Rotating Hele-Shaw cells with ferrofluids

Abstract

We investigate the flow of two immiscible, viscous fluids in a rotating HeleShaw cell, when one of the fluids is a ferrofluid and an external magnetic field is applied. The interplay between centrifugal and magnetic forces in determining the instability of the fluid-fluid interface is analyzed. The linear stability analysis of the problem shows that a non-uniform, azimuthal magnetic field, applied tangential to the cell, tends to stabilize the interface. We verify that maximum growth rate selection of initial patterns is influenced by the applied field, which tends to decrease the number of interface ripples. We contrast these results with the situation in which a uniform magnetic field is applied normally to the plane defined by the rotating Hele-Shaw cell.

Interfacial instability in a time-periodic rotating Hele-Shaw Cell

“…It turns out that an increase in the Froude number, corresponds to increasing the amplitude modulation of the angular velocity Ω m , acts to stabilize the interface. Furthermore, it is worth noting that, when the Froude number decreases the marginal stability curve converge toward that obtained by Miranda [6] corresponding to F r = 0.…”

“…The parameters α 1 and α 2 can be expressed as a function of the Atwood number with α 1 = 1+A 2 and α 2 = 1−A 2 . Remark that in the limit case corresponding to Fr = 0, the solution determined in this work, and given by equations (25), tends to the solution corresponding to the marginal stability equation of Miranda [6] (equation (2) in [6] without magnetic bond number N B ).…”

“…Several theoretical and experimental works have been carried out to study the interfacial instability in an annular Hele-Shaw cell [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]. These works have been extended to include effects arising from a constant rotation rate of the system and have mainly focused on the study of the linear growth rate, also, on the understanding fingering mechanisms of the interface when one of two immiscible fluids is accelerated toward the other under centrifugal forces.…”

“…By performing experiments in pre-wet and dry conditions, they have shown that the stability of the interfaces depends substantially on the wetting conditions at the leading interface. Later on, there has been interest of interfacial instabilities in ferroflua e-mail: saniss@hotmail.com ids confined within Hele-Shaw cell [6][7]. Miranda [6] has treated the case in which the inner fluid is a ferrofluid in the presence of an external magnetic fields.…”

“…Later on, there has been interest of interfacial instabilities in ferroflua e-mail: saniss@hotmail.com ids confined within Hele-Shaw cell [6][7]. Miranda [6] has treated the case in which the inner fluid is a ferrofluid in the presence of an external magnetic fields. Using a linear stability analysis and neglecting coriolis forces, he has determined the growth rate when both the centrifugal forces and magnetic forces are induced and has shown that the magnetic forces act to stabilize the fluid interface.…”