Convection in a rotating binary ferrofluid

Abstract

In this work we report theoretical and numerical results on convection for a binary magnetic mixture under rotation. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system for stationary convection. Finally, we analyze the stabilizing effect of rotation on instability thresholds for aqueous suspensions. r 2006 Published by Elsevier B.V.

Thermal convection thresholds in a Oldroyd magnetic fluid

“…The magnetic numbers have the following order of magnitude M 1 $ 10 À4 À10, M 3 \ 1, M 4 $ M 5 $ 10 À6 for typical magnetic field strengths [29,30]. For aqueous suspensions it is suggested that the Deborah number is about G $ 10 À3 À10 À1 [56,[64][65][66], but for other kinds of viscoelastic fluids the Deborah number can be of the order of G $ 10 3 .…”

“…When the magnetophoretic effect can be neglected, we have analyzed the thermal convection for rotating ferrofluids. 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].…”

Stationary convection in a rotating binary magnetic fluid

“…For aqueous suspensions of ferrofluid, we assume the separation ratio ψ positive, so there is only the stationary convection case. The magnetic numbers have the following order of magnitude M 1 = 10 −4 − 10 1 , M 3 ≈ 1.1, M 4 ≈ M 5 ≈ 10 −6 [7]. The values of M 4 , M 5 and F are very small, so in our calculation we will not take them into account.…”

“…They did so in terms of a binary mixture where the magnetophoretic effect, as well as magnetic stresses, have been taken into account in the static and dynamic parts of the ferrofluid equations. Recently, when the magnetophoretic effect can be neglected, we analyzed the thermal convection for rotating ferrofluid for idealized boundary condition for the typical conductive state in the stationary case and was found that an analytical expression for the Rayleigh number as function of control parameters [7].…”

Stationary thermal convection in a viscoelastic ferrofluid

“…When the magnetophoretic effect can be neglected, we have analyzed the thermal convection for rotating ferrofluids. 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 [29]. Recently, the weakly nonlinear analysis for stationary convection in a rotating magnetic binary mixture was studied [30].…”