Weakly nonlinear stability analysis of a thin magnetic fluid during spin coating
type: Item
instance of: scholarly article
title: Weakly nonlinear stability analysis of a thin magnetic fluid during spin coating
zbMATH Open document ID: 1201.78008
DOI: 10.1155/2010/987891
author: Yanyan Li
published in: Mathematical Problems in Engineering
publication date: 2010-09-30T00:00:00Z
full work available at URL: https://eudml.org/doc/231440
review text: The study of MHD (magnetohydrodynamic) effects is important inter alia in thin film materials technology, namely, in the stabilization of the film flow by applying a magnetic field is advantageous since neither electrical nor mechanical contacts wiht the fluid are necessary and the active control of the technological process is simple. That is why the spin coating process is fundamental in chip manufactoring process of integrated circuits (wafer, manufactoring, photolithography and sputtering deposition). Here a weakly nonlinear stability analysis of a thin electrically conductive fluid under an applied uniform magnetic field on a rotating disc (spin coating) is presented. Since during spin coating the magnetic induced field can. be neglected, the magnetic Reynolds number is much smaller than unity. The disc radius is much larger than the film thickness, the peripheral effects are negligible in comparison to the total film area. The stability is revealed in the region near the rotating axis due to centrifugal force and MHD-effects. The influence of the rotational motion, disk size and Hartmann number on the equilibrium finite amplitude is studied and characterized. Several numerical examples are presented to show the effectivity of the modeling approach.
Mathematics Subject Classification ID: 78A30
Mathematics Subject Classification ID: 76W05
zbMATH DE Number: 5793807
Wikidata QID: Q58653467
reviewed by: Iván Abonyi
MaRDI profile type: Publication
OpenAlex ID: W2009963642
cites work: Hydromagnetic stability of current-induced flow in a small gap between concentric rotating cylinders
cites work: Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space
cites work: The modified decomposition method and Padé approximants for the MHD flow over a non-linear stretching sheet
cites work: A note on decay of potential vortex in an Oldroyd-B fluid through a porous space
cites work: MHD flow of a micropolar fluid near a stagnation-point towards a nonlinear stretching surface
cites work: Solution of the MHD Falkner-Skan flow by homotopy analysis method
cites work: MHD stagnation-point flow of an upper-convected Maxwell fluid over a stretching surface
cites work: Solution of the MHD Falkner-Skan flow by Hankel-Padé method
cites work: The influence of Hall current in a circular duct
cites work: Flow of a Viscous Liquid on a Rotating Disk
cites work: Film flow on a rotating disk
cites work: Asymptotic analysis of the formation of thin liquid film in spin coating
cites work: Q5518219
cites work: Q3230984
cites work: Q3231956
cites work: Stability of Liquid Flow down an Inclined Plane
cites work: Wave formation on vertical falling liquid films
cites work: Long Waves on Liquid Films
cites work: Occurrence of Finite-Amplitude Surface Waves on Falling Liquid Films
cites work: Long waves on a thin layer of conducting fluid flowing down an inclined plane in an electromagnetic field
cites work: Stability of liquid film falling down a vertical non-uniformly heated wall
cites work: Superlattice patterns in surface waves
cites work: An Oscillatory Hydromagnetic Couette Flow in a Rotating System
cites work: Nonlinear hydromagnetic stability analysis of condensation film flow down a vertical plate
cites work: Measuring interfacial waves on film flowing down tube inner wall using laser focus displacement meter
cites work: Analytic solution for MHD rotating flow of a second grade fluid over a shrinking surface
cites work: Nonlinear stability analysis of thin condensate falling film inside a rotating vertical cylinder
cites work: Weakly nonlinear stability analysis of condensate film flow down a vertical cylinder
cites work: Weakly nonlinear hydrodynamic stability of the thin Newtonian fluid flowing on a rotating circular disk
cites work: Q5330852
cites work: Nonlinear stability of a viscous film with respect to three-dimensional side-band disturbances
cites work: Surface waves on viscoelastic magnetic fluid film flow down a vertical column
cites work: Nonlinear stability characterization of the thin micropolar liquid film flowing down the inner surface of a rotating vertical cylinder
description: scientific article; zbMATH DE number 5793807