Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
type: Item
instance of: scholarly article
title: Dynamics of labyrinthine pattern formation in magnetic fluids: A mean-field theory
zbMATH Open document ID: 0905.35068
author: Felix Otto
published in: Archive for Rational Mechanics and Analysis
publication date: 1999-02-02T00:00:00Z
review text: The paper deals with the Hele-shaw cell; it is made of two horizontal sheets of glass which have a very small spacing \(b\). Part of the gap is filled with a ferroliquid (a colloidal suspension of iron particles), the rest is filled with an ordinary fluid. The ferroliquid fills a cylindrical domain \(\Omega \times(0,b)\) so the phase configuration is described by the two-dimensional cross section \(\Omega\). The effect of a strong magnetic field perpendicular to the cell is applied. The dynamics is governed by two competing forces: surface tension and magnetostatic repulsion. The paper starts from a model for the evolution proposed by Jackson et al.. The conventional analysis does not bridge the gap between the early stages (captured by the linearization) and the late stages of the evolution (described by a variational problem). The numerical analysis only describes the early stages. The author presents a new type of analysis for the intermediate stage. An evolution equation is derived for the local volume fraction of the gap filled by the ferroliquid. The analysis is based on the discovery that this type of strongly overdamped flow problems can be considered as a gradient flux of the relevant energy functionals.
Mathematics Subject Classification ID: 35Q35
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 1154551
zbMATH Keywords: magnetization
zbMATH Keywords: stability analysis
zbMATH Keywords: microstructure evolution
zbMATH Keywords: Hele-shaw cell
zbMATH Keywords: ferroliquid
zbMATH Keywords: surface tension
zbMATH Keywords: magnetostatic repulsion
zbMATH Keywords: gradient flux
zbMATH Keywords: energy functional
reviewed by: L. Vázquez
MaRDI profile type: Publication
full work available at URL: s002050050073
OpenAlex ID: W2076578223
Wikidata QID: Q125995316
DOI: 10.1007/S002050050073
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description: scientific article; zbMATH DE number 1154551