Faraday instability on viscous ferrofluids in a horizontal magnetic field: Oblique rolls of arbitrary orientation

Abstract

A linear stability analysis of the free surface of a horizontally unbounded ferrofluid layer of arbitrary depth subjected to vertical vibrations and a horizontal magnetic field is performed. A nonmonotonic dependence of the stability threshold on the magnetic field is found at high frequencies of the vibrations. The reasons of the decrease of the critical acceleration amplitude caused by a horizontal magnetic field are discussed. It is revealed that the magnetic field can be used to select the first unstable pattern of Faraday waves. In particular, a rhombic pattern as a superposition of two different oblique rolls can occur. A scaling law is presented which maps all data into one graph for the tested range of viscosities, frequencies, magnetic fields and layer thicknesses.

Chain-induced effects in the Faraday instability on ferrofluids in a horizontal magnetic field

“…With the further decrease of the frequency, transitions to higher order response occur 26,34,37 , and the frequency of the Faraday waves remains high enough to leave the orientation of chains in nonequilibrium. Fig.…”

“…Here the functions W n depend additionally on the coupling constant ε in contrast to the corresponding functions in the previous paper 37 . Equation (11) has to be satisfied for all times which implies that each term of the sum equals to zero.…”

Modelling of an Oscillatory Magnetic Field Action on a Ferrofluid Layer

“…Thus H ef f is the horizontal component of the magnetic field parallel to k, whose magnitude is H ext cosθ. This means that we should consider also the natural extension of a Faraday instability studied by Mekhonoshkin and Lange (2002) to our present problem. Indeed, these authors stressed that the induction B ef f = μ 0 μH ef f plays on the pattern selection of the Faraday case, extending thus the original approach considered by Cebers and Maiorov (1989).…”

“…The correct general mathematical formulation extends the problem studied originally by Cebers and Maiorov (1989) and explains where Bajaj went astray (Bajaj and Malik 2002;Bajaj 2003). The numerical study of the problem, which is under progress, will enable to compare the results with the Faraday vertical oscillations or with lateral vibrations (Mekhonoshkin and Lange 2002).…”

Phase Transition effect on the Parametric Instability of Liquid Crystals

“…It appears when the vessel containing the liquid is vibrated vertically with a given acceleration until the quiescent equilibrium interface develops unstable surface waves. It has been observed in Newtonian fluids [6], but their most interesting realizations occur in complex fluids where their viscoelastic responses are present due to different time scales associated with the molecular relaxation processes [8,16]. Therefore, it is important to determine how the onset of the Faraday instability is determined by the underlying bulk fluid elasticity.…”