A new boundary integral formulation to describe three-dimensional motions of interfaces between magnetic fluids

Cunha, Francisco Ricardo; Couto, H.L.G.

doi:10.1016/j.amc.2007.09.035

Cited by 10 publications

(6 citation statements)

References 17 publications

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“…For emulsions at the dilute regime, that is, with dispersed phase concentration less than 20% in volume, the hydrodynamic interactions between two or more drops can be neglected, and studies of a single droplet – as the present one – applies straightforwardly to numerical investigations on emulsion rheology. Some modified BI formulations have also been proposed to investigate emulsions in compressible Stokes' flows and emulsions of magnetic drops under the action of external fields . Also, recent advances have been made in order to compute the dynamics of deformable particles including drops, vesicles, and capsules using the BI method .…”

Section: Introductionmentioning

confidence: 99%

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Siqueira

Rebouças

Oliveira

et al. 2016

Numerical Methods in Fluids

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Summary We present a numerical methodology for the simulation of a viscous drop under simple shear flows by using the boundary integral method. The present work treats only a single drop in an unbounded fluid‐flow, but the results can be directly applied to studies on the rheology of dilute emulsions, in which the hydrodynamic interactions between two or more drops can be neglected. Singular and non‐singular integral representations of the velocity field are considered. Several aspects of the method are presented, including a new mesh relaxation approach and an automatic time‐step control method. The relaxation strategy is used in order to contain the distortion of the mesh and is performed by using relaxation iterations in a virtual temporal march between each physical time step of the simulation and monitoring the standard deviation of the areas of the elements. The automatic time‐step control method uses a global quantity related to the drop deformation in order to automatically set the temporal integration time step. It is carried out in a way to keep the local integration error less than a given tolerance. This strategy reduces the computational cost of the simulation by dramatically reducing the number of time steps in the temporal integration process. Copyright © 2016 John Wiley & Sons, Ltd.

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Section: Introductionmentioning

confidence: 99%

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Siqueira

Rebouças

Oliveira

et al. 2016

Numerical Methods in Fluids

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“…Since then, numerous studies in the field of ferrofluid dynamic bearings have been carried out. Both static and dynamic characteristics of these bearings have been studied theoretically [10]- [17]. Moreover, recent trends in the ferrofluid lubrication applications are described and discussed [18]- [24].…”

Section: Introductionmentioning

confidence: 99%

Magnetic pressure and shape of ferrofluid seals in cylindrical structures

Ravaud

Lemarquand

2009

Journal of Applied Physics

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This paper presents a three-dimensional analytical model for studying the shape and the pressure of ferrofluid seals submitted to intense magnetic fields produced by permanent magnet ironless structures. This three-dimensional analytical approach is based on the exact calculation of the magnetic field components created by ring permanent magnets whose polarizations are either radial or axial. We assume that the ferromagnetic particles of the ferrofluid are saturated and the static behaviour of the ferrofluid seal depends on both the magnetic field produced by the permanent magnets and the saturation magnetization of the ferrofluid particles. In our applications, ferrofluid seals are always submitted to very high magnetic fields. Consequently, the accurate knowledge of the ferrofluid seal shape as well as the magnetic pressure inside the ferrofluid seal is very useful for the design of devices using both permanent magnets and ferrofluid seals. It is emphasized here that our structures are completely ironless and thus, there are no iron-base piston for these structures. Then, this paper makes a review of the main structures using ring permanent magnets and ferrofluid seals. For each ironless structure, the shape and the pressure of the ferrofluid seals are determined. To our knowledge, this way of characterizing the static behaviour of ferrofluid seals submitted to intense magnetic fields appears for the first time in the literature. Indeed, we think that a three-dimensional analytical model is interesting for such a study because it is simple to use and has a very low computational cost.

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“…Most of the calculations are analytical and the method used is based on a geometrical approach. The assumptions taken throughout this paper are based on the papers published by Cunha [28] and Matthies [29]. However, in this paper, the intensity of magnetization of a magnetic particle (M ) is saturated because the magnetic field we use is higher than 1 T. Consequently, the relation between M and H is not linear.…”

Section: Introductionmentioning

confidence: 99%

Design of Ironless Loudspeakers With Ferrofluid Seals: Analytical Study Based on the Coulombian Model

Ravaud¹,

Lemarquand²

2009

PIER B

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Abstract-This paper presents an analytical method based on the coulombian model of a magnet for studying a ferrofluid seal in ironless electrodynamic loudspeakers. Such an approach differs from the ones generally used for studying such geometries because the ferrofluid used is submitted to a magnetic field greater than 1 T which saturates the ferrofluid. Consequently, its shape and its mechanical properties depend mainly on the magnetic field produced by the permanent magnets that constitute the ironless structure. The motor is constituted of outer stacked ring permanent magnets and the inner moving part is a piston. In addition, one ferrofluid seal is used for centering the moving part and ensuring the airtightness between the loudspeaker faces. The ferrofluid seal also exerts a pull back force on the moving piston. It is noted that this force depends on the lateral shape of the moving piston. Therefore, the piston profile is analytically studied in this paper. A peculiar attention is given to profiles that ensure the axial pull back force to be proportional to the piston displacement. Furthermore, a geometrical method is presented to design the shape of the ferrofluid seal according to the chosen piston profile. It can be noted that such a profile is elliptical in this study. Then, the magnetic energy of the ferrofluid seal is determined with the analytical expression of the magnetic energy density. Such an expression allows us to calculate the axial force created by the ferrofluid seal for a given profile.

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A new boundary integral formulation to describe three-dimensional motions of interfaces between magnetic fluids

Cited by 10 publications

References 17 publications

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

A new mesh relaxation approach and automatic time‐step control method for boundary integral simulations of a viscous drop

Magnetic pressure and shape of ferrofluid seals in cylindrical structures

Design of Ironless Loudspeakers With Ferrofluid Seals: Analytical Study Based on the Coulombian Model

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