Nonlinear theory of pattern formation in ferrofluid films at high field strengths

被引:14
作者
Richardi, J [1 ]
Pileni, MP [1 ]
机构
[1] Univ Paris 06, CNRS, UMR 7070, Lab mat Mesoscop & Nanometr, F-75230 Paris 05, France
来源
PHYSICAL REVIEW E | 2004年 / 69卷 / 01期
关键词
D O I
10.1103/PhysRevE.69.016304
中图分类号
O35 [流体力学]; O53 [等离子体物理学];
学科分类号
070204 ; 080103 ; 080704 ;
摘要
When a magnetic field is applied to a thin layer of a suspension of magnetic nanoparticles (ferrofluid), the formation of labyrinthine and hexagonal patterns is observed. We introduce a theory to describe ferrofluid patterns at high field, where a nonlinear relationship between field and magnetization is expected. The computational difficulties due to the use of a nonlinear magnetization curve are solved by a reformulation of the magnetic energy equation. The evolution of the pattern size at intermediate and very high fields can be understood by an analysis of limiting cases of the magnetization curve. In particular, at a very high field the pattern size reaches a constant saturation value which has been recently confirmed by experiments. The field for the onset of a nonlinear behavior is shifted to higher field strength due to a demagnetization effect. This can partially explain the ability of linear approaches to reproduce experimental data even at a high field. Finally, the impact of the nonlinearity of the magnetization curve on the transition between hexagonal and labyrinthine patterns is discussed.
引用
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页数:9
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