Pattern selection in magnetic fluids with surface adsorption

• Published in: International journal of engineering science Vol. 34; no. 9; pp. 1077 - 1092
• Main Authors: Bajaj, Renu, Malik, S.K.
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.07.1996; Elsevier
• Subjects: Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Nonlinearity (including bifurcation theory); Pattern selection; pattern formation; Physics; Surface-tension-driven instability; Mode selection; Magnetic permeability; Electric field effects; Hydrodynamic instability; Bifurcation; Theoretical study; Free surface; Surfactants; Non linear effect; Magnetic fluids
• ISSN: 0020-7225; 1879-2197
• DOI: 10.1016/0020-7225(96)00007-9

A magnetic fluid surface subject to normal magnetic field H, results in pattern formation when H exceeds some critical value H c. The critical value H c of a magnetic field for the onset of surface instability has been determined as a function of surface concentration. By using symmetric bifurcation theory, periodic patterns are studied in a magnetic fluid with surface adsorption. The various non-linear coefficients in the normal forms for square lattice and hexagonal lattice have been computed from the non-linear differential equations. Bifurcation diagrams have been obtained for the physical values of parameter space. The various regions of stability and instability of different patterns resulting in rolls, squares and hexagons have been identified. The phenomenon of surface adsorption makes rolls stable for a certain range of values of magnetic permeability of magnetic fluid which are otherwise unstable in the absence of surface adsorption.