Thin viscous ferrofluid film in a magnetic field
File(s)thin magnetic films PoF 2015.pdf (538.63 KB)
Published version
Author(s)
Conroy, DT
Matar, OK
Type
Journal Article
Abstract
We consider a thin, ferrofluidic film flowing down an inclined substrate, under the action of a magnetic field, bounded above by an inviscid gas. Its dynamics are governed by a coupled system of the steady Maxwell’s, the Navier-Stokes, and the continuity equations. The magnetization of the film is a function of the magnetic field and may be prescribed by a Langevin function. We make use of a long-wave reduction in order to solve for the dynamics of the pressure and velocity fields inside the film. In addition, we investigate the problem in the limit of a large magnetic permeability. Imposition of appropriate interfacial conditions allows for the construction of an evolution equation for the interfacial shape via use of the kinematic condition. The resultant one-dimensional equations are solved numerically using spectral methods. The magnetic effects give rise to a non-local contribution. We conduct a parametric study of both the linear and nonlinear stabilities of the system in order to evaluate the effects of the magnetic field. Through a linear stability analysis, we verify that the Maxwell’s pressure generated from a normally applied magnetic field is destabilizing and can be used to control the size and shape of lobes and collars on the free surface. We also find that in the case of a falling drop, the magnetic field causes an increase in the velocity and capillary ridge of the drop.
Date Issued
2015-09-15
Online Publication Date
2015-09-15
2017-02-01T11:06:02Z
Date Acceptance
2015-07-19
ISSN
1089-7666
Publisher
AIP Publishing
Journal / Book Title
Physics of Fluids
Volume
27
Issue
9
Copyright Statement
© 2015 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 27(9) and may be found at http://dx.doi.org/10.1063/1.4930010
Source Database
web-of-science
Identifier
http://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&KeyUT=WOS:000362570800022&DestLinkType=FullRecord&DestApp=ALL_WOS&UsrCustomerID=1ba7043ffcc86c417c072aa74d649202
Subjects
Science & Technology
Technology
Physical Sciences
Mechanics
Physics, Fluids & Plasmas
Physics
INCLINED PLANE
SURFACE-WAVES
LIQUID-FILMS
STABILITY
DYNAMICS
INSTABILITY
EVOLUTION
FLUID
Fluids & Plasmas
01 Mathematical Sciences
02 Physical Sciences
09 Engineering
Publication Status
Published
Article Number
ARTN 092102