Pattern formation by surface instabilities in a ferrofluid is studied as a function of an applied vertical magnetic field H. The effects of sidewalls are neglected. The problem is formulated as a bifurcation problem on an appropriately chosen doubly-periodic lattice. Normal forms for both square and hexagonal lattices are given and the necessary coefficients computed from the partial differential equations. On the square lattice solutions in the form of parallel ridges are never stable near onset. For a relative magnetic permeability μ<1.4 stable squares are formed. On the hexagonal lattice a finite amplitude instability produces hexagons. Analysis of a degenerate bifurcation predicts a hysteretic transition to ridges with increasing H.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Applied Mathematics