NONLINEAR INSTABILITY OF FERROFLUIDS IN POROUS MEDIA UNDER A HORIZONTAL MAGNETIC FIELD

Document Type : Research and Reference

Authors

1 DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, BANHA UNI VERSITY, BANHA 13518, EGYPT

2 DEPARTMENT OF MATHEMATICS, FACULTY OF SCIENCE, BANHA UNIVERSITY, BANHA 13518, EGYPT

Abstract

The nonlinear instability analysis of the free surface of two weak
VIscous magnetic fluids, subjected to vertical vibrations and a
horizontal magnetic Tield, has been examined in porous media. Ihe
two fluids are immiscible in all properties. Both have Tinite-
thickneSs, homogeneous, and incompressible fluids. Although the
 
motionS are assumed to be irrotational, weak VIscous erects are
 
include d in the boundary conditions of the normal stress tensor
balance. The influence of both surface tension and gravity torce is
also considered. The method of multiple scale perturbations is used
to obtain a dispersion relation for the lin ear theory and a Gin zburg-
Landau equation for the nonlinear theory, describing the behaviour
of the System. nere 1S also the obtaining of a nonlinear diffusion
equation, describing the evolution of the wave packets, near the
marginal state. Further, the online ar Schrodin ger equation Is
obtained when the effect of both the viscosity and Darcy's
coefficients are neglected. The stability conditions are discussed
and the interplay between the applied magnetic field and several
other factors in determining the interface behavior is analyzed
Stability analysis and numerical calculations are used to describe
linear and nonlinear stages of the interface evolution. The numerical
calculations indicate the existence or more than a new region of
stability and instability due to the noniinear effects. In the linear
theory, it is found that the horizpntal magnetic field decreases as
the wave number increases. his'means that the magnetic field has
a stabilizing influence on the wave motion. While the vis co sity and
Darcy's coefficients have a destabilizing effect. In the nonlinear
theory, it is found that these parameters have an important role in
the stability criterion of the problem.

Files

Share

How to cite

Statistics