of the system. Interesting studies on convection in ferrofluids and for various situations have been theoretically conducted in [22][23][24][25][26][27].…”

Section: Introductionmentioning

confidence: 99%

Stationary convection in a binary mixture of ferrofluids in a porous medium

Hounsou¹,

Monwanou²,

Miwadinou³

et al. 2020

Fluid Dyn. Res.

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The Brinkman model is used to study the criterion of appearance of stationary convection in a porous horizontal layer saturated by a binary mixture of ferrofluids and heated from below. The analytical expression of the Rayleigh number is determined by dimensionless numbers for the combined effects of buoyancy and magnetic force on the one hand and magnetic force alone on the other. The effect of Darcy's number, ratio of viscosities, each of the magnetic parameters and the binary parameter is illustrated on the appearance and size of the convection cells. The increasing of the number of Darcy D a , each of the magnetic parameters M 1 , M 3 , ψ m and the separation ratio ψ accelerates the appearance of stationary convection. On the other hand, when the ratio of the viscosity ∧ or the magnetic parameter M 2 is increased, the beginning of the convection is delayed and the system is stable. We have also noticed that the size of the convection structures is contracted with each of the parameters M 1 , M 2 , ψ, ψ m and for low values of the parameter M 3 . But by increasing the number of Darcy, the ratio of viscosities or for very high values of M 3 the size of the convection cells is enlarged. Finally, it should be noted that convection sets in with great delay when the magnetic mechanisms alone are highlighted.

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Amplitude Equation for Stationary Convection in a Rotating Binary Ferrofluid

Cited by 13 publications

References 12 publications

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel

The influence of invariant solutions on the transient behaviour of an air bubble in a Hele-Shaw channel

Thermal convection thresholds in a Oldroyd magnetic fluid

Stationary convection in a binary mixture of ferrofluids in a porous medium

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