The Amplitude Equation for the Rosensweig Instability in Magnetic Fluids and Gels

被引:7
作者
Bohlius, Stefan [1 ]
Pleiner, Harald [1 ]
Brand, Helmut R. [2 ]
机构
[1] Max Planck Inst Polymer Res, D-55021 Mainz, Germany
[2] Univ Bayreuth, D-95440 Bayreuth, Germany
来源
PROGRESS OF THEORETICAL PHYSICS | 2011年 / 125卷 / 01期
关键词
BENARD-MARANGONI CONVECTION; FERROMAGNETIC FLUID; MAXIMAL GROWTH; FERROGELS; SURFACE; PATTERN; FERROFLUIDS; COMPETITION; STABILITY; SELECTION;
D O I
10.1143/PTP.125.1
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Rosensweig instability has a special character among the frequently discussed instabilities. One distinct property is the necessary presence of a deformable surface, and another very important fact is that the driving force acts purely via the surface and shows no bulk effect. These properties make it rather difficult to give a correct weakly nonlinear analysis. In this paper we give a detailed derivation of the appropriate amplitude equation based on the hydrodynamic equations emphasizing the conceptually new procedures necessary to deal with the distinct properties mentioned above. First the deformable surface requires a fully dynamic treatment of the instability and the observed stationary case can be interpreted as the limiting case of a frozen-in characteristic mode. Second, the fact that the driving force is manifest in the boundary conditions, only, requires a considerable change in the formalism of weakly nonlinear bifurcation theory. To obtain the amplitude equations a combination of solubility conditions and (normal stress) boundary conditions has to be invoked in all orders of the expansions.
引用
收藏
页码:1 / 46
页数:46
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